| {"q_id": "science-forum-test-1307", "query": "does every prime divide some fibonacci number?", "doc_id": ["324382", "214643", "306717", "1309621", "1049398", "32013"], "answers": ["yes"]} | |
| {"q_id": "science-search-test-34", "query": "5 coins are tossed how many outcomes?", "doc_id": ["1250781", "206352", "855696", "1131991", "1218331", "176740", "206329", "289304", "420472", "574890", "1158947", "1440862", "1329774"], "answers": ["There are $2^5$ equally likely strings of length $5$ made up of the letters H and/or T", "there are $\\;2^5 = 32$ possible outcomes"]} | |
| {"q_id": "science-search-test-503", "query": "how to make electromagnetic waves visible?", "doc_id": ["1473660", "1526642", "1475753"], "answers": ["by using them to make something else emit energy in a frequency we can see", "liquid crystals are applied on an RF absorbing film and change color when RF waves heat the film"]} | |
| {"q_id": "science-search-test-68", "query": "are all cosets the same size?", "doc_id": ["293948", "160260", "408876", "1181114", "951135", "1316167", "1054760", "94555", "723153", "1229034", "382444", "289925", "750541", "1223731"], "answers": ["the size of every coset is equal to the size of $H$"]} | |
| {"q_id": "science-forum-test-636", "query": "do mathematicians, in the end, always agree?", "doc_id": ["1464186", "405467", "447078", "1207483", "1306797", "540677", "1260698", "271726", "1499895", "189462", "404112", "466962", "592129", "871322", "644990", "194471", "666458", "1473707", "390275", "1074111", "404252", "322458", "405579", "907603", "974938", "618569", "982302", "1561429", "363062", "661648", "856882"], "answers": ["no"]} | |
| {"q_id": "science-search-test-41", "query": "does the square root of a negative number exist?", "doc_id": ["300001", "229704", "299896", "945137", "58092", "5608", "625568", "330646", "884541", "751845", "1194347", "1193541", "1137071", "823584", "38215", "299895", "1273261", "574442", "489926", "430347", "339608", "726979", "605859", "1033797", "890294", "1086133", "1409777", "839411", "1087252", "300050", "713716", "892122", "1061006"], "answers": ["When we say that the square root of a negative number \"doesn't exist", "we mean that there is no real number solution"]} | |
| {"q_id": "science-forum-test-1862", "query": "is it possible to place 26 points inside a rectangle that is 20 cm by 15 cm so that the distance between every pair of points is greater than 5 cm?", "doc_id": ["873158", "873964", "873116", "930557", "444025", "133747", "253991", "535769", "285241", "738313"], "answers": ["No", "with all distances strictly greater than 5cm it is not possible to place 26 points"]} | |
| {"q_id": "science-search-test-391", "query": "how does the mass of an object affect its velocity?", "doc_id": ["1575310", "1615774", "1539716", "1575979", "1540162", "1474192", "1553475", "1624601", "1659477", "1480198", "1546053", "1627667", "1582512", "1466493", "1504233", "1480292", "1627181", "1545710", "1497471", "1473809", "1656456", "1627653", "1627682", "1652016", "1485851", "1586272", "1615994", "1508150", "1661721"], "answers": ["It determines how quickly an object can change speed (accelerate) under the action of a given force", "mass determines how strong a force has to be to accelerate an object at a given rate"]} | |
| {"q_id": "science-search-test-1", "query": "2 is the only prime even number because?", "doc_id": ["834245", "460512", "786477", "859468", "325697", "776232", "1197503", "627522", "1157235", "1077990", "224118", "761928", "1312331"], "answers": ["Because every even number other than 2 is obviously divisible by 2"]} | |
| {"q_id": "science-forum-test-570", "query": "why is integration so much harder than differentiation?", "doc_id": ["623523", "11410", "269368", "333145", "408539", "220488", "465930"], "answers": ["differentiation, you can mechanically apply the rules. For integration, you need to recognize patterns"]} | |
| {"q_id": "science-search-test-505", "query": "what is the basic difference between compton effect and photoelectric effect?", "doc_id": ["1527923", "1529128", "1572462", "1663659", "1589100", "1603468", "1546507", "1641007"], "answers": ["Photo electric effect occur in bound electron, while compton effect occur in free electron"]} | |
| {"q_id": "science-forum-test-1642", "query": "is there a math expression equivalent to the conditional ternary operator?", "doc_id": ["1144901", "1144039", "705201", "633510", "1144461"], "answers": ["Kronecker Delta"]} | |
| {"q_id": "science-forum-test-1849", "query": "every nonzero element in a finite ring is either a unit or a zero divisor", "doc_id": ["401050", "1111161", "1027465", "32338", "266364", "1081118", "50992", "49459", "1025688", "345664", "32339", "33165", "1417687", "178112", "1346971", "188596", "229119", "1209785", "33159", "764477", "500734", "1186556", "506441", "1377592"], "answers": ["every nonzero element is either a zero-divisor or a unit"]} | |
| {"q_id": "science-forum-test-587", "query": "in classical logic, why is $(p\\rightarrow q)$ true if both $p$ and $q$ are false?", "doc_id": ["1158748", "638639", "1146964", "389488", "387398", "183418", "390004", "37314", "30891", "454708", "1353345", "250492"], "answers": ["since the empty set is a subset of any set, a false statement implies any statement"]} | |
| {"q_id": "science-forum-test-2011", "query": "why isnt a virus alive?", "doc_id": ["1671533", "1671520", "1670035", "1687076", "1679360", "1671958", "1673042", "1676991", "1681316", "1674327", "1686706", "1693210", "1669019", "1679283", "1675345", "1686916", "1685057", "1691810", "1676652", "1691803", "1689374", "1660788"], "answers": ["they always rely on the host for the machinery with which to replicate"]} | |
| {"q_id": "science-forum-test-1188", "query": "how can one prove that $e<\\pi$?", "doc_id": ["1005889", "227918", "947462"], "answers": ["Use $e<3$ and $\\pi>3$"]} | |
| {"q_id": "science-forum-test-1268", "query": "how do i tell if matrices are similar?", "doc_id": ["1289899", "1377961", "82192", "1226802", "101167", "7921", "766761", "326659", "60002", "59041"], "answers": ["if and only if they have the same characteristic polynomial, and neither of them is a scalar matrix", "if and only if identical lists of invariant factors are found"]} | |
| {"q_id": "science-search-test-517", "query": "prove that kinetic energy is not conserved in inelastic collision?", "doc_id": ["1639928", "1625706", "1653168", "1608764", "1651317", "1503484", "1617233", "1664224", "1485178", "1485842", "1549183", "1647023", "1635757", "1561312", "1519440", "1629108", "1544865", "1662724", "1515357", "1566845", "1541740", "1605887", "1563959", "1523221", "1558340", "1617448", "1473551", "1607773", "1502767", "1650357", "1474323", "1598447", "1563513", "1521839", "1663312", "1664240", "1623086", "1553253", "1569351", "1519399", "1600434", "1637069", "1485175", "1632567", "1621175", "1653328", "1469907", "1612709"], "answers": ["kinetic energy is turned into heat, so although energy is conserved, kinetic energy is not"]} | |
| {"q_id": "science-search-test-354", "query": "what is the physical significance of hysteresis loop of ferromagnetic material?", "doc_id": ["1551912", "1522127", "1593566", "1662356", "1577622", "1482190", "1541056", "1570945"], "answers": ["The area inside the hysteresis loop is the energy dissipated in the material per cycle"]} | |
| {"q_id": "science-search-test-495", "query": "are ripples in water circular?", "doc_id": ["1466291", "1474433", "1553766", "1572161", "1096126", "169470", "1490871", "1630704", "1515696", "1633910", "1636185", "1591505", "1652751", "1600997", "1522643", "1477321", "1082243"], "answers": ["ripples are not circular at all", "the ripples in water are always circular"]} | |
| {"q_id": "science-search-test-352", "query": "is potential energy a state function?", "doc_id": ["1665036", "1521129", "1618367", "1540409", "1600457", "1570105", "1663984", "958766", "1665620"], "answers": ["potential energy is a state function"]} | |
| {"q_id": "science-search-test-335", "query": "what does find the magnitude of acceleration mean?", "doc_id": ["117411", "1660208", "1570069", "1615707", "677284", "1490567", "1514154", "1577475", "1619531", "1557127", "1581372", "1584712", "1595252", "1522801", "1630348", "1575595", "299633", "1661154", "1592418", "1466504", "1610413", "792358", "1629093", "1599566", "1504724", "1504726", "1652318", "1620736", "1489963", "1508119", "1502647", "1625775", "1527355", "1560616", "1641626", "1609472", "1214787", "1475706", "1514169", "1578134", "580357", "1505413", "1571643", "1571151"], "answers": ["how quickly your speed changes in a given unit of time", "how quickly velocity changes"]} | |
| {"q_id": "science-search-test-389", "query": "why atmosphere is the bad conductor of heat?", "doc_id": ["1527155", "1474532", "1664134", "1611561", "1569783", "1481236", "1592987", "1569910", "1576882", "1570309", "1569828", "1504659", "1572445", "1474531", "1559575", "1631949", "1536002", "1601666", "1664101", "1536023", "1484725", "1591612", "1619467"], "answers": ["the very low density of gases that make them bad conductors of heat", "The particles in air are far apart", "Heat does not travel easily by conduction through air"]} | |
| {"q_id": "science-search-test-482", "query": "is dough a solid or liquid?", "doc_id": ["1493918", "1543204", "1596323", "1469745"], "answers": ["Dough, and Play-Doh, are best described as non-Newtonian fluids"]} | |
| {"q_id": "science-forum-test-31", "query": "why does nasa use gold foil on equipment and gold-coated visors?", "doc_id": ["1496900", "1662833", "1566364", "1524837"], "answers": ["reflects IR to keep it from getting \u201chot"]} | |
| {"q_id": "science-search-test-238", "query": "are all quadratic equations functions?", "doc_id": ["177235", "1205626"], "answers": ["No"]} | |
| {"q_id": "science-search-test-172", "query": "what is the main difference between continuous mapping at point and the uniform continuous?", "doc_id": ["686633", "373529", "292119", "1062418", "290665", "497062", "341611", "550130", "863606"], "answers": ["continuity is defined at a point $c$, whereas uniform continuity is defined on a set $A$"]} | |
| {"q_id": "science-search-test-547", "query": "are objects always in motion?", "doc_id": ["1667948", "1540640", "1466571", "1596588", "1583999", "1663145", "1466570", "1519612", "1639537", "1518866", "1600543", "1503815", "1656617", "1507500", "1478534", "1616070", "1474346"], "answers": ["all objects are in motion with respect to some other object"]} | |
| {"q_id": "science-forum-test-1781", "query": "what structure does the alternating group preserve?", "doc_id": ["1197340", "233308", "3076", "922525", "1103687", "150821"], "answers": ["orientation"]} | |
| {"q_id": "science-search-test-479", "query": "what is the relationship of sound intensity to sound pressure?", "doc_id": ["1470447", "1470449", "1583154", "1582057", "1562744", "1633153", "1645097", "1562279", "1622787", "1465923", "1559571", "1528902", "1595129", "1545151", "1667783", "1607175", "1548474", "1506556", "1521341", "1633324", "1590163", "1514216", "1511801", "1546505", "1600615"], "answers": ["The intensity of the sound wave, however, is proportional to the square of the sound pressure"]} | |
| {"q_id": "science-search-test-520", "query": "what is the physical relationship between mass and speed?", "doc_id": ["1604640", "1597810", "1556273", "1635031", "1550032", "1507795", "1480292", "1516198", "1565798", "1582512", "1553475", "1535220", "1545537", "1646522", "1508118", "1661721", "1663345", "1466522", "1473809", "1516431", "1542649"], "answers": ["mass determines how strong a force has to be to accelerate an object"]} | |
| {"q_id": "science-search-test-92", "query": "if two events are mutually exclusive are they independent or dependent?", "doc_id": ["396636", "396638", "129251", "1147254", "772302", "1431483", "734839", "356519", "1355662", "462651", "213795", "509515", "1352317", "1163467", "158229", "1355671", "734846", "730875", "193619", "411191", "743536", "193622", "28965", "1431489", "7527", "1091744", "319185", "948023", "647910", "538253", "1120893", "540180", "1302650"], "answers": ["mutually exclusive events are not independent, and independent events cannot be mutually exclusive", "if the two events are mutually exclusive, they can not be independent"]} | |
| {"q_id": "science-search-test-260", "query": "are sat scores discrete or continuous?", "doc_id": ["283873", "328799", "751427", "1621783", "223214", "1035852", "273965", "446656"], "answers": ["discrete"]} | |
| {"q_id": "science-search-test-195", "query": "is square root of negative 1 a rational number?", "doc_id": ["1251330", "1641890", "1142948", "574442", "1327369", "782732", "100373", "417039", "35609", "554707", "14", "531125", "773", "144331", "492197", "73073", "330646", "229704", "1198484", "666139", "100372", "100377", "100383", "478315", "661710", "794345", "300001", "14465", "1086133", "180801", "100376", "353699"], "answers": ["it cannot be rational", "it is not rational", "it is neither rational nor irrational", "not a rational number"]} | |
| {"q_id": "science-forum-test-1683", "query": "difference between supremum and maximum", "doc_id": ["81053", "81055", "81054", "1366350", "1126397", "84070", "134821", "882870", "205091", "184456", "602620", "453863", "422947", "903866", "982823", "1295397", "1016366", "666201", "907026", "483745", "28771", "187132", "565590", "28742", "261587", "1209064", "666206", "1260056", "982792", "10346", "828342", "483315", "565595", "1118305", "494110", "810593"], "answers": ["A maximum of a set must be an element of the set. A supremum need not be", "maximum is the largest member of the set, while the supremum is the smallest upper bound"]} | |
| {"q_id": "science-forum-test-10", "query": "why do ballpoint pens write better on pages that have pages below them?", "doc_id": ["1584424", "1584400"], "answers": ["the steel ball of the pen makes a better deeper contact by indentation with side cushioning"]} | |
| {"q_id": "science-search-test-599", "query": "natural selection occurs at which level?", "doc_id": ["1675996", "1675995", "1690119", "1685908", "1679345", "1671129", "1672705", "1690173", "1675614", "1669218", "1685845", "1675624", "1679798", "1673841", "1691696", "1672260", "1682033", "1691706", "1685837", "1677712", "1679594", "1685939", "1673764", "1675043", "1673835", "1675044", "1673236", "1687073", "1680226", "1668507", "1681179", "1685166", "1690130", "1681602", "1672760", "1686569", "1673334", "1680203", "1675056", "1681606", "1680206", "1690201", "1677747", "1686210", "1670099"], "answers": ["individual", "population"]} | |
| {"q_id": "science-forum-test-1605", "query": "are there any turing-undecidable problems whose undecidability is independent of the halting problem?", "doc_id": ["834182", "700020", "10663", "123233", "38551", "189069", "530017", "53049", "1568911", "13026", "1075741", "1372595", "1630398", "447037", "825588", "829591", "464660"], "answers": ["Yes"]} | |
| {"q_id": "science-forum-test-157", "query": "can we theoretically balance a perfectly symmetrical pencil on its one-atom tip?", "doc_id": ["1530441", "1530424", "1530425", "1531612", "1531577", "1531580", "1626578", "1530423", "1491522", "1598768", "1491524", "1618582", "1514518", "1469492"], "answers": ["NO", "No"]} | |
| {"q_id": "science-forum-test-1323", "query": "what is a good book for learning math, from middle school level?", "doc_id": ["626724"], "answers": ["How to solve it"]} | |
| {"q_id": "science-forum-test-1634", "query": "is it possible to write a sum as an integral to solve it?", "doc_id": ["928910", "869249", "1320246", "980219", "676231", "451252", "1033323", "113713", "526523", "60996", "1134052", "420618", "1196719"], "answers": ["Yes you can use the Euler Maclaruin formula to write the sum as an integral"]} | |
| {"q_id": "science-search-test-166", "query": "are mutually exclusive events also independent?", "doc_id": ["396636", "396638", "129251", "1120893", "1431483", "533461", "734839", "1355662", "462651", "213795", "1118189", "509515", "339379", "158229", "1355671", "734846", "730875", "193619", "213447", "1061195", "411191", "743536", "193622", "1340218", "28965", "193617", "1431489", "1091744", "1007637", "319185", "948023", "647910", "854147", "936736", "538253", "540180"], "answers": ["mutually exclusive events are not independent, and independent events cannot be mutually exclusive", "if the two events are mutually exclusive, they can not be independent"]} | |
| {"q_id": "science-forum-test-206", "query": "why does rainwater form moving waves on the ground? is there a name for this effect?", "doc_id": ["1573371"], "answers": ["These waves are called \"roll waves.\" They are due to an instability in shallow shear flows"]} | |
| {"q_id": "science-forum-test-1356", "query": "why do the french count so strangely?", "doc_id": ["853805", "183952"], "answers": ["80 is also not invented, it is 4 20s, quatre-vingt"]} | |
| {"q_id": "science-forum-test-1364", "query": "if a coin toss is observed to come up as heads many times, does that affect the probability of the next toss?", "doc_id": ["554655", "701850", "1461591", "1334858", "941703", "1366799", "949991", "1349041", "402266", "521908", "191627", "466608", "509955", "717626", "391048", "1240232", "667343", "717469", "643750", "771505", "1240337", "771493", "1240565", "1146084", "22305", "1083042", "306483", "191624", "1494926", "461243", "342268", "554151", "949919", "188441", "960490", "571559"], "answers": ["LLN doesn't tell you anything about the probability of the next (or any) trial"]} | |
| {"q_id": "science-search-test-499", "query": "do ac circuits need ground?", "doc_id": ["1512205", "1512184", "1588893", "1644185", "1537962", "1534147", "1506559", "1473443", "1648072", "1619358", "1648763", "1662505", "1529695", "1662539", "1612727", "1512936", "1611427", "1653192", "1654428", "1594675", "1641202", "1510849", "1593555", "1659887", "1472954", "1588792"], "answers": ["You can absolutely operate an AC circuit without a ground wire"]} | |
| {"q_id": "science-forum-test-1995", "query": "what is the evolutionary advantage of red-green color blindness?", "doc_id": ["1680821", "1680823", "1670414", "1683541", "1676084"], "answers": ["differentiate between much more shades of khaki than unaffected people", "help detecting camouflaged food in a green environment", "better at detecting color-camouflaged objects", "spotting hidden dangers (predators) or finding camouflaged foods"]} | |
| {"q_id": "science-forum-test-127", "query": "thought experiment - would you notice if you fell into a black hole?", "doc_id": ["1533679", "1533990", "1558414", "1620172", "1538700", "1558406", "1538482", "1473564", "1522349", "1478643", "1467116", "1478691", "1528277", "1478308", "1483034", "1486485", "1533680", "1511501", "1535912", "1504649", "1547770", "1480321", "1540812", "1466065", "1616418", "1479003", "1576640", "1531646", "1538935", "1524390", "1657211", "1578790", "1482438", "1478870", "1484090", "1533835", "1467018", "1533400", "1476966", "1614482", "1658039", "1542037", "1647789", "1583293", "1467669"], "answers": ["A falling observer does not experience passing through an event horizon"]} | |
| {"q_id": "science-search-test-146", "query": "how to calculate manhattan distance between two vectors?", "doc_id": ["1054141", "70741", "1022554", "191922", "413150", "276757", "414293", "260430", "677285", "11955", "70740", "1173417", "831829"], "answers": ["Take the sum of the absolute values of the differences of the coordinates", "subtract the values of a dimensiin then abs them and add all the results"]} | |
| {"q_id": "science-search-test-490", "query": "are glass a good conductor of heat?", "doc_id": ["1603003", "1521214", "1638092", "1576930", "1641457", "1561335", "1518495", "1555663", "1573260", "1503039", "1576882", "1489431", "1616966", "1551869", "1476406", "1504659", "1603738", "1494372", "1472863", "1634828"], "answers": ["Glass is a very poor heat conductor"]} | |
| {"q_id": "science-search-test-199", "query": "can scientific notation be negative?", "doc_id": ["574113", "574385", "443209", "912027", "281981", "330782", "381627", "1360927", "1456993", "205369", "221411", "768876", "475545", "369008", "1103737", "464319", "1058128", "636592", "319864", "935265", "1139233", "543688", "806509", "662335", "892625", "79390", "1632636"], "answers": ["no problem having a negative number shown in scientific notation", "Yes, you can use negative numbers too"]} | |
| {"q_id": "science-forum-test-2003", "query": "how come large herbivores have such thin legs?", "doc_id": ["1686364", "1672459", "1495382"], "answers": ["Less mass in the lower leg means it swings easier"]} | |
| {"q_id": "science-search-test-16", "query": "the square root of a negative number does not exist?", "doc_id": ["300001", "229704", "1033797", "636351", "807403", "299993", "1327369", "1194347", "144331", "492197", "823584", "299895", "1247838", "1070188", "574442", "489926", "1250572", "430347", "34264", "1455233", "726979", "125351", "1193541", "890294", "1409777", "269585", "311538", "1087252", "713716"], "answers": ["negative numbers can't have square roots"]} | |
| {"q_id": "science-forum-test-463", "query": "what is the difference between singular value and eigenvalue?", "doc_id": ["521148", "977064", "750424", "778331", "65090", "1461029", "1350307", "467155", "1552806", "271880"], "answers": ["singular values are always real, while eigenvalues need not be real"]} | |
| {"q_id": "science-forum-test-542", "query": "what is the probability that a point chosen randomly from inside an equilateral triangle is closer to the center than to any of the edges?", "doc_id": ["661776"], "answers": ["${5\\over27}$"]} | |
| {"q_id": "science-forum-test-585", "query": "is the inverse of a symmetric matrix also symmetric?", "doc_id": ["1152157", "609069", "1447039", "1180978", "306692", "483917", "154927", "951026", "766009", "946885", "618033", "154939", "475552", "156007", "607123"], "answers": ["Yes"]} | |
| {"q_id": "science-forum-test-212", "query": "what is spin as it relates to subatomic particles?", "doc_id": ["1482772", "1465514", "1665172", "1515137", "1639051", "1513762", "1554909", "1574259", "1631705", "1536181", "1628404", "1517165", "1647919", "1565987", "1543660", "1606869", "1518351", "1663980", "1493554", "1599154", "1595041", "1645234", "1553613", "1595441", "1494662", "1632681", "1653836", "1558616", "1578773", "1584872", "1656308", "1542192", "1533655", "1615990", "1656561", "1494186", "1640619", "1509554", "1515314", "1573590", "1482226", "1496608", "1574203", "1595042", "1489288", "1555804", "1481032", "1585893", "1646557", "1647357", "1560622", "1645205", "1508728", "1489757", "1638888", "1649828", "1619021", "1594945", "1626299", "1585892"], "answers": ["Spin is a technical term specifically referring to intrinsic angular momentum of particles", "Spin is angular momentum of particles"]} | |
| {"q_id": "science-search-test-560", "query": "are bugs attracted to infrared light?", "doc_id": ["1686743", "1545857", "1684992"], "answers": ["insects do see, and are attracted to, IR light"]} | |
| {"q_id": "science-search-test-374", "query": "have electrons ever been observed?", "doc_id": ["1538071", "1489802", "1620225", "1518688", "1487048", "1536178", "1543741", "1465984", "1607256", "1548173", "1536420", "1532003", "1543874", "1538880", "1551681", "1512017"], "answers": ["only indirectly observed"]} | |
| {"q_id": "science-forum-test-1453", "query": "the last digit of $2^{2006}$", "doc_id": ["136853", "136773", "136772", "952378", "498769", "136775", "1200513", "136767", "136839", "1341757", "136771", "486137"], "answers": ["$2^{2006}$ ends in a $4$", "$4$", "4$"]} | |
| {"q_id": "science-forum-test-1029", "query": "what exactly are eigen-things?", "doc_id": ["143749", "973643", "25300", "25651", "1396495", "143751", "566199", "14576", "118423", "172320", "10687", "1635598", "837002", "943604", "1631814", "316892", "953856", "194436", "118415", "605395", "642551", "127297", "904319", "1547417", "1576439"], "answers": ["vectors that exhibit especially simple behaviour under a linear transformation"]} | |
| {"q_id": "science-forum-test-231", "query": "why doesnt the moon fall onto the earth?", "doc_id": ["1571090", "1598227", "1518253", "1537406", "1575230", "1508841", "1541593", "1576763", "1489630", "1519287", "1585742", "1570295", "1470409", "1623278", "1571108", "1483813", "1642909", "1626314", "1470446", "1576677", "1489632", "1617239", "1517054", "1328949"], "answers": ["the pull on the Moon is just enough to keep it in a circular orbit around Earth"]} | |
| {"q_id": "science-forum-test-108", "query": "how can anything ever fall into a black hole as seen from an outside observer?", "doc_id": ["1555965", "1595095", "1626928", "1549063", "1578790", "1483556", "1566433", "1539651", "1649954", "1478643", "1547770", "1467381", "1538700", "1547269", "1477937", "1475741", "1540226", "1611244", "1660753", "1476214", "1476165", "1583293", "1478870", "1465796", "1548491", "1549484", "1598114", "1485571", "1577108", "1654970", "1535912", "1542964", "1549105", "1467116", "1548595", "1594464", "1511501"], "answers": ["from an outside perspective, nothing can ever pass the event horizon"]} | |
| {"q_id": "science-forum-test-1197", "query": "compact sets are closed?", "doc_id": ["343146", "116838", "387450", "132532", "187957", "1078693", "577970", "994443", "614776", "883986", "94441", "175448", "499100", "1086964", "601138", "16889", "558130", "858153", "1305139", "1100977", "1010751", "5685", "646136", "966823", "858156", "321691", "298920", "233836", "1112967", "1121433", "303756", "221651", "364959", "116839", "298917", "712724", "1218524", "1325393", "1115764", "1442493", "1439478", "94444", "715642", "1023130"], "answers": ["not actually true that a compact subset of an arbitrary topological space is closed", "Compact subsets of metric spaces are closed"]} | |
| {"q_id": "science-search-test-193", "query": "what is the difference between discrete and finite?", "doc_id": ["480385", "461056", "882063", "1344160", "725987", "309596", "719320", "1555798", "1665300", "1632913", "1621783"], "answers": ["Discrete just have to be separated from one another, finite means the total number must be $<\\infty$"]} | |
| {"q_id": "science-forum-test-44", "query": "why does stephen hawking say black holes dont exist?", "doc_id": ["1504169", "1534155", "1666282", "1504011", "1613741", "1612954", "1606757"], "answers": ["Stephen Hawking doesn't say that black holes don't exist"]} | |
| {"q_id": "science-forum-test-1693", "query": "is an irrational number odd or even?", "doc_id": ["516509", "512895", "512891", "513119"], "answers": ["only integers are even or odd", "an irrational number, or in fact any number which is not an integer, is neither odd nor even"]} | |
| {"q_id": "science-forum-test-32", "query": "how do moving charges produce magnetic fields?", "doc_id": ["1487369", "1563461", "1606889", "1667099", "1581079", "1650576", "1493274", "1501696", "1549759", "1500921", "1587935", "1556941", "1493275", "1643978", "1658659", "1587450", "1665341"], "answers": ["charged particle moves through the \"pervasive\" EM field (space), it perturbs the EM field and generates a magnetic field"]} | |
| {"q_id": "science-forum-test-1748", "query": "an easy example of a non-constructive proof without an obvious fix?", "doc_id": ["459132", "460313"], "answers": ["Uncountability of the real numbers"]} | |
| {"q_id": "science-forum-test-1104", "query": "does associativity imply commutativity?", "doc_id": ["575207", "1102166", "753522", "74255", "1380812", "703061", "643268", "699720", "177636", "605955", "1216713", "650424", "860523", "365544", "411031", "1218046", "448272", "1041736", "1349162", "643271", "273891", "1238928", "633673", "1154811", "1041731", "1041737", "345793", "959503", "1138459", "215955"], "answers": ["does not"]} | |
| {"q_id": "science-forum-test-1561", "query": "how many 7-note musical scales are possible within the 12-note system?", "doc_id": ["697594", "724869", "697593"], "answers": ["$38$ possible heptatonic scales", "60"]} | |
| {"q_id": "science-search-test-613", "query": "is fatty acid a polymer?", "doc_id": ["1689277", "1689291"], "answers": ["not considered polymers"]} | |
| {"q_id": "science-search-test-283", "query": "is pi an imaginary number?", "doc_id": ["584748", "148461", "658459", "622622", "890080", "237531", "235509", "718595", "24523", "1116772", "1634140", "14", "330982", "940433", "468349", "1116774", "830201", "1116999", "275135", "923195", "270617", "100377", "1116717", "218811", "48436", "577346"], "answers": ["not an imaginary number"]} | |
| {"q_id": "science-search-test-123", "query": "6 options how many combinations?", "doc_id": ["208403", "58938"], "answers": ["2^6, which is 64"]} | |
| {"q_id": "science-search-test-220", "query": "is pde harder than ode?", "doc_id": ["559724", "1461455", "297276", "928812", "1582827", "1126472", "1369983", "1502996", "1083354", "562366", "1009864", "1172894", "1083805", "1604486", "984341", "364700", "559826"], "answers": ["PDEs are generally more difficult to understand the solutions to than ODEs"]} | |
| {"q_id": "science-forum-test-524", "query": "intuitive interpretation of the laplacian", "doc_id": ["349026", "1686315", "1475891", "1663557", "1427200", "26804", "1615333", "579599", "1387168", "1075433", "1520165", "65498"], "answers": ["behaves like a local averaging operator", "Laplacian as behaving like an 'average rate of change", "local averaging operator"]} | |
| {"q_id": "science-search-test-336", "query": "does normal force affect the coefficient of friction?", "doc_id": ["1550798", "1543410", "1550800", "1588774", "1516695", "1591568", "1550796", "1551971", "1535156", "1646636"], "answers": ["the coefficient does not change"]} | |
| {"q_id": "science-forum-test-1919", "query": "sum of two closed sets in $\\mathbb r$ is closed?", "doc_id": ["67169", "197711", "577970", "1045622", "143012", "322888", "226996", "1257397", "5205", "101541", "488803", "1291540", "908874", "1076128", "298020", "1303507", "496965", "969614", "806110", "454481", "1297239"], "answers": ["The sum $E +F$ may fail to be closed even if $E$ and $F$ are closed"]} | |
| {"q_id": "science-search-test-610", "query": "can octopus go on land?", "doc_id": ["1680602", "1686835", "1557300"], "answers": ["for short periods"]} | |
| {"q_id": "science-forum-test-1924", "query": "is it possible to plot a graph of any shape?", "doc_id": ["567218", "428765", "153466", "566859"], "answers": ["Definitely not"]} | |
| {"q_id": "science-search-test-183", "query": "why are adjoint functor important?", "doc_id": ["79988", "852106", "732365", "1088633", "13904", "1207158", "1285077", "13935", "94395", "817982", "94425", "598808", "368305", "1352418", "49921", "13912"], "answers": ["they show up everywhere and are an extremely useful organizing principle"]} | |
| {"q_id": "science-search-test-508", "query": "what are the 2 types of current flow in a semiconductor?", "doc_id": ["1527611", "1573409", "1549314", "1551167", "1605869", "1503602", "1583912", "1495563", "1588176", "1526120", "1580726", "1630530", "1662486", "1589151", "1663768"], "answers": ["the electron current and the hole current"]} | |
| {"q_id": "science-forum-test-1564", "query": "what is the size of each side of the square?", "doc_id": ["1310976", "1310993", "1310989"], "answers": ["$18$", "18$"]} | |
| {"q_id": "science-forum-test-203", "query": "if you are vacuuming your carpet and you wrap the cord around your body do you become a magnet?", "doc_id": ["1560936", "1561211", "1578928", "1574310", "1560937", "1589580", "1561044", "1495919", "1472151", "1690246"], "answers": ["No"]} | |
| {"q_id": "science-search-test-4", "query": "every real number has a decimal expansion?", "doc_id": ["192257", "975947", "192258", "672665", "33333", "817045", "1411977", "585483", "1450814", "423030", "289382", "1310284", "717063", "448092", "938863", "299960", "1311030", "773", "221411", "173714", "835708", "207872", "143300", "361478", "752943", "591140", "350658", "731047", "74585", "659009", "579376", "10584", "1465183", "650970", "670743", "1038888", "493824", "301735", "1195579"], "answers": ["yes", "Yes", "Every real number $x$ has a decimal expression $$x = a_0.a_1a_2a_3\\ldots"]} | |
| {"q_id": "science-search-test-168", "query": "are imaginary numbers and complex numbers the same?", "doc_id": ["145177", "14", "1448906", "1668204", "1334069", "584748", "962070", "840116", "1110822", "1311999", "737284", "275139", "575959", "334328", "1624081", "586658", "976657", "378895", "1641890", "535487", "1566511", "853564", "1116772", "1108962", "1116781", "1087252", "757059", "717713", "26040", "323074", "1073149"], "answers": ["imaginaries are a subset of the complex numbers"]} | |
| {"q_id": "science-search-test-426", "query": "are neutrinos affected by gravity?", "doc_id": ["1477432", "1551362", "1535952", "1598078", "1473358", "1473369", "1639785", "1557340", "1557906", "1612063", "1490643", "1554651", "1656300", "1557469", "1472650", "1495210", "1636218", "1498629", "1582873", "1477121", "1651171", "1637183", "1645695", "1607231"], "answers": ["Neutrinos are certainly affected by gravity", "All particles, even massless ones, are affected by gravity"]} | |
| {"q_id": "science-forum-test-220", "query": "will a hole cut into a metal disk expand or shrink when the disc is heated?", "doc_id": ["1483868", "1472091", "1474779", "1481933", "1476698", "1485194", "1476697", "1593743", "1537891", "1555092", "1541461", "1622271", "1477301", "1476714", "1537900", "1593731"], "answers": ["the hole would still get larger", "the hole will expand", "Heat a hole, and it expands"]} | |
| {"q_id": "science-forum-test-1121", "query": "reference request: introduction to commutative algebra", "doc_id": ["273153", "1029236", "522079", "402032", "21779", "19976", "1330375", "480199", "838050", "20002", "280703", "64802", "30221", "1108463", "161486"], "answers": ["A Singular Introduction to Commutative Algebra", "\"Commutative Algebra with a view towards algebraic geometry"]} | |
| {"q_id": "science-forum-test-1024", "query": "what is lost when we move from reals to complex numbers?", "doc_id": ["125622", "1142948", "1009848", "27279", "1009849", "1010673", "414150", "1124266", "1009853", "308958", "980361", "433087", "302004", "156341", "1560160", "417535", "93984", "121554", "1009845", "117269", "1079901", "1453576", "1355476", "560125", "1297915", "450253", "1076853", "1009850"], "answers": ["the notion of an order", "ordering", "order"]} | |
| {"q_id": "science-search-test-302", "query": "are all bounded sequences convergent?", "doc_id": ["135486", "135485", "135481", "815540", "484915", "247052", "53896", "725549", "487067", "689058", "491208", "342233", "1329845", "1317271", "766015", "937880", "1103330", "2804", "815506", "1041020", "1450450", "618866", "144714", "168145", "1211670", "602501", "33071", "982823", "1045856", "1430766", "995009", "53897", "659009", "888382", "27734", "736857", "747843", "398502", "277072", "863727", "468038", "671582", "33170", "1281406", "9764", "8807", "481815", "738984", "1063108", "537983"], "answers": ["No"]} | |
| {"q_id": "science-search-test-52", "query": "are pivot columns linearly independent?", "doc_id": ["1453880", "1300951", "956017", "3054", "1188584", "822712", "866621", "229952", "1246727", "862157", "1222264", "1111999", "1199413", "643651", "959290", "106332", "875900", "926102", "1324107", "236751", "395580", "16775", "959265", "325085", "980863", "714704", "1092943"], "answers": ["Pivot columns are linearly independent", "Yes of course pivot columns are linearly independent"]} | |
| {"q_id": "science-search-test-329", "query": "what is a non-conservative field?", "doc_id": ["335476", "1553829", "1536925", "1489600", "897421", "1611494", "1522163", "1655999", "1635530", "1573929", "1519649", "1667245", "1667981", "212082", "1600503", "1597504", "1498683", "1479696", "1583229", "541579", "1540978", "1564072", "1618880", "1528275", "1527406", "1553314"], "answers": ["one where the integral along some path is not zero"]} | |
| {"q_id": "science-search-test-586", "query": "what is the difference between cell line and cell strain?", "doc_id": ["1682721"], "answers": ["A cell strain is a subpopulation of a cell line that has been positively selected from the culture"]} | |
| {"q_id": "science-search-test-194", "query": "what is the probability of getting a pair in a deck of cards?", "doc_id": ["1116807", "406029", "1398774", "103710", "1263441", "40593", "1265826"], "answers": ["3/51 = 1/17"]} | |
| {"q_id": "science-forum-test-1977", "query": "can hiv be transmitted via mosquitos?", "doc_id": ["1681060", "1681074", "1691319", "1689978", "1685080", "1691317"], "answers": ["No"]} | |
| {"q_id": "science-forum-test-874", "query": "is it possible to represent every huge number in abbreviated form?", "doc_id": ["506128", "57507", "2045", "1131826", "190441", "1577643", "1028753", "715837", "460203", "779397", "1182032"], "answers": ["No"]} | |
| {"q_id": "science-forum-test-1841", "query": "average distance between random points on a line segment", "doc_id": ["565994", "98354"], "answers": ["$\\frac L 3$", "D=L/3"]} | |
| {"q_id": "science-search-test-305", "query": "what is the difference between analytical and numerical methods?", "doc_id": ["394641", "733286", "1609992", "1582827", "875554", "1176390", "1519122", "1596752", "792474", "568761", "1176913", "1545616", "409853", "1625534", "1176389", "649991", "1523167", "394659", "878034", "971981", "512820", "1625162", "1202451", "179895", "1102935", "1501392"], "answers": ["Analytical is exact; numerical is approximate"]} | |
| {"q_id": "science-search-test-468", "query": "a body moving with a constant velocity will have?", "doc_id": ["1659591", "1644400", "1509624", "1551808", "1495549", "1654639", "1561063", "1643724", "1633641", "1575173", "1159911", "1539685", "1530458", "1649713", "1657715", "1589843", "1571432", "1545017", "1661660", "1627682", "1653116", "1653006", "1665425", "1487608", "1611936", "1558003", "1477838", "1623217"], "answers": ["the total of all the forces applied to it is zero"]} | |
| {"q_id": "science-search-test-387", "query": "in uniform circular motion acceleration is uniform or variable?", "doc_id": ["1610418", "1610407", "1650386", "1557439", "1620130", "1618718", "1620129", "1629149", "1619608", "1560938", "1622881", "1595252", "1570996", "1543164", "1647620", "1359406", "1568441", "1531782", "1495515", "1571151", "1631099", "1645411", "1599366", "1592234", "1572098", "1635658", "1663272", "1658060", "1541284", "1580534", "1658122", "1667073", "1644716", "1492165", "1645098", "1539837", "1640911", "1596887", "1528518", "1599566", "1654019", "1550695", "1511547", "1650557"], "answers": ["variable"]} | |
| {"q_id": "science-forum-test-1500", "query": "how to know if a point is inside a circle?", "doc_id": ["280912", "160977", "238105", "545382", "440332", "808375", "355351", "177373", "181847", "763035", "181869", "126491", "378100", "655350", "99566", "61040", "1376419", "800", "545378", "1138199", "149623", "149620"], "answers": ["if the distance from it to the center is less than $r$"]} | |
| {"q_id": "science-forum-test-672", "query": "is zero odd or even?", "doc_id": ["457515", "291349", "8695", "646939", "983973", "457185", "516509", "1220440", "1248108", "333038", "153891", "1129994", "486091", "139651", "759611", "1031170", "512921", "1198661", "247235", "52792", "247240", "481833", "654764", "8713", "214164", "1032744", "1164447", "292189", "1324368", "457198", "718687", "1172659", "249172", "162456"], "answers": ["even"]} | |
| {"q_id": "science-search-test-141", "query": "can mutually exclusive events be independent and dependent?", "doc_id": ["948023", "730875", "1007637", "411191", "1163467", "158229", "396636", "396638", "647910", "1431483", "540180", "1302650"], "answers": ["mutually exclusive events are not independent, and independent events cannot be mutually exclusive", "if the two events are mutually exclusive, they can not be independent", "If two events are independent, they cannot be mutually exclusive"]} | |
| {"q_id": "science-search-test-486", "query": "what is the relationship between ir rays and heat?", "doc_id": ["1532456", "1499335", "1499332", "1566381", "1672445", "1611831", "1659986", "1567175", "1538282", "1677221", "1471549", "1566583", "1496579", "1641642", "1666639", "1676489", "1555096", "1500148", "1650400", "1591327", "1537172", "1566641", "1496981", "1475657", "1525681", "1621614", "1626304", "1579358", "1555099", "1538816", "1608808", "1508997", "1567193", "1466694", "1566658", "1659975", "1549549", "1576746", "1589344", "1619253", "1469317", "1626990", "1551746"], "answers": ["energy carried away by the infrared radiation reduces the heat content of the radiating body", "most bodies radiate most of their heat in the infrared spectrum"]} | |
| {"q_id": "science-search-test-282", "query": "can 2 events be independent and mutually exclusive?", "doc_id": ["462651", "396636", "396638", "977911", "1147254", "1120893", "772302", "734839", "356519", "1355662", "213795", "538253", "509515", "63016", "158229", "1355671", "734846", "730875", "411191", "1340218", "1007637", "319185", "647910", "408134", "129251", "540180"], "answers": ["This of course means mutually exclusive events are not independent, and independent events cannot be mutually exclusive", "If two events are independent, they cannot be mutually exclusive", "a mutually exclusive pair of nontrivial events are also necessarily dependent events"]} | |
| {"q_id": "science-forum-test-597", "query": "what is the jacobian matrix?", "doc_id": ["310255", "1345113", "1017372", "906384", "337138", "1217178", "47008", "213776", "838972", "766646", "18261", "1099435", "232321", "1057005", "1003334", "760943", "934193", "400384", "1283000", "620090", "1416993", "554308", "1029603", "207223", "679514", "172873", "492366", "542264", "1402801", "1458490", "1068020", "1048519", "968522", "1446263", "234082", "596150", "72565", "1409337", "1199758", "720499", "572424", "329060", "75825", "497841", "873784", "1083715", "402324", "1068029", "421891", "766649", "565290", "175775"], "answers": ["a matrix of partial derivatives"]} | |
| {"q_id": "science-search-test-222", "query": "what is the difference between analytical and empirical?", "doc_id": ["996233", "1553468", "61877", "1248305", "1521998", "171459", "1542170", "1658966", "1556834", "1474274", "1573200"], "answers": ["empirical: based on, concerned with, or verified by observation or experience. analytical: based on analysis or logic"]} | |
| {"q_id": "science-search-test-356", "query": "why are hermitian matrices important?", "doc_id": ["550818", "1589609", "1625692", "877810", "1213124", "1631137", "1055021", "983609", "1114795", "50036"], "answers": ["because we have the spectral theorem for them, i.e. they admit an orthonormal eigenbasis"]} | |
| {"q_id": "science-search-test-87", "query": "are prime numbers still prime in other bases?", "doc_id": ["99559", "300213", "446528", "787530"], "answers": ["A prime number is a prime by defination, irrespective of base", "It is prime, no matter how you represent it"]} | |
| {"q_id": "science-forum-test-1573", "query": "explicit norm on $\\mathcal{c}^0(\\mathbb{r},\\mathbb{r})$", "doc_id": ["423604", "1356842", "787890", "751504"], "answers": ["There is no explicit norm on $\\mathcal{C}^0(\\mathbb{R}, \\mathbb{R})$"]} | |
| {"q_id": "science-forum-test-334", "query": "is there a 0-1 law for the theory of groups?", "doc_id": ["739064", "99875", "19506", "394024", "393968", "1062964", "211715"], "answers": ["a FO 0-1 law for group theory as defined by Dominik doesn't exist and may never exist", "such a law cannot exist for the whole group theory or even for finite group theory"]} | |
| {"q_id": "science-forum-test-1968", "query": "why are so few foods blue?", "doc_id": ["1683833", "1683841", "1683926"], "answers": ["Blue color is rare in both the animal and plant Kingdoms in general"]} | |
| {"q_id": "science-forum-test-1975", "query": "what is the effect of non-vaccinated people on vaccinated people?", "doc_id": ["1688597", "1688600", "1688620", "1692591", "1683297", "1692185", "1437917"], "answers": ["vaccinated people are still at risk of disease following exposure to unvaccinated people"]} | |
| {"q_id": "science-forum-test-1928", "query": "there exists a power of 2 such that the last five digits are all 3s or 6s. find the last 5 digits of this number", "doc_id": ["282091", "282205", "282092"], "answers": ["66336"]} | |
| {"q_id": "science-forum-test-1195", "query": "probability of 3 people in a room of 30 having the same birthday", "doc_id": ["678124", "14133"], "answers": ["$$P(365,30,3)\\simeq 2,85\\%$$"]} | |
| {"q_id": "science-forum-test-216", "query": "is there a symmetry associated to the conservation of information?", "doc_id": ["1659091", "1622154", "1504118", "1515843", "1643205", "1517800", "1591024", "1476327", "1578795", "1563641", "1538893", "1496603", "1560874", "1485085", "1477756", "1577952", "1518097"], "answers": ["Liouville theorem, which can be interpreted in terms of time-translation symmetries", "there is a symmetry associated with information conservation"]} | |
| {"q_id": "science-search-test-182", "query": "is sin x one to one?", "doc_id": ["465300", "716071", "1391895", "1016659", "86195", "1258055", "843742", "1387542", "775960", "767843", "1026967", "399372", "506670", "1199938", "1401507", "1046603", "1330674", "858462", "996559", "448040", "1046658", "686271", "998641", "1066805", "1135642", "369784", "6192", "811374"], "answers": ["it is not one-to-one"]} | |
| {"q_id": "science-forum-test-584", "query": "help find hard integrals that evaluate to $59$?", "doc_id": ["84992"], "answers": ["$$ \\frac{64}{\\pi^3} \\int_0^\\infty \\frac{ (\\ln x)^2 (15-2x)}{(x^4+1)(x^2+1)}\\ dx $$"]} | |
| {"q_id": "science-forum-test-174", "query": "does juggling balls reduce the total weight of the juggler and balls?", "doc_id": ["1644726", "1644954", "1663834", "1483500", "1483485", "1483484", "1483515"], "answers": ["no"]} | |
| {"q_id": "science-search-test-308", "query": "are sinx and cosx orthogonal?", "doc_id": ["541480", "288168", "570900", "165133", "114675", "411502", "211218", "1272871", "804262", "310067", "541470", "1157155", "774889", "78053", "965468", "1558203", "430001", "557873", "611557", "847105", "116068", "1387521", "228886", "478769"], "answers": ["$\\sin(x),\\cos(x)$ are orthogonal"]} | |
| {"q_id": "science-forum-test-487", "query": "whats 4 times more likely than 80%?", "doc_id": ["217451"], "answers": ["95\\%"]} | |
| {"q_id": "science-search-test-162", "query": "is sin x an onto function?", "doc_id": ["444522", "465299", "224903", "506670", "1330674", "419049", "75125", "1220440", "1096508", "444520", "246249", "411224", "1387542", "650637", "1243867", "465300", "1111170", "1114981", "881935", "808236", "1392525", "39891"], "answers": ["The sine is not onto", "not onto"]} | |
| {"q_id": "science-forum-test-1837", "query": "number of onto functions", "doc_id": ["159165", "513456"], "answers": ["$n!S(m,n)$"]} | |
| {"q_id": "science-forum-test-1181", "query": "intuitive explanation of a definition of the fisher information", "doc_id": ["179480", "1616815", "595000", "1485271", "1538227", "1325306", "128709", "1037972", "1634698"], "answers": ["a measure of the \"curvature\" of the support curve near the maximum likelihood estimate of \u03b8"]} | |
| {"q_id": "science-forum-test-1777", "query": "is it possible for a function to be smooth everywhere, analytic nowhere, yet taylor series at any point converges in a nonzero radius?", "doc_id": ["242631", "282004"], "answers": ["No"]} | |
| {"q_id": "science-search-test-311", "query": "how to calculate the difference between two negative numbers?", "doc_id": ["573025", "825745", "728692", "747999", "836911"], "answers": ["subtract the smaller absolute value from the larger absolute value"]} | |
| {"q_id": "science-forum-test-1235", "query": "why is radian so common in maths?", "doc_id": ["858507", "749365", "451248", "59585", "224038", "1276322", "692885", "1545026", "693352", "139688"], "answers": ["Radians are simply the natural units for measuring angles", "radians are the natural unit of measure for angles"]} | |
| {"q_id": "science-search-test-527", "query": "are all central forces conservative?", "doc_id": ["1651002", "1535396", "1583225", "1543750", "1666249", "1479696", "1526738", "1550432", "1613281", "1613401", "1619493", "589120", "1488635", "1497264", "1583229"], "answers": ["central forces are conservative"]} | |
| {"q_id": "science-forum-test-1505", "query": "matrices commute if and only if they share a common basis of eigenvectors?", "doc_id": ["1294816", "659795", "87527", "1599671", "516160", "818331", "1119631", "495532", "3681", "705409", "1640222", "358239", "1081016", "1599163", "1665956", "1163678", "479381", "1543532", "705417", "1129275", "1550046", "933314", "495486", "1093977", "1213977"], "answers": ["This is false"]} | |
| {"q_id": "science-forum-test-551", "query": "how to find solutions of linear diophantine ax + by = c?", "doc_id": ["263986", "949230", "85658", "7214", "203498", "73519", "85656", "698658", "239649", "644255", "1039271", "11458", "11450", "583066", "11454", "1112456", "474324", "771387", "1224379", "1184620", "701971", "254881"], "answers": ["use the extended Euclidean algorithm", "extended Euclidean algorithm"]} | |
| {"q_id": "science-forum-test-136", "query": "why is there a scarcity of lithium?", "doc_id": ["1471439", "1472232", "1471426", "1537029", "1654363"], "answers": ["there is quite a lot of lithium in the earth that is not so easy to obtain", "it is found in many rocks and some brines, but always in very low concentrations", "it does not tend to accumulate in rich geological deposits"]} | |
| {"q_id": "science-forum-test-179", "query": "am i attracting pluto?", "doc_id": ["1477610", "1537775", "1537677", "1547232", "1537705", "1477603", "1631300", "1537622", "1543155", "1537848"], "answers": ["The mass that makes up your body and everything inside your body is attracting Pluto"]} | |
| {"q_id": "science-search-test-189", "query": "are two disjoint events independent?", "doc_id": ["705588", "705585", "977911", "107960", "1442332", "63014", "640016", "1137669", "356519", "1393764", "304555", "1355467", "509515", "1288091", "1355671", "1433108", "705600", "394496", "593658", "622738", "1355498", "1412333", "1151763", "396636", "319185", "546489", "772302", "1347068", "211308", "1448262"], "answers": ["Two disjoint events can never be independent, except in the case that one of the events is null", "Disjoint events aren't independent, unless one event is impossible"]} | |
| {"q_id": "science-forum-test-838", "query": "can you make a sphere out of a plane?", "doc_id": ["1286649", "1286417", "164174", "411547", "546371", "1036217", "1478439", "149649", "1475732", "1383824", "770799", "616975", "111554", "1484239", "1286648", "6078", "1645", "907134"], "answers": ["impossible"]} | |
| {"q_id": "science-search-test-320", "query": "how many meal combinations are possible with the current menu?", "doc_id": ["574803", "1433820", "574798"], "answers": ["96"]} | |
| {"q_id": "science-forum-test-497", "query": "why do units (from physics) behave like numbers?", "doc_id": ["758616", "342696", "758776", "1639030"], "answers": ["units are not separate from numbers but rather extensions of numbers"]} | |
| {"q_id": "science-search-test-332", "query": "what is the difference between wave and pulse?", "doc_id": ["1525296", "1562955", "1510263"], "answers": ["A single vibration is called pulse and continued vibration of a particle in medium is called wave"]} | |
| {"q_id": "science-forum-test-534", "query": "why is negative times negative = positive?", "doc_id": ["596892", "309749", "5657", "1229956", "79953", "113365", "1344050", "5726", "1544045", "178549", "596885", "1116909", "101105"], "answers": ["doing the opposite twice means doing the usual"]} | |
| {"q_id": "science-search-test-449", "query": "are top floor apartments hotter?", "doc_id": ["1471566", "1597885", "1664134", "1519855", "1471567"], "answers": ["The top floor can be very hot in a cement apartments flat without an attic"]} | |
| {"q_id": "science-search-test-292", "query": "how many numbers from 1 to 100 are not divisible by 2 3 and 5?", "doc_id": ["209483", "209503", "584843"], "answers": ["26"]} | |
| {"q_id": "science-forum-test-1000", "query": "is zero positive or negative?", "doc_id": ["14568", "506406", "1152032", "14612", "457185", "10272", "995613", "1340502", "1539521", "415921", "840722", "1201788", "1111701", "1618109", "609486", "415736", "18438", "1030796", "552926", "303240", "79953", "621051", "276225", "1437039", "853011", "726979", "14569", "1523818"], "answers": ["neither positive nor negative", "neither a negative or a positive"]} | |
| {"q_id": "science-search-test-120", "query": "subgroup of abelian group is abelian?", "doc_id": ["1162995", "1253498", "14330", "542207", "1049383", "1381715", "94728", "466711", "304113", "380447", "1216736", "365197", "102959", "380438", "1299036", "106556", "965389", "789974", "505627", "1351935", "719410", "365198", "1199839"], "answers": ["Yes, subgroups of abelian groups are indeed abelian"]} | |
| {"q_id": "science-forum-test-889", "query": "what concept does an open set axiomatise?", "doc_id": ["394058", "17218", "817859"], "answers": ["semidecidable property"]} | |
| {"q_id": "science-forum-test-831", "query": "is arrow notation for vectors not mathematically mature?", "doc_id": ["752261", "450306", "735758", "450144", "393640", "450272", "468954", "93399", "287829", "1534735", "1501074", "699720", "1085120"], "answers": ["No"]} | |
| {"q_id": "science-forum-test-72", "query": "why is the vibration in my wire acting so oddly?", "doc_id": ["1557069"], "answers": ["the stiffness and elasticity of it is not homogenous lengthwise or even along cross-section"]} | |
| {"q_id": "science-forum-test-1910", "query": "how to find a basis for the intersection of two vector spaces in $\\mathbb{r}^n$?", "doc_id": ["151036", "13860", "13859"], "answers": ["Parameterize both vector spaces (using different variables!) and set them equal to each other"]} | |
| {"q_id": "science-forum-test-971", "query": "what does surface area of a sphere actually mean (in terms of elementary school mathematics)?", "doc_id": ["1298096", "1299422", "1297597", "1285971"], "answers": ["painting the surface area, and working out how much paint was required to paint the sphere's complete surface"]} | |
| {"q_id": "science-search-test-244", "query": "what is the difference between binomial and bernoulli distribution?", "doc_id": ["358538", "1018772", "67983", "628863", "358542", "1317941", "837050", "1019060", "487929", "1437166", "1069648", "669956", "1087142", "1123381", "735330", "358540", "591146", "870607"], "answers": ["All Bernoulli distributions are binomial distributions, but most binomial distributions are not Bernoulli distributions"]} | |
| {"q_id": "science-forum-test-985", "query": "in linear algebra, what is a vector?", "doc_id": ["744461", "744334", "744331", "744369", "745390", "46135", "1601812", "620241", "713436", "33280", "1045794", "1046730", "288019", "1560877", "1555149", "403636", "1661778", "1074610", "69101", "1489258", "693241", "1348518", "1331383", "294466", "1629152", "1549411", "1655969", "167648", "1661697", "1592918", "744498", "1457094", "145098", "764262", "849263", "458463", "752261", "872561", "1196197", "9812", "1496041", "93471", "620224", "1313425", "145114", "1582282", "388884", "959728", "244800", "1251890", "971954", "620221", "27268", "162323", "417237", "1650800", "1209321", "1325358", "1627005", "555635", "655313", "994782", "179020", "1281031", "1253392", "514444", "370875"], "answers": ["a quantity with magnitude and direction", "an element of a vector space"]} | |
| {"q_id": "science-search-test-406", "query": "what is the highest frequency of electromagnetic radiation?", "doc_id": ["1485212", "1639082", "1491954", "1553140", "1549549", "1618218", "1584083", "1506462", "1580078", "1548829", "1517225", "1524916", "1650317", "1567175", "1599466", "1531955", "1536506"], "answers": ["Gamma-rays"]} | |
| {"q_id": "science-forum-test-2001", "query": "can a woman give birth to twins with different fathers?", "doc_id": ["1675779", "1675762", "1687855", "1669758", "1672639", "1693844", "1670352"], "answers": ["there have been documented cases where twins had different fathers"]} | |
| {"q_id": "science-search-test-563", "query": "what is 5' and 3' dna?", "doc_id": ["1672969", "1672970", "1692809", "1684393", "1691215", "1685421", "1679355", "1689292", "1681274", "1676183", "1692810", "1680326", "1693290", "1693543", "1683386", "1682427", "1682656", "1687269", "1692359", "1691533"], "answers": ["5' carbon has a phosphate group attached to it and the 3' carbon a hydroxyl (-OH) group", "five prime\" and \"three prime\", which indicate the carbon numbers in the DNA's sugar backbone"]} | |
| {"q_id": "science-forum-test-278", "query": "in russian roulette, is it best to go first?", "doc_id": ["190979", "49996", "254347", "1032593", "1387280", "412316", "314287", "575753", "492681"], "answers": ["Your best bet is actually to go last", "it's a disadvantage to go first"]} | |
| {"q_id": "science-search-test-143", "query": "is a 2x3 matrix invertible?", "doc_id": ["934250", "30103", "937414", "367713", "730546", "157923", "290229", "602022", "486557", "1279209", "256462", "533511", "109536", "998008", "263919", "1005915", "1180389", "709315", "757280", "651597", "1204914", "305282", "486713", "1307935", "298588", "216987", "847563", "773893", "574129", "810590"], "answers": ["No"]} | |
| {"q_id": "science-forum-test-988", "query": "are all mathematicians human calculators?", "doc_id": ["251817", "251857", "618569", "251934", "251824", "282831", "251928", "321523", "66023", "1041017", "780520", "489447", "1312850", "65969", "70039", "257888", "186496", "380720", "250406", "353461", "293430", "1016118", "404330", "907603", "780524", "328935", "328907", "267824", "156376", "75112", "283490", "322458"], "answers": ["no", "No"]} | |
| {"q_id": "science-forum-test-1985", "query": "death because of distilled water consumption", "doc_id": ["1670603", "1669263", "1674428", "1680564", "1669276", "1682077", "1679748", "1681493", "1680039", "1671253", "1676752"], "answers": ["related to hyperhydration/water intoxication", "to drink nothing but distilled water, and eat no food, you probably would die of hyponatremia"]} | |
| {"q_id": "science-forum-test-1414", "query": "where does the word torsion in algebra come from?", "doc_id": ["143945", "143944", "14401"], "answers": ["Its origin lies in algebraic (or combinatorial) topology"]} | |
| {"q_id": "science-forum-test-599", "query": "is there a known well ordering of the reals?", "doc_id": ["163469", "578516", "1362046", "523984", "46256", "774587", "179565", "433200", "1295528", "1463303", "3803", "106955", "260255", "687667", "580614", "754763"], "answers": ["No"]} | |
| {"q_id": "science-forum-test-1336", "query": "what exactly is a number?", "doc_id": ["6984", "283054", "535825", "328675", "368385", "443395", "278749", "1142948", "773", "177561", "832160", "402255", "368704", "446475", "119338", "119350", "368389", "462081", "230051", "230481", "1624077", "25439", "535828", "897191", "268036"], "answers": ["a mathematical notion which represents quantity"]} | |
| {"q_id": "science-search-test-384", "query": "is gas a good conductor of electricity?", "doc_id": ["1484117", "1500549", "1507923", "1578765", "1489679", "1618752", "1525424", "1496723", "1501354", "1582301", "1647970", "1572230", "1562073", "1498768", "1533106", "1531325", "1589200"], "answers": ["At atmospheric pressure, air and other gases are poor conductors"]} | |
| {"q_id": "science-forum-test-1148", "query": "naturally occurring non-hausdorff spaces?", "doc_id": ["1337442"], "answers": ["Sierpi\u0144ski space"]} | |
| {"q_id": "science-forum-test-1905", "query": "why does an integral change signs when flipping the boundaries?", "doc_id": ["901699", "1204009", "1378639", "609150", "999274", "1666698", "526114", "528300", "384903", "1022592", "1568220", "369619", "1236009", "1603643", "496105", "526250", "526113", "558381", "304642"], "answers": ["$\\int_a^b f(x) dx + \\int_b^a f(x) dx = \\int_a^a f(x) dx$. But $\\int_a^a f(x) dx = 0$, so if we want this formula to hold, we need $\\int_a^b f(x) dx = -\\int_b^a f(x) dx $", "The change in $x$, $dx$ becomes negative"]} | |
| {"q_id": "science-forum-test-34", "query": "why do we not have spin greater than 2?", "doc_id": ["1473315", "1556243"], "answers": ["a consequence of little group invariance and charge conservation"]} | |
| {"q_id": "science-forum-test-1958", "query": "function that is the sum of all of its derivatives", "doc_id": ["645433", "639957"], "answers": ["$f(x)=\\exp(\\frac{1}{2}x)$"]} | |
| {"q_id": "science-forum-test-480", "query": "intuitively, what is the difference between eigendecomposition and singular value decomposition?", "doc_id": ["1040128"], "answers": ["SVD is for bilinear forms and the eigendecomposition is for quadratic forms"]} | |
| {"q_id": "science-forum-test-1399", "query": "is the law of large numbers empirically proven?", "doc_id": ["1556675", "171459", "464234", "1248307", "461620", "461220", "1640905", "667343", "931686", "896493", "702944", "1554701", "1564069", "461615", "1277628", "1354427", "1523548", "461397", "1177845", "993400", "1565062"], "answers": ["we cannot empirically verify LLN", "not empirically proven"]} | |
| {"q_id": "science-forum-test-501", "query": "what is the difference between regression and classification?", "doc_id": ["568067", "71596", "92227", "373495", "242202", "311072", "395018", "916579", "616663"], "answers": ["Regression: the output variable takes continuous values. Classification: the output variable takes class labels", "Regression involves estimating or predicting a response. Classification is identifying group membership", "regression predicts a value from a continuous set, whereas classification predicts the 'belonging' to the class"]} | |
| {"q_id": "science-search-test-575", "query": "prawn is not a fish but an?", "doc_id": ["1682824", "1673578", "1685290", "1692346", "1680813"], "answers": ["Crustacean"]} | |
| {"q_id": "science-forum-test-1838", "query": "what does := mean?", "doc_id": ["304481", "309992", "1058635", "15830", "397944", "1453228", "1066573", "13778", "240963", "478946", "33693", "639508", "127281", "1066536", "707964", "1066537"], "answers": ["item on the left hand side is being defined to be what is on the right hand side"]} | |
| {"q_id": "science-forum-test-1946", "query": "are rational points dense on every circle in the coordinate plane?", "doc_id": ["1196410", "1192703", "1091580", "845160", "1148250", "583278", "4205", "102672", "211847", "722917", "963537"], "answers": ["The set of rational points on a circle are dense in the circle"]} | |
| {"q_id": "science-search-test-178", "query": "what does express in terms of x mean?", "doc_id": ["1036189", "749547", "430377", "993650", "515263", "565062", "1390424"], "answers": ["to write an algebraic expression using only that variable or variables"]} | |
| {"q_id": "science-forum-test-56", "query": "does someone falling into a black hole see the end of the universe?", "doc_id": ["1590376", "1499957", "1499968", "1502641", "1497128", "1637479", "1654684", "1489620", "1540812", "1482790", "1521464", "1538700", "1521712", "1491549", "1644016", "1468913", "1598114", "1647789", "1509074", "1467677", "1575650", "1511501", "1644978", "1503353", "1478643", "1533400", "1479003", "1616744", "1467669", "1628184", "1547770", "1548491", "1523628", "1497435", "1623509", "1522349", "1535912", "1576640", "1542993", "1482238", "1557504", "1533679"], "answers": ["they will not see the end of the universe"]} | |
| {"q_id": "science-search-test-440", "query": "what is the magnitude of acceleration called?", "doc_id": ["1577475", "1572105", "1538137", "1572367", "1629647", "677284", "1571643", "1504726", "1533162", "1577333", "1504724", "1599566", "1620736", "1635510", "1641626", "1473311", "1514169", "1490567"], "answers": ["magnitude of the acceleration vector"]} | |
| {"q_id": "science-forum-test-310", "query": "can you answer my sons fourth-grade homework question: which numbers are prime, have digits adding to ten and have a three in the tens place?", "doc_id": ["35283", "239219"], "answers": ["37", "433", "631"]} | |
| {"q_id": "science-search-test-227", "query": "can mutually exclusive events also be independent of one another?", "doc_id": ["396636", "396638", "129251", "1120893", "1431483", "772302", "734839", "356519", "1355662", "462651", "213795", "1118189", "509515", "158229", "1355671", "734846", "730875", "193619", "213447", "1061195", "411191", "193622", "1340218", "28965", "1431489", "1091744", "319185", "734841", "948023", "647910", "558530", "193617", "538253", "540180", "977911"], "answers": ["mutually exclusive events are not independent, and independent events cannot be mutually exclusive", "if the two events are mutually exclusive, they can not be independent", "If two events are independent, they cannot be mutually exclusive"]} | |
| {"q_id": "science-forum-test-1730", "query": "what does \u2208 mean?", "doc_id": ["239515", "914264", "222541", "580293", "878294", "803135", "816554", "716273", "917392", "1184070", "167203", "909501", "361418", "878299", "857904", "1210807", "574193", "737957", "526584", "259949"], "answers": ["an element of", "element in the set of", "Element of"]} | |
| {"q_id": "science-forum-test-1087", "query": "how many connected components does $\\mathrm{gl}_n(\\mathbb r)$ have?", "doc_id": ["1410488", "573073", "381425", "695090", "818392", "305913", "1078722", "1431139", "8726", "52224", "150395", "318637", "893023", "1087354", "910809", "330233", "41014", "596931", "52219", "718671", "52264", "1037229", "381353", "52220", "1107444", "394713", "1284227", "746789", "96473", "166911"], "answers": ["two components"]} | |
| {"q_id": "science-forum-test-1352", "query": "fourier transform of derivative", "doc_id": ["62173", "335577", "452705", "947373", "1111362", "789581", "1498237", "201844", "1294156", "115069", "674851", "974441", "147295", "1384396", "780335", "214982"], "answers": ["$ \\mathcal{F}(f')(\\xi)=2\\pi i\\xi\\cdot\\mathcal{F}(f)(\\xi)"]} | |
| {"q_id": "science-forum-test-1621", "query": "is the power set of the natural numbers countable?", "doc_id": ["40818", "1384653", "1201308", "1234043", "368753", "55698", "904450", "1387724", "698072", "87265", "1315312", "66590", "221411", "481900", "610409", "546759", "948074", "146631", "215415", "178009", "91836", "889491", "812575", "904407", "735864", "1072771"], "answers": ["uncountable"]} | |
| {"q_id": "science-forum-test-1343", "query": "if we randomly select 25 integers between 1 and 100, how many consecutive integers should we expect?", "doc_id": ["618862", "612120", "612094", "1108470"], "answers": ["\\begin{align} E[X] &= E[X_1] + E[X_2] + \\cdots +E[X_{99}]\\\\ &= 99E[X_1]\\\\ &= 99\\frac{25}{100}\\frac{24}{99} = 6 \\end{align}", "$$ 24 {99\\choose 24} \\times {100\\choose 25}^{-1} = 6.$$"]} | |
| {"q_id": "science-forum-test-33", "query": "how does a knife cut things at the atomic level?", "doc_id": ["1516707", "1518908", "1516706", "1507584", "1476303", "1552882", "1499252", "1544643", "1483882", "1510322", "1592789", "1578677", "1602993"], "answers": ["the atoms amorphise in the immediate vicinity due to the high pressure and then deform around the blade", "material either fractures along faults in the lattice, or you separate molecules (as when you cut bread"]} | |
| {"q_id": "science-search-test-51", "query": "how to show a curve has no turning points?", "doc_id": ["404596", "1139295", "337972", "404598"], "answers": ["The curve has no turning point when its derivative takes constant sign", "A differentiable function $f(x)$ has no turning points if its derivative $f'(x)$ has no real roots"]} | |
| {"q_id": "science-search-test-343", "query": "light is electromagnetic wave or not?", "doc_id": ["1485055", "1548996", "1523966", "1527987", "1571824", "1658307", "1506462", "1540269", "1658306", "1512799", "1646585", "1664465", "1512629", "1581900", "1584337", "1485061", "1623653", "1594141", "1649540", "1527988", "1514250", "1651977", "1523869", "1614880", "1640313", "1637344", "1584121", "1659620", "1548999", "1667432", "1544662", "1526241", "1552213", "1480861", "1584083", "1591238", "1608088", "1541535", "1509259", "1482795", "1631612", "1544180", "1490445", "1485056", "1473652", "1619620", "1658310", "1641974", "1612464", "1509421", "1610199", "1473116", "1643141", "1489574", "1475397", "1666491", "1485067", "1555113", "1658321", "1618896", "1593365", "1556041", "1541442", "1574880", "1531664", "1643137", "1643546", "1568596"], "answers": ["yes"]} | |
| {"q_id": "science-forum-test-1299", "query": "every subsequence of $x_n$ has a further subsequence which converges to $x$. then the sequence $x_n$ converges to $x$.", "doc_id": ["235431", "1361558", "515942", "168954", "924028", "11733", "467201", "1305090", "459052", "465585", "908447", "287504", "815787", "1065709", "186967", "1375631", "890739", "894682", "1427828", "553874", "623966", "1155478", "27222", "195005", "310792", "629542", "930404", "898914", "1421515", "65570", "1379708", "1011485", "1421208", "828596", "9764", "1272443", "1422397", "1311422", "1280511", "149267", "670692", "145593", "357359", "168371", "807121", "161331", "947091"], "answers": ["TRUE"]} | |
| {"q_id": "science-forum-test-52", "query": "is $\\pi^2 \\approx g$ a coincidence?", "doc_id": ["1559644", "1559658"], "answers": ["pure coincidence"]} | |
| {"q_id": "science-search-test-378", "query": "is time orthogonal to space?", "doc_id": ["1503808", "1524030", "146855", "1529761", "1665282", "1623141", "1551336", "1511205", "1542160", "1500825", "1615203", "1647294", "1576987", "1475801", "467772", "1529450", "1548373", "1534545", "1618070", "1632185"], "answers": ["Time is orthogonal to space"]} | |
| {"q_id": "science-forum-test-653", "query": "why is it important for a matrix to be square?", "doc_id": ["1037771", "172320", "86755"], "answers": ["powers of a matrix only make sense if the matrix is square"]} | |
| {"q_id": "science-forum-test-53", "query": "why does a mirror split my laser beam?", "doc_id": ["1549273", "1631058", "1549288"], "answers": ["You are getting reflections from the front (glass surface) and back (mirrored) surface, including (multiple) internal reflections"]} | |
| {"q_id": "science-search-test-325", "query": "is torque measured in joules?", "doc_id": ["1483789", "1611741", "1566252", "1517629", "1483792", "1640239", "1552607", "1658423", "1600556", "1643260", "1500728", "1650987", "1559155", "1597134", "1640173", "1518245"], "answers": ["The units for torque, as you stated, are Newton-meters", "Joules are generally not appropriate units for torque"]} | |
| {"q_id": "science-forum-test-861", "query": "is $0! = 1$ because there is only one way to do nothing?", "doc_id": ["785605", "13842", "800246", "562551", "226176", "722678", "325328", "14092", "710876", "1439015", "772021", "625666", "573718", "109522", "308100", "1341017", "711114", "710905", "494153", "488733", "711186", "1178102", "710938", "1430997"], "answers": ["Yes"]} | |
| {"q_id": "science-forum-test-200", "query": "why does a full moon seem uniformly bright from earth, shouldnt it be dimmer at the border?", "doc_id": ["1563675", "1563657", "1563663", "1535679", "1469550", "1587428"], "answers": ["Surface roughness is the main reason the edges are not as dim as the sphere model predicts"]} | |
| {"q_id": "science-search-test-348", "query": "what is the difference between an electron neutrino and a muon neutrino?", "doc_id": ["1486328", "1628574", "1639621", "1520615", "1495209", "1651623", "1600350", "1593415"], "answers": ["muon neutrinos scattering on protons created muons, whereas electron neutrinos created electrons"]} | |
| {"q_id": "science-forum-test-491", "query": "apparently sometimes $1/2 < 1/4$?", "doc_id": ["835369", "835111"], "answers": ["$1/2$ is NOT smaller than $1/4$"]} | |
| {"q_id": "science-forum-test-1998", "query": "is there any evidence that sexual selection may lead to extinction of species?", "doc_id": ["1668348", "1671193", "1689093", "1686249", "1688793", "1678381", "1670551", "1692819"], "answers": ["sexual selection increased risks of local extinction"]} | |
| {"q_id": "science-forum-test-77", "query": "does a particle exert force on itself?", "doc_id": ["1617787", "1615990", "1592605", "1489153", "1656351", "1664390", "1563371", "1624744", "1615895", "1487198", "1626160", "1619194", "1615920", "1594434", "1628149"], "answers": ["in quantum mechanics, we find that particles do indeed interact with themselves", "a real self-interaction is excluded by the principles of Newtonian mechanics"]} | |
| {"q_id": "science-search-test-594", "query": "do sieve tubes have mitochondria?", "doc_id": ["1672021", "1692752", "1685608"], "answers": ["retain mitochondria"]} | |
| {"q_id": "science-search-test-555", "query": "natural selection occurs at which level individual or population?", "doc_id": ["1688834", "1690119", "1690130", "1681602", "1687073", "1675996", "1672760", "1675044", "1675043", "1677712", "1669967", "1679345", "1686210", "1670099", "1673841", "1675104", "1681179", "1680206", "1685845", "1685908", "1681692", "1685166", "1682961", "1679594", "1687462", "1690173", "1671129", "1670329"], "answers": ["population level"]} | |
| {"q_id": "science-search-test-107", "query": "a is 25 percent more efficient than b?", "doc_id": ["747978"], "answers": ["A is 25% more efficient than B"]} | |
| {"q_id": "science-search-test-425", "query": "do any gases conduct electricity?", "doc_id": ["1500549", "1594254", "1520603", "1544098", "1597266", "1547528", "1599470", "1525424", "1607638", "1484117", "1587812", "1546645", "1608462", "1600282", "1501354", "1582301", "1548285", "1486981", "1647970", "1472545", "1584285", "1498203", "1498768", "1496723", "1658411", "1544105", "1657500", "1533106"], "answers": ["Gases do conduct electricity"]} | |
| {"q_id": "science-forum-test-1229", "query": "what is the largest eigenvalue of the following matrix?", "doc_id": ["977419", "977001", "985696", "977479", "977627", "977161"], "answers": ["21"]} | |
| {"q_id": "science-forum-test-552", "query": "what is category theory useful for?", "doc_id": ["149114", "149127", "412824", "1052452", "644433", "1480522", "4946", "350520", "490055", "852106", "638892", "2350", "85342", "941109", "907603", "143986", "597533", "44328", "841257", "4008", "641905", "924902", "1467748", "1302936", "259411", "1042142", "1087656", "427151", "45760", "1087684", "135282", "1433915", "15836", "85341", "58864", "1245893"], "answers": ["to talk about structures recurring throughout other disciplines of mathematics"]} | |
| {"q_id": "science-forum-test-175", "query": "why does a remote car key work when held to your head/body?", "doc_id": ["1505995", "1506621", "1468633"], "answers": ["your body is reasonably conductive", "it can couple to RF sources capacitively"]} | |
| {"q_id": "science-forum-test-783", "query": "given a die, what is the probability that the second roll of a die will be less than the first roll?", "doc_id": ["137089", "52099", "790118", "52071", "52033", "52030"], "answers": ["5/12"]} | |
| {"q_id": "science-forum-test-298", "query": "how discontinuous can a derivative be?", "doc_id": ["275766", "198415", "300026", "948053", "34805", "918974", "87727", "57636"], "answers": ["$D$ can be dense in $\\mathbb R$. $D$ can have cardinality $c$ in every interval", "$D$ can have positive measure in every interval", "$D$ can have full measure in every interval"]} | |
| {"q_id": "science-forum-test-1643", "query": "understanding g\u00f6dels incompleteness theorem", "doc_id": ["9154", "1403631", "540553", "1501138", "417438", "425104", "72989", "1461669", "104213", "901272", "1338906", "591221", "526050", "91084", "85424", "279876", "102773", "19506", "795648", "9166", "544519", "351047", "1473230", "221445", "850658", "1064275", "280277", "9152", "868096", "9153", "1333844", "1464738", "204266", "217708", "1033699", "446125", "1338779", "343280", "410142", "530706", "929961", "1264338", "639269"], "answers": ["any effectively generated formal system which is sufficiently powerful is either inconsistent or incomplete"]} | |
| {"q_id": "science-forum-test-718", "query": "are all algebraic integers with absolute value 1 roots of unity?", "doc_id": ["2566", "2579", "1177565", "1169377", "152339", "553873", "1412555", "2571", "767699", "274809", "19525", "7579", "413902", "31662", "495400", "36089", "63912", "567083", "512013", "875568", "594257", "88307"], "answers": ["No", "no"]} | |
| {"q_id": "science-search-test-124", "query": "are sinx and cosx linearly independent?", "doc_id": ["130603", "1205786", "711317", "1098277", "382963", "669509", "204524", "591190", "541622", "677403", "130611", "1192666", "205951", "90201"], "answers": ["$\\sin x$ and $\\cos x$ are linearly independent on any interval $I$"]} | |
| {"q_id": "science-forum-test-1873", "query": "development of the idea of the determinant", "doc_id": ["55482", "114198", "757810", "449972", "486402"], "answers": ["as a property which tests for the existence of unique solutions for a system of linear equations"]} | |
| {"q_id": "science-search-test-554", "query": "what instrument is used to measure optical density?", "doc_id": ["1677065", "1545400", "1689252", "1687315", "1676527", "1674800", "1671179", "1692356"], "answers": ["spectrophotometer"]} | |
| {"q_id": "science-forum-test-1011", "query": "is there a function with a removable discontinuity at every point?", "doc_id": ["2252", "813100", "136067"], "answers": ["No"]} | |
| {"q_id": "science-forum-test-1812", "query": "how far can one see over the ocean?", "doc_id": ["382761"], "answers": ["5 nautical miles of visibility (1nm = 1852m)"]} | |
| {"q_id": "science-forum-test-4", "query": "did the big bang happen at a point?", "doc_id": ["1478328", "1517817", "1572050", "1501251", "1652139", "1545038", "1543156", "1583794", "1529560", "1512959", "1641455", "1517043", "1468446", "1522253", "1544534", "1517821", "1475741", "1469562", "1468350", "1641580", "1552539", "1481871", "1567274", "1564354", "1468122", "1483830", "1495606", "1542370", "1497825", "1507400", "1473405", "1601243"], "answers": ["there was a \"beginning point singularity", "representing universe in 4D then big bang had happened at a point", "in 3D the big bang should have happened in every point of the universe"]} | |
| {"q_id": "science-search-test-593", "query": "is a cell wall an organelle?", "doc_id": ["1687936", "1681565", "1681559", "1668944", "1685713"], "answers": ["isn't an organelle"]} | |
| {"q_id": "science-search-test-55", "query": "is gcd an injective function?", "doc_id": ["74926", "529834", "420732", "420734", "1326367", "1399151", "552442", "552494", "736908", "514656", "244821", "552434", "716416", "149469", "460709", "43725", "369240", "1338868", "1371571", "786122"], "answers": ["it is not injective"]} | |
| {"q_id": "science-search-test-511", "query": "a body is moving with a constant velocity?", "doc_id": ["1546101", "1509624", "1506387", "1495510", "1654639", "1561063", "1643724", "1523790", "1624601", "1539685", "1527540", "1580534", "1657715", "1661660", "1627682", "1653006", "1558581", "1558003", "1656145", "1587853", "1585590"], "answers": ["the total of all the forces applied to it is zero"]} | |
| {"q_id": "science-forum-test-589", "query": "how were old-school mathematics graphics created?", "doc_id": ["362469", "362258", "370700", "362115"], "answers": ["drawn by hand"]} | |
| {"q_id": "science-forum-test-1091", "query": "is it bad form to write mysterious proofs without explaining what one intends to do?", "doc_id": ["46855", "1046246", "1011365", "444976", "1101014", "664222", "788562", "57501", "789004", "1024628", "914705", "497601", "612897", "49592", "25077", "788824", "1390286", "463661", "1405967", "1001303", "77868", "315011", "99105", "236319", "1361082", "1060782"], "answers": ["If your proof is obscure, then you have failed to communicate"]} | |
| {"q_id": "science-forum-test-1598", "query": "is it possible that a counter-example exists but it cannot be found", "doc_id": ["328396", "786938", "886702", "328636", "329092", "1110783", "344526", "63137", "1260698", "1123928", "181606", "110915", "780519", "1248305", "1422110", "1352792", "740671", "786120", "445218", "1248307", "1216831", "697178", "1166562", "259253", "715376", "1406684", "963032", "43671", "1496496", "689365", "99719", "517966", "446125", "329133", "896019", "1201183", "1086020", "398136", "979653", "325", "1207833", "1629822", "445215", "306515", "329688", "549110", "1104941", "632815", "1147861", "964049", "281810", "1445792", "1373292", "132593", "1584178", "1568867", "328392", "1550734", "313747", "201406", "599399", "328646", "1334541", "882748", "476793", "814578"], "answers": ["Yes"]} | |
| {"q_id": "science-forum-test-1443", "query": "is there such a thing as proof by example (not counter example)", "doc_id": ["160419", "160189", "160548", "182460", "1201183", "160187", "113721", "160252"], "answers": ["there is such a thing as a proof by example", "any proofs of existential claims will qualify as a proof by example"]} | |
| {"q_id": "science-forum-test-1354", "query": "what is the standard basis for fields of complex numbers?", "doc_id": ["1113268", "63130", "570964", "816899", "85901", "737284", "921341", "140450", "1387232", "1411579"], "answers": ["$\\left\\lbrace(1,0),\\, (0,1)\\right\\rbrace$"]} | |
| {"q_id": "science-forum-test-1603", "query": "is $6.12345678910111213141516171819202122\\ldots$ transcendental?", "doc_id": ["29062", "338077", "13776", "3840"], "answers": ["This is a transcendental number"]} | |
| {"q_id": "science-forum-test-832", "query": "i roll a die repeatedly until i get 6, and then count the number of 3s i got. whats my expected number of 3s?", "doc_id": ["566574", "566074", "565165", "565209", "566137", "565167", "565163", "566623", "565169", "566085", "566416"], "answers": ["1"]} | |
| {"q_id": "science-search-test-576", "query": "are both eyes exactly the same?", "doc_id": ["1639711", "1677089", "1545570", "1687467", "1680134", "1444551", "1531988", "1465875", "1681144", "1486876", "1497222", "1691572", "1179625", "1671425", "1601348", "1686309", "1579120", "1565146"], "answers": ["No"]} | |
| {"q_id": "science-search-test-247", "query": "can disjoint events be independent?", "doc_id": ["1393764", "763787", "499127", "622738", "394496", "801496", "929230", "1355467", "705585", "546489", "1355498", "1288091", "107960", "1137669", "1442332", "211308", "1138592", "1433108", "1448262", "705588", "1151763", "462651", "355856", "153987", "1347067", "1347068", "790812"], "answers": ["Disjoint events aren't independent, unless one event is impossible, which makes the two events trivially independent"]} | |
| {"q_id": "science-forum-test-1992", "query": "why do humans not produce vitamin c like other mammals?", "doc_id": ["1668427", "1693828", "1674937", "1673046"], "answers": ["due to a mutation in the GULO (gulonolactone oxidase) gene"]} | |
| {"q_id": "science-search-test-129", "query": "are all finite sets closed?", "doc_id": ["1172275", "610669", "1250882", "1299190", "1159367", "978876", "1217016", "654183", "856140", "298993", "155420", "501241", "109832", "1063576", "1088529", "112360", "935847", "96554", "1240710", "896746", "786610", "1236369", "175865", "1255487"], "answers": ["every finite set is closed in a metric space"]} | |
| {"q_id": "science-search-test-484", "query": "what is the physical significance of electric dipole moment?", "doc_id": ["1602492", "1602494", "1620947", "1630938", "1660552", "1602316", "1663977", "1565099", "1609915", "1470862", "1507722", "1656212", "1574211", "1544903", "1593692", "1471064", "1488717", "1648264", "1660316"], "answers": ["it gives a measure of the polarity/polarization of a net neutral system"]} | |
| {"q_id": "science-search-test-564", "query": "do all prokaryotes have introns?", "doc_id": ["1670140", "1669450", "1681292", "1689079", "1672991", "1669059", "1669029", "1670602", "1672992", "1673629"], "answers": ["Prokaryotes can't have introns"]} | |
| {"q_id": "science-forum-test-1502", "query": "explanation on arg min", "doc_id": ["584545", "861403", "421265", "818854", "714477", "1280045", "111914", "1069119", "489626", "499477", "1464131", "193509", "1401286", "569349"], "answers": ["$\\arg\\min _{x} f(x)$ is the value of $x$ for which $f(x)$ attains its minimum", "$arg min$ (or $arg max$) return the input for minimum (or maximum) output"]} | |
| {"q_id": "science-forum-test-348", "query": "meaning of rays in polar plot of prime numbers", "doc_id": ["376408"], "answers": ["Each ray thus corresponds to an arithmetic progression $a\\pmod{710}$"]} | |
| {"q_id": "science-search-test-102", "query": "are all isosceles triangles equilateral?", "doc_id": ["413797", "1243090", "1359941", "1452537", "1338980", "1381714", "13413", "1351297", "793008", "1033575", "1046146", "811335", "933791"], "answers": ["every equilateral triangle is isosceles, but not every isosceles triangle is equilateral"]} | |
| {"q_id": "science-forum-test-626", "query": "is infinity a number?", "doc_id": ["19437", "19472", "90870", "1116637", "1100322", "26173", "251985", "971219", "424576", "415630", "1240786", "126201", "1142301", "115434", "19406", "121925", "1659548", "294057", "1276809", "326759", "1185849", "1205320", "1332076", "866521", "727419", "15720", "700587", "584599", "326778", "825527", "1158927", "1175241", "1173859", "1381187", "327977", "1368484", "377833", "707486", "47206", "1396499", "47203", "707497", "727588", "91813", "980643", "927473", "1028907", "1080182", "1203403", "368069"], "answers": ["no", "not a number"]} | |
| {"q_id": "science-forum-test-320", "query": "why are rings called rings?", "doc_id": ["32605", "37530"], "answers": ["derived from Hilbert's term \"Zahlring\" (number ring"]} | |
| {"q_id": "science-forum-test-665", "query": "why do we still do symbolic math?", "doc_id": ["374884", "374764", "652549", "374759", "376912", "1539811", "374846", "374752"], "answers": ["theory behind numerical estimates is based on 'symbolic' math"]} | |
| {"q_id": "science-search-test-40", "query": "are all fields vector spaces?", "doc_id": ["65395", "403431", "1147561", "254642", "993048", "1416093", "836945", "821283", "406266", "375679", "72248", "66782", "591871", "406267", "565527", "139957", "86752", "489356", "771849", "376932", "1411002"], "answers": ["a field is always a vector space over itself"]} | |
| {"q_id": "science-forum-test-95", "query": "why do electrons, according to my textbook, exist forever?", "doc_id": ["1616532", "1645425", "1593975", "1531285", "1625739", "1568340"], "answers": ["Electrons are the lightest negatively charged particle and therefore cannot decay into lighter particles"]} | |
| {"q_id": "science-forum-test-1297", "query": "there are 4 cups of liquid. three are water and one is poison. if you were to drink 3 of the 4 cups, what is the probability of being poisoned?", "doc_id": ["1027475", "1026983", "1027408", "1027080", "1027002", "1028017", "1027469", "1027362", "1027788", "1027786"], "answers": ["3/4", "$1-\\frac{3!}{4!} = \\frac34$", "25%", "75%", "1/2"]} | |
| {"q_id": "science-forum-test-152", "query": "why does hot water clean better than cold water?", "doc_id": ["1510739", "1676230", "1510740"], "answers": ["hot water melts oil/grease/etc while cold water would solidify it", "hot water is a better solvent than cold water"]} | |
| {"q_id": "science-search-test-137", "query": "are sets closed under addition?", "doc_id": ["139462", "270177", "313645", "1223019", "1175619", "313644", "391374", "1162248", "376498", "538549", "313646", "111794", "1239154"], "answers": ["not closed under addition", "not closed under this kind of addition"]} | |
| {"q_id": "science-forum-test-1143", "query": "why should we prove obvious things?", "doc_id": ["329918", "329858", "329854"], "answers": ["sometimes things that should be \"obvious\" turn out to be completely false", "something that seems obvious may be wrong"]} | |
| {"q_id": "science-forum-test-1746", "query": "difference between bijection and isomorphism?", "doc_id": ["262927", "1270280", "553882", "779100", "77233", "151867", "1275071", "178928", "1293382", "452223", "864933", "359906", "618877", "503888", "537503", "1419392", "312184", "298848", "767870", "438744", "519106", "28838", "731484", "74599", "28816", "1316289", "298856", "74598", "1361056", "109935", "78406", "1419258", "1260114", "451104", "1073887", "741359", "438743", "264084", "514940"], "answers": ["an isomorphism (in the context of algebra) needs to map between the operations involved, while a bijection doesn't"]} | |
| {"q_id": "science-forum-test-1891", "query": "a conjectured closed form of $\\int\\limits_0^\\infty\\frac{x-1}{\\sqrt{2^x-1}\\ \\ln\\left(2^x-1\\right)}dx$", "doc_id": ["240164"], "answers": ["$$ \\frac{1}{2\\log^2{2}}\\int_{0}^{\\infty} \\frac{du}{\\cosh{(u/2)}} = \\frac{\\pi}{2 \\log^2{2}} $$ as correctly conjectured"]} | |
| {"q_id": "science-search-test-309", "query": "what is the greatest common factor of all four-digit palindromes?", "doc_id": ["265374", "265380", "851567"], "answers": ["$11$"]} | |
| {"q_id": "science-forum-test-1392", "query": "how does a calculator calculate the sine, cosine, tangent using just a number?", "doc_id": ["401206", "694212", "1286459", "185885", "1376233", "240476", "241076", "137532", "1051528", "796814", "1095234", "1426222", "609358", "712219", "609409"], "answers": ["Taylor Series for $\\sin / \\cos$ or the CORDIC algorithm"]} | |
| {"q_id": "science-forum-test-508", "query": "what is the difference between a point and a vector?", "doc_id": ["1624405", "752261", "1661857", "1624780", "1665370", "1075924", "1536432", "1580540", "69101", "1547573", "93471", "1661697", "872561", "1648703", "287854", "288352", "1663192", "320123", "194429", "1667913", "24490", "1183010", "619241", "879134", "1655969", "1494058", "287824", "818726", "738275", "1513694", "1590170", "480491", "287868", "654856", "695032", "93973", "287823", "1340359"], "answers": ["Points describe locations while vectors describe directions", "Points are locations in space. Vectors are displacements in space"]} | |
| {"q_id": "science-forum-test-1912", "query": "the generating function for the fibonacci numbers", "doc_id": ["161140", "1031900", "785346", "376410", "1149621", "1182631", "682780", "847512", "562477", "161145", "161143", "497293", "381673", "1044488", "336305", "290368", "1219093", "371768", "889245", "161528", "291795", "1411039", "631540", "1386253", "982187", "1200717", "353474", "377401", "1411030", "245353", "69527"], "answers": ["$\\dfrac{1}{1-(z+z^2)}=1+(z+z^2)+(z+z^2)^2....$", "$$ \\sum_{n=0}^\\infty F_nz^n = \\frac{1}{1-(z+z^2)} $$", "$$F(x)=\\frac{1}{1-x-x^2}$$"]} | |
| {"q_id": "science-forum-test-1395", "query": "probability that random moves in the game 2048 will win", "doc_id": ["319036", "1459764", "1205421", "318157", "716132", "335279"], "answers": ["essentially zero"]} | |
| {"q_id": "science-forum-test-502", "query": "how to put 9 pigs into 4 pens so that there are an odd number of pigs in each pen?", "doc_id": ["253295", "253293"], "answers": ["It's not possible", "The problem as stated is impossible under the usual interpretation"]} | |
| {"q_id": "science-search-test-538", "query": "is length an intensive property?", "doc_id": ["1609867", "1518087", "1505025", "1515477", "1472482", "1589396", "1576699", "1614910", "1516546", "1688417", "1643908", "1561028", "47203", "1590977", "1517419", "779462", "1663633"], "answers": ["Length is an extensive property"]} | |
| {"q_id": "science-search-test-49", "query": "do irrational roots come in pairs?", "doc_id": ["1117891", "647961", "994703", "1213128", "783138", "1461126", "21636", "431237", "428733", "840672", "674690", "349189", "1146047", "270164", "970153", "1079785", "394843", "1012184", "1014909", "866873", "66250", "178930", "846002", "269126", "1225881", "173092", "1122792", "80290", "623227", "1146621"], "answers": ["The complex roots of a polynomial with real coefficients always come in conjugate pairs"]} | |
| {"q_id": "science-search-test-297", "query": "a and b are mutually exclusive are they independent?", "doc_id": ["462651", "396636", "396638", "977911", "892995", "1120893", "734839", "356519", "1355662", "213795", "509515", "1081633", "1352317", "1012994", "158229", "734846", "1355671", "513400", "730875", "1061195", "411191", "193622", "97374", "28965", "924752", "1431489", "1007637", "1118187", "319185", "948023", "647910", "408134", "936736"], "answers": ["mutually exclusive events are not independent", "if the two events are mutually exclusive, they can not be independent", "a mutually exclusive pair of nontrivial events are also necessarily dependent events"]} | |
| {"q_id": "science-search-test-98", "query": "if events a b and c are disjoint then they are independent?", "doc_id": ["705588", "705585", "107960", "674209", "1147254", "1442332", "1137669", "913984", "462651", "1393764", "12367", "1288091", "1012994", "1347068", "1347067", "705600", "394496", "593658", "622738", "1355498", "1340218", "1036860", "1151763", "1412333", "1369988", "193617", "540180", "499127", "396636", "790812", "319185", "618698", "546489", "583024", "91457", "1355467", "153987", "1269810", "1448262", "1433108", "904463"], "answers": ["Two disjoint events can never be independent", "Disjoint events aren't independent"]} | |
| {"q_id": "science-search-test-164", "query": "is cdf the integral of pdf?", "doc_id": ["521086", "521085", "741282", "120521", "698522", "412349", "307240", "823193", "934477", "1220777", "763753", "693189", "1095529", "1158950", "176654", "47015", "619358", "515256", "1177714", "586416", "860780", "426348", "104448", "863817", "968776", "438446", "177444", "1437926", "669998", "107518", "1387064", "671470", "99575", "763750"], "answers": ["Yes", "yes"]} | |
| {"q_id": "science-forum-test-1619", "query": "what\u2019s the difference between analytical and numerical approaches to problems?", "doc_id": ["394659", "394641", "1609992", "1582827", "1501392", "733286", "1623264", "384952", "1519122", "394665", "642376", "568761", "1544925", "389241", "479525", "1596752", "1638645", "1545616", "409853", "562366", "1625534", "1176389", "649991", "1202451", "228694", "986662", "586459", "875554", "1102935"], "answers": ["Analytical is exact; numerical is approximate", "Analytical solutions can be obtained exactly with pencil and paper; Numerical solutions cannot be obtained exactly"]} | |
| {"q_id": "science-forum-test-225", "query": "why does a rubber band become a lighter color when stretched?", "doc_id": ["1634293", "1634631", "1634328", "1634323"], "answers": ["the amount of absorption per unit area decreases, and the band become lighter in color"]} | |
| {"q_id": "science-search-test-179", "query": "are upper triangular matrices invertible?", "doc_id": ["802552", "320740", "655274", "1456419", "886682", "794474", "738616", "160425", "925904", "655275", "1052514", "148658", "419604", "1380716"], "answers": ["only if it has no zeros on the main diagonal"]} | |
| {"q_id": "science-search-test-156", "query": "are all differentiable functions integrable?", "doc_id": ["64950", "1255660", "322442", "185872", "64948", "862898", "498107", "64953", "946174"], "answers": ["If you are thinking Riemann integrable, Then every differentiable function is continuous and then integrable"]} | |
| {"q_id": "science-forum-test-230", "query": "what was the major discovery on gravitational waves made march 17th, 2014, in the bicep2 experiment?", "doc_id": ["1506765", "1506674", "1506689", "1548343", "1574960", "1506890", "1512232", "1634155", "1512409", "1550286", "1511814", "1506790", "1506685"], "answers": ["gravitational waves from inflation during the early universe are being indirectly observed", "the detection of inflationary gravitational waves in the B-mode power spectrum", "It is the first indirect observation of gravitational waves produced by inflation"]} | |
| {"q_id": "science-forum-test-826", "query": "is the vector cross product only defined for 3d?", "doc_id": ["1533058", "486634", "745681", "943099", "1551805"], "answers": ["Yes"]} | |
| {"q_id": "science-forum-test-1544", "query": "number of monic irreducible polynomials of prime degree $p$ over finite fields", "doc_id": ["21753", "1390024", "21791"], "answers": ["Gauss\u2019s formula $$\\frac{1}{n}\\sum\\limits_{d \\mid n} \\ \\mu(n/d) \\cdot q^{d}$$", "$\\displaystyle \\frac{q^{p}-q}{p}$"]} | |
| {"q_id": "science-search-test-101", "query": "can cosh x be zero?", "doc_id": ["565267", "1454338", "1370066", "844200", "801371", "70099", "1231577", "1399136", "800643", "674509", "428162", "1364444", "610521", "816038", "264151", "1109629", "1254124", "800657", "169481", "1383598", "528401", "39837", "576649", "1325455", "655279", "424864", "549317", "157748"], "answers": ["$\\cosh x$ is always non-zero"]} | |
| {"q_id": "science-forum-test-346", "query": "why can a venn diagram for $4+$ sets not be constructed using circles?", "doc_id": ["354121", "929", "663143", "959249"], "answers": ["a graph created in such a way from a 4-set Venn diagram cannot be planar\u2014a contradiction"]} | |
| {"q_id": "science-forum-test-560", "query": "what remains in a students mind", "doc_id": ["231324", "80509", "877402"], "answers": ["a vague outline of the terminology and theorems"]} | |
| {"q_id": "science-search-test-608", "query": "amla is citrus fruit or not?", "doc_id": ["1684493", "1679422"], "answers": ["No"]} | |
| {"q_id": "science-forum-test-2000", "query": "why does it hurt the next day after doing significant exercise?", "doc_id": ["1685305", "1671041", "1676950", "1664563", "1670439", "1675791", "1671939"], "answers": ["due to microtrauma or micro ruptures in the muscle fibers"]} | |
| {"q_id": "science-forum-test-23", "query": "why do we bend a book to keep it straight?", "doc_id": ["1614818", "1601828", "1471166"], "answers": ["curving the paper effectively multiplies it's stiffness by several orders"]} | |
| {"q_id": "science-forum-test-104", "query": "is it possible to start fire using moonlight?", "doc_id": ["1545486", "1661107", "1655063", "1689435", "1589283", "1501618", "1565034", "1576311", "1612611", "1578345", "1548424", "1561756", "1557148", "1518919", "1581305", "1560790"], "answers": ["no"]} | |
| {"q_id": "science-forum-test-59", "query": "is temperature a lorentz invariant in relativity?", "doc_id": ["1568248", "1619645", "1625079"], "answers": ["There is no universal relativistic temperature transformation of the form $T' = T(v)$"]} | |
| {"q_id": "science-forum-test-664", "query": "why, historically, do we multiply matrices as we do?", "doc_id": ["843203", "23006", "1124530", "1253392", "783701", "765100", "1179913", "79279", "156610", "775746", "205497", "961050", "871054", "13392", "365302", "131691", "1028079", "1062978", "1209321", "175421", "1278256", "961026", "1151928", "1045175"], "answers": ["symbolic way of substituting one linear change of variables into another one"]} | |
| {"q_id": "science-forum-test-1067", "query": "what is the meaning of the third derivative of a function at a point", "doc_id": ["1490404", "229257", "132595", "8318", "8317"], "answers": ["jerk"]} | |
| {"q_id": "science-forum-test-1816", "query": "is there a purely algebraic proof of the fundamental theorem of algebra?", "doc_id": ["749008", "531446", "165184", "821124", "83753", "114124", "1457826", "304364"], "answers": ["No"]} | |
| {"q_id": "science-forum-test-1728", "query": "how to tell if a set of vectors spans a space?", "doc_id": ["1115959", "741874", "29832", "1260886", "694735", "62410", "368105", "832819", "1311886", "1152393", "29836", "365463"], "answers": ["set up a matrix and use Gaussian elimination"]} | |
| {"q_id": "science-search-test-112", "query": "can all nfa be converted to dfa?", "doc_id": ["109160", "239303", "490828", "29412", "1103997", "1054848", "1429775", "393018", "404487", "273757", "748128", "285486", "12506", "396823", "61365", "47484", "255874", "1311949", "393026", "150624", "641218", "596955"], "answers": ["every NFA can be converted to an equivalent DFA", "DFAs, NFAs and regular expressions are all equivalent"]} | |
| {"q_id": "science-search-test-609", "query": "can oxaloacetate cross mitochondrial membrane?", "doc_id": ["1683653", "1681780", "1680687"], "answers": ["cannot cross"]} | |
| {"q_id": "science-forum-test-596", "query": "what is the difference between independent and mutually exclusive events?", "doc_id": ["396636", "396638", "129251", "1120893", "1431483", "734839", "356519", "1355662", "462651", "854147", "538253", "509515", "63016", "339379", "158229", "1355671", "734846", "730875", "193619", "411191", "1061195", "193622", "1340218", "7527", "1091744", "1007637", "319185", "948023", "647910", "513401", "1118189", "286495", "1431489", "540180"], "answers": ["mutually exclusive events are not independent, and independent events cannot be mutually exclusive"]} | |
| {"q_id": "science-forum-test-234", "query": "is $\\frac{\\textrm{d}y}{\\textrm{d}x}$ not a ratio?", "doc_id": ["11701", "1417757", "1450179", "274935", "253206", "1258642", "41529", "942085", "1061087", "286590", "859022", "1389102", "261469", "1450082", "1081433", "972503", "1581281", "1125868", "955308", "764123", "231765", "1323864", "450262", "940183", "13104", "814102", "733432", "222001", "493316", "188356", "418134", "853842", "192418"], "answers": ["It is not a ratio"]} | |
| {"q_id": "science-search-test-185", "query": "sets are important in mathematics?", "doc_id": ["1475745", "256239", "1085364", "246051", "138051", "442896", "310016", "170872", "524322", "1185316", "1480522", "177561", "246114", "373580"], "answers": ["every field of mathematics uses or refers to sets"]} | |
| {"q_id": "science-forum-test-201", "query": "why is information indestructible?", "doc_id": ["1593560", "1579241", "1587934", "1495627", "1476327", "776391", "1495683", "447605", "1594739", "1673371", "1610296", "1534779", "1509252", "1496290", "1515972", "1652517", "1527338", "1496864", "1471275", "1649301", "1620868"], "answers": ["physical laws are reversible and therefore it stands to reason that information cannot be lost"]} | |
| {"q_id": "science-forum-test-1954", "query": "are commutative c*-algebras really dual to locally compact hausdorff spaces?", "doc_id": ["244849", "97739", "145571", "129764", "1022920", "671504", "112587", "1179379", "4222", "1448014", "368228", "880155", "1119623", "602724", "295851", "1337991", "329052", "262572", "1236563", "23232", "137160", "232255", "514352", "126425", "732620", "233548", "1299083", "1185873"], "answers": ["we simply don't have this duality as stated", "the dual of this category is equivalent to the category of locally compact Hausdorff spaces"]} | |
| {"q_id": "science-search-test-97", "query": "how to prove that two vectors are perpendicular to each other?", "doc_id": ["295448", "189372", "189373", "99919", "456010", "1331434", "1315385", "1176422", "1576929", "1195298", "169084", "1375467", "1596278", "1344247", "1598876", "1140459", "1507854", "1552533", "528793", "1157180", "344473", "1637526", "1568578", "484634", "281442", "574691", "1136481", "971407", "545206", "813342", "770972", "620234", "1311032", "447715", "239784"], "answers": ["the scalar (dot) product between the two considered vectors must be zero $(0)$"]} | |
| {"q_id": "science-search-test-493", "query": "why are quantum gates reversible?", "doc_id": ["1558129", "1553526", "1560572", "1521649", "1571794", "1623076", "1525888", "1489562", "1484482", "1578944", "1605101", "1501886", "1485255", "589206", "1636205", "1554538"], "answers": ["because quantum mechanics is reversible"]} | |
| {"q_id": "science-forum-test-1554", "query": "is there a function whose antiderivative can be found but whose derivative cannot?", "doc_id": ["615279", "709165", "906500", "626358", "715415"], "answers": ["no"]} | |
| {"q_id": "science-forum-test-568", "query": "why does lhopitals rule fail in calculating $\\lim_{x \\to \\infty} \\frac{x}{x+\\sin(x)}$?", "doc_id": ["597655", "427735", "1124376", "663488", "45562", "270908", "366569", "604529", "663045", "858990", "1140554", "1445355", "924452", "663200", "663048", "946227", "411937", "449788", "601496", "215838", "884835", "544453", "394474", "527473"], "answers": ["limit of $f'$ over $g'$ doesn't exist", "l'Hopital requires existence of the limit of the ratio of the derivatives"]} | |
| {"q_id": "science-forum-test-1662", "query": "natural example of cosets", "doc_id": ["662161"], "answers": ["Hopf fibers"]} | |
| {"q_id": "science-forum-test-564", "query": "can an irrational number raised to an irrational power be rational?", "doc_id": ["229509", "602184", "388841", "385882", "774939", "1400502", "53687", "533802", "1027764", "154330", "388846", "100656", "1246666", "1146880", "1222819", "331239", "1412997"], "answers": ["Yes"]} | |
| {"q_id": "science-search-test-431", "query": "what is the difference between transparent and white?", "doc_id": ["1515328", "1527740", "1517125", "1480845", "1465947", "1510937", "1603799", "1510945", "1476119", "1589751"], "answers": ["So while transparent materials transmit light, white materials reflect it"]} | |
| {"q_id": "science-forum-test-26", "query": "why is googles quantum supremacy experiment impressive?", "doc_id": ["1625033", "1624969"], "answers": ["they have achieved sufficient experimental control over a circuit containing 53 qubits"]} | |
| {"q_id": "science-search-test-2", "query": "if vectors are linearly independent do they span?", "doc_id": ["368646", "1076588", "245858", "1286882", "903540", "1388598", "831433", "1351559", "146277", "1292834", "674143", "1368388", "996601", "432089", "1007265", "399437", "708729", "565554", "1398186", "390511", "202415", "1132810", "197666", "818831", "924065", "690444"], "answers": ["Any set of linearly independent vectors can be said to span a space"]} | |
| {"q_id": "science-search-test-211", "query": "are all injective functions invertible?", "doc_id": ["1263575", "659923", "535508", "123475", "358243", "571769", "357519", "574414", "923258", "574150", "717132", "1374978", "303264", "574151", "802726", "1054565", "1311616", "215410", "60296", "925738", "1178273", "1052714", "1166350", "518597", "209074", "1453976", "1275706", "493227", "803748", "90138", "419049", "1380810", "324651"], "answers": ["only if it is bijective"]} | |
| {"q_id": "science-forum-test-1773", "query": "why is the laplacian important in riemannian geometry?", "doc_id": ["1502456", "1492285", "7852", "783432", "1236632"], "answers": ["eigenvalues of the Laplacian provide invariants of the Riemannian manifold"]} | |
| {"q_id": "science-forum-test-224", "query": "why must a physical theory be mathematically self-consistent?", "doc_id": ["1467358", "461476", "1496982", "175381", "1663760", "1555620"], "answers": ["because we expect nature to stick to laws that can be described mathematically"]} | |
| {"q_id": "science-forum-test-1845", "query": "what is the implicit function theorem?", "doc_id": ["505175", "822268", "619902", "324224", "264111", "822258", "502748", "155457", "459408", "217216", "1246253", "1027705", "597608", "50611", "1183389", "1433690", "528475", "47670", "1101488", "323791", "784152", "557477", "652468", "161682", "23067", "1432959", "1494284", "472222", "871533", "300229", "1461004", "667634", "1016689", "950323", "1442012", "1392314", "25851", "1298055", "691112", "1413131"], "answers": ["a set defined by $$ S=\\{z\\in{\\Bbb R}^d|f(z)=0\\} $$ is locally a graph of some function"]} | |
| {"q_id": "science-search-test-459", "query": "why are rms values used?", "doc_id": ["1485083", "1485079", "1485078", "89421", "1486480", "1646852", "1655035", "799488", "596034", "1638554", "1598351", "1487158", "1518997", "1591934", "1603594", "1518999", "1638553", "1665413", "1573732", "1519014", "1585903", "1665411", "1573738", "1665420", "1548474", "1594026", "683261", "1473274", "1529289", "1560515"], "answers": ["using the RMS values makes the power easy to calculate", "They help to find the effective value of AC (voltage or current", "The rms value, not the peak value, is the equivalent DC value that gives the same average power"]} | |
| {"q_id": "science-forum-test-531", "query": "division by $0$", "doc_id": ["32546", "658134", "1062114", "754482", "99897", "117846", "1112450", "496111", "496321", "1380766", "114173", "496117", "295957", "1144349", "560818", "997040", "258374", "548044", "385439", "1162822", "200580", "713768", "303240", "1430228", "623492", "986940", "98829", "827284", "609693", "90033", "200581", "545915", "199190", "554707", "834557", "817416", "1062076", "894009", "1154891", "313841"], "answers": ["would mean multiplying by the reciprocal of 0. But 0 has no reciprocal", "division by 0 has no meaning in the set of real numbers"]} | |
| {"q_id": "science-search-test-568", "query": "what is the focal length of eye lens?", "doc_id": ["1686430"], "answers": ["18.5 mm"]} | |
| {"q_id": "science-forum-test-1152", "query": "is $ 0.112123123412345123456\\dots $ algebraic or transcendental?", "doc_id": ["929346", "214527", "13775", "450500", "1217041", "1119662", "5892", "783710", "1413492", "662596"], "answers": ["transcendental"]} | |
| {"q_id": "science-search-test-462", "query": "can coefficient of restitution be negative?", "doc_id": ["1604158", "864755", "1634772", "1635065", "1617448", "1493513", "1616390", "1513679", "1573694"], "answers": ["It can never be negative"]} | |
| {"q_id": "science-search-test-381", "query": "are electrons affected by gravity?", "doc_id": ["1635620", "1482099", "1571455", "1566169", "1643019", "1514309", "1615864", "1520766", "1576854", "1578188", "1611233", "1473725", "1492709", "1566168", "1634288", "1591166", "1488559", "1576853", "1607439", "1491726", "1519227", "1482678", "1544074", "1527025", "1575947"], "answers": ["everything is affected by gravity, just like everything is affected by inertial forces. This includes electrons"]} | |
| {"q_id": "science-forum-test-1684", "query": "what is difference between a ring and a field?", "doc_id": ["245754", "1416093", "262017", "5462", "1105783", "1031127", "1028985", "1129815", "565536", "699720", "1357354", "1386958", "63405", "1191202", "800426", "37", "1381067", "276448", "71531", "45", "1176596", "82850", "928922", "71811", "7178", "748535", "713768", "561603", "49894", "515599"], "answers": ["A field has multiplicative inverses, rings don't need to have that"]} | |
| {"q_id": "science-forum-test-184", "query": "why do scientists think that all the laws of physics that apply in our galaxy apply in other galaxies?", "doc_id": ["1647382", "1631767", "1645794", "1564352", "1477235", "1660796", "1598059", "1656716", "1633542", "1598001", "1510199", "1584149", "1490930", "1623254"], "answers": ["Because what we can observe doesn't differ according to distance from us"]} | |
| {"q_id": "science-search-test-94", "query": "how often will a calendar repeat itself?", "doc_id": ["329599", "246369"], "answers": ["after $28$ years"]} | |
| {"q_id": "science-search-test-399", "query": "why do noble gases behave ideally?", "doc_id": ["1579288", "1567659", "1638970", "1617075"], "answers": ["because they are monatomic and interact only by van der Waals forces"]} | |
| {"q_id": "science-forum-test-2002", "query": "are there organisms with fewer than 1000 neurons?", "doc_id": ["1684220", "1684217", "1684216", "1684287", "1675157", "1684244", "1688901", "1684245", "1679842", "1685126", "1670545", "1688146"], "answers": ["roundworm C. elegens, a nematode with only 302 neurons", "water snail with 8 distinct neurons"]} | |
| {"q_id": "science-search-test-397", "query": "what is the relationship between absolute pressure atmospheric pressure and gauge pressure?", "doc_id": ["1475767", "1475768", "1616001", "1647787", "1503233", "1475773", "1502088", "1688502", "1525439", "1596341", "1530167", "1475416", "1475769", "1507614", "1604934", "1571576", "1550802", "1553855"], "answers": ["Absolute pressure is zero-referenced against a perfect vacuum, so it is equal to gauge pressure plus atmospheric pressure", "Gauge pressure is zero-referenced against ambient air pressure, so it is equal to absolute pressure minus atmospheric"]} | |
| {"q_id": "science-search-test-526", "query": "what is non conservative field?", "doc_id": ["1540978", "1553829", "1638141", "1519274", "1655999", "1573929", "1536925", "1626904", "1489600", "1498683", "541579", "1611494", "1583229", "1519649", "1528275", "1522163", "1667981", "1597504", "1562076", "1527406", "1553314"], "answers": ["the integral along some path is not zero"]} | |
| {"q_id": "science-forum-test-968", "query": "what is bra and ket notation and how does it relate to hilbert spaces?", "doc_id": ["686164", "1566947", "1534937", "1512113", "1648169", "1560015", "1581260", "1488180", "1492332", "1490680", "1545814", "1546059", "920110", "1561726", "1632075", "1610406", "1612659", "1519445", "1563926", "1496079", "1400057", "1554870", "1523523", "1660012", "1660032", "1660028", "1547621", "1631328", "1648737", "686193", "1491628", "1624491", "705216", "1642283", "686207", "1516902"], "answers": ["kets are vectors on your Hilbert space, while bras are linear functionals of the kets"]} | |
| {"q_id": "science-forum-test-1339", "query": "why do we not have to prove definitions?", "doc_id": ["505014", "1461669", "556520", "1289260", "1069285", "1344435", "556511", "556514", "1203384", "556727", "1280598", "540251", "1392668", "556734", "556552", "506354", "1133346"], "answers": ["because the act of defining is to give a meaning to a particular concept"]} | |
| {"q_id": "science-forum-test-1519", "query": "is it possible to have three real numbers that have both their sum and product equal to $1$?", "doc_id": ["787487"], "answers": ["$\\left(-1,1-\\sqrt{2},1+\\sqrt{2}\\right)$ and $\\left(-1,1+\\sqrt{2},1-\\sqrt{2}\\right)$ are valid answers"]} | |
| {"q_id": "science-forum-test-1660", "query": "what is the fastest/most efficient algorithm for estimating eulers constant $\\gamma$?", "doc_id": ["66185", "88002"], "answers": ["Brent-McMillan algorithm"]} | |
| {"q_id": "science-search-test-585", "query": "how does bpg help at high altitudes?", "doc_id": ["1680900", "1678057", "1670667", "1688664", "1680904"], "answers": ["stabilizes the T- (taut; oxygen unbound) form of haemoglobin"]} | |
| {"q_id": "science-forum-test-506", "query": "why do we use the word scalar and not number in linear algebra?", "doc_id": ["1547608", "1071784", "706379", "706392", "1664378", "1190422", "1017106", "706383", "706899", "872561", "706593", "706662", "673667", "1662227", "1330537", "699720", "1598933", "1583335", "1518977"], "answers": ["number is an individual entity in a ring while a scalar is an operation on a vector space", "scalar\" was a convenient name to use for the real multipliers of the vector elements", "scalar conveys a notion of proportion and product, while number is more specialized, possibly involving ordering"]} | |
| {"q_id": "science-search-test-100", "query": "root 3 is irrational number?", "doc_id": ["494281", "735402", "1275633", "638463", "685155", "680637", "34252", "237691", "398194", "483458", "392948", "312875", "66886", "744581", "66926", "469371", "1412997", "1050937", "1199799", "978555", "942593", "72474", "808754", "476951", "230644"], "answers": ["The number $\\sqrt{3}$ is irrational"]} | |
| {"q_id": "science-forum-test-1286", "query": "can $18$ consecutive integers be separated into two groups,such that their product is equal?", "doc_id": ["285187", "285319", "1213444", "929624", "1411651", "1325338", "1251812", "990654", "731235", "1039410"], "answers": ["This is impossible"]} | |
| {"q_id": "science-forum-test-1427", "query": "are there any examples of non-computable real numbers?", "doc_id": ["459132", "30799", "709270", "30322", "305128", "196070", "1459820", "596035", "216111", "1452560", "1474129", "441446", "1350736", "1475745", "1361176", "52284", "295719", "33191", "1445792", "1135021", "148226", "508584", "1147313", "1339618", "1452544"], "answers": ["Chaitin's constant"]} | |
| {"q_id": "science-search-test-467", "query": "what is gravity like in the center of the earth?", "doc_id": ["1466981", "1530916", "1474819", "1642505", "1499456", "1522775", "1526951", "1603046", "1544979", "1526938", "1546434", "1644054", "1655618", "1649618", "1505164", "1562199", "1487952", "1526936", "1539099", "1593626", "1505153", "1470908"], "answers": ["the gravitational force is zero, but the gravitational well is at its deepest"]} | |
| {"q_id": "science-search-test-228", "query": "what is the difference between null space and kernel?", "doc_id": ["723821", "114747", "25089", "1200280", "861287", "1058908", "62937", "657177", "937278", "430435", "1234759", "114746", "1285561", "1406092", "1616145", "1141741", "477989", "76411"], "answers": ["nullspace when referring to a matrix and the word kernel when referring to an abstract linear transformation", "kernel\" is used more generally whereas \"nullspace\" is used essentially only in Linear Algebra"]} | |
| {"q_id": "science-forum-test-786", "query": "what seemingly innocuous results in mathematics require advanced proofs?", "doc_id": ["899727"], "answers": ["Jordan Curve Theorem"]} | |
| {"q_id": "science-search-test-393", "query": "does friction always do negative work?", "doc_id": ["1552116"], "answers": ["the work friction does is always negative"]} | |
| {"q_id": "science-forum-test-2016", "query": "why does cracking a joint make noise?", "doc_id": ["1674526", "1677617", "1470554", "1621965", "1669354"], "answers": ["rapid collapsing of cavities inside the joint", "breaking of intra-articular adhesions", "caused by the formation of a gas cavity in synovial fluid of the joints"]} | |
| {"q_id": "science-search-test-475", "query": "can gravity waves travel faster than light?", "doc_id": ["1487192", "1561886", "1504894", "1547896", "1660147", "1661759", "1635743", "1573111", "1597250", "1490987", "1650938", "1469412", "1661834", "1477536", "1610392", "1495205", "1521116", "1530730", "1482787", "1570620", "1537785", "1525928", "1494631", "1615958", "1563353", "1594538", "1628091", "1621458", "1495210", "1619630", "1472148", "1662097", "1584809", "1527921", "1479023", "1617963", "1628090"], "answers": ["No"]} | |
| {"q_id": "science-forum-test-1476", "query": "can a number have infinitely many digits before the decimal point?", "doc_id": ["397774", "398000", "397777", "397781", "397784", "1192781", "1382792", "897080", "825467", "736971", "1433062", "1311030", "221411", "29323", "728011", "173714", "823151", "301735", "302897", "1052513", "397845", "1058106", "409438", "1222822", "183532", "659009", "54886", "1247286", "397773", "25587", "1088260", "761403", "1338410", "1081805", "633253"], "answers": ["there are numbers that have infinite digits before the decimal point", "You can't have infinitely many digits before the decimal point"]} | |
| {"q_id": "science-forum-test-1886", "query": "the identity cannot be a commutator in a banach algebra?", "doc_id": ["28906", "954861", "156960", "220027", "1400411"], "answers": ["Corollary 2.2.2 concludes that the identity is not a commutator"]} | |
| {"q_id": "science-forum-test-439", "query": "discontinuous derivative.", "doc_id": ["140193"], "answers": ["Volterra\u2019s Function is differentiable everywhere, but its derivative is discontinuous on a set of positive measure"]} | |
| {"q_id": "science-search-test-537", "query": "what does breaking stress depends on?", "doc_id": ["1570178", "1613341", "1625301", "1474040", "1515707", "1556415", "1627908", "1541359", "1645707", "1524073", "1515622", "1486956", "1627445", "1596470", "1548436", "1494148", "1675628", "1523181", "1534592", "1511956", "1586159", "1569283", "1484390", "1603011", "1567988", "1510801", "1545841", "1507001", "1538859", "1567986", "1541704", "1518047", "1659883", "1643622", "1544643", "1596359", "1596338", "1569241", "1568415", "1538063", "1514872", "1552497", "1506288"], "answers": ["the nature of the material"]} | |
| {"q_id": "science-forum-test-168", "query": "does a gun exert enough gravity on the bullet it fired to stop it?", "doc_id": ["1539196", "1539297", "1579727", "1539195", "1496199", "1614285", "1529668", "1517545", "1517543"], "answers": ["The gun's gravity is never going to be enough to stop that bullet"]} | |
| {"q_id": "science-search-test-122", "query": "are the natural numbers finite?", "doc_id": ["610454", "532385", "1247286", "850070", "569436", "967975", "1331791", "363335", "443829", "72092", "534214", "91813", "1118285", "1184432", "748446", "594135", "173741", "844578", "1092208", "365191", "1371969", "968414", "594321", "967891", "443216", "1264045", "811", "167814", "961940"], "answers": ["not finite but rather infinite"]} | |
| {"q_id": "science-forum-test-1417", "query": "unexpected approximations which have led to important mathematical discoveries", "doc_id": [], "answers": ["the fast inverse square root"]} | |
| {"q_id": "science-forum-test-469", "query": "do most mathematicians know most topics in mathematics?", "doc_id": ["892336", "892542", "892451", "70347", "69740", "1045588", "472044", "1260698", "95013", "283490", "66023", "249716", "562383", "501643", "405257", "248073", "937398", "892295", "907603", "538473", "270240", "818557", "146629", "840054", "49259", "726784", "34048", "424179", "783817", "184095", "618569", "251824"], "answers": ["I expect an average mathematician to have decent knowledge of between 5% and 15% of topics", "No", "no"]} | |
| {"q_id": "science-forum-test-1815", "query": "on average, how many friends would i need to have to have at least one friends birthday every day?", "doc_id": ["566412", "554131", "1424245", "1376681", "455577", "10223"], "answers": ["about $365\\cdot(\\ln(365)+0.577)=2364$ friends"]} | |
| {"q_id": "science-forum-test-669", "query": "in a family with two children, what are the chances, if one of the children is a girl, that both children are girls?", "doc_id": ["1326798", "1437938", "18053", "8572", "8441", "820895", "584739", "1197538", "584950", "180166", "1330054", "463744", "18039", "8533", "584769", "934050", "816378", "1193030", "1193016", "818584", "585002", "1208461", "1110706", "8427", "8428", "8431", "1168301", "694125", "816439", "74502", "1981", "893099", "600137", "1759", "885884"], "answers": ["1/3", "1/2", "33%"]} | |
| {"q_id": "science-forum-test-1300", "query": "intuitive explanation of a positive semidefinite matrix", "doc_id": ["794316", "14974", "1182322", "377479", "1381656", "1135385", "1178002", "67126", "5556"], "answers": ["a matrix that's \"like\" a single number $\\geq 0$"]} | |
| {"q_id": "science-forum-test-1589", "query": "what is the arithmetic mean of no numbers?", "doc_id": ["385221", "385477", "385248"], "answers": ["should not exist", "Error"]} | |
| {"q_id": "science-forum-test-727", "query": "true or false? $x^2\\ne x\\implies x\\ne 1$", "doc_id": ["46144", "132869", "46145"], "answers": ["TRUE"]} | |
| {"q_id": "science-search-test-191", "query": "what is the difference between a group and a ring?", "doc_id": ["37", "45", "79988", "386100", "565536", "71532", "1375135", "1127207", "542618", "495735", "7178", "1028985", "466628", "588459", "1082966", "565529", "1129815", "474487", "3876"], "answers": ["A ring is a group with an additional operation, where the second operation is associative"]} | |
| {"q_id": "science-forum-test-942", "query": "what is the tor functor?", "doc_id": ["723858", "1002202", "39402", "1208367", "379389", "196758", "9126", "1126178", "753706", "100901", "1187953", "102605", "1356849", "55605", "693888", "316584", "23661", "1062438", "20469", "1327016", "1120640", "787016", "264949", "939729", "828268", "386535", "17584", "525893", "1258238", "332048"], "answers": ["the derived functors of the tensor product"]} | |
| {"q_id": "science-forum-test-580", "query": "how do you explain to a 5th grader why division by zero is meaningless?", "doc_id": ["1062114", "1062316", "1162873", "1062243", "1162822", "1144349", "1062120", "303240", "117916", "344988", "90033", "613374", "117970", "1162890", "200581", "32546", "380482"], "answers": ["no number of times you can add zero to itself to get a non-zero sum", "zero cookies and you split them evenly among zero friends"]} | |
| {"q_id": "science-forum-test-394", "query": "proof that the trace of a matrix is the sum of its eigenvalues", "doc_id": ["249904", "967573", "637540", "61087", "30608", "1378957", "591763", "1603548", "143550", "780185", "462313", "95000", "1350828", "939275", "1008893", "629294", "1311592", "1447318", "277803", "1384875", "916618", "940276", "300223", "213976", "127491", "997402", "1419775", "512459", "588429", "578311", "701399", "974886", "552559", "167956", "709604", "488993", "863899", "1514102", "317363", "755536", "944924", "490716", "1444090", "964334", "1084796", "117664", "578314", "398724", "890198", "201058", "826192"], "answers": ["matrix has its eigenvalues on the diagonal, its trace is the sum (with multiplicity) of its eigenvalues"]} | |
| {"q_id": "science-search-test-518", "query": "are leptons fermions or bosons?", "doc_id": ["1522307", "1522249", "1522248", "1574051", "1527373", "197680", "1641952", "1538537", "1510186", "1494440", "1537552", "1522250", "1624890", "1554232", "1639442", "1597826", "1575511", "1521360", "1617974", "1491062", "1615990", "1662269", "1578671", "1532961", "1635815", "1473993", "1516601", "1517245", "1494770", "1514941", "1593325", "1476525"], "answers": ["fermions"]} | |
| {"q_id": "science-forum-test-240", "query": "whats an intuitive way to think about the determinant?", "doc_id": ["1137890", "30097", "447", "511090", "1278368", "739493", "860023", "1267548", "765089", "931158", "939717", "1204730", "65262", "400", "1028079", "1162740", "1046730", "484512", "616", "1287404", "995677", "1325723", "818653", "184991", "121539", "775209", "1192550", "256462", "1042197", "1190949", "1058869", "557997", "284219", "1204980", "695302", "558360"], "answers": ["think of a determinant as a volume"]} | |
| {"q_id": "science-search-test-266", "query": "what is the answer to an exponent called?", "doc_id": ["838309", "344411", "343950", "1403563", "201598", "605107", "472534", "1345882", "832256", "276009", "343944", "656904", "791066"], "answers": ["power of", "power"]} | |
| {"q_id": "science-forum-test-450", "query": "why does factoring eliminate a hole in the limit?", "doc_id": ["33731", "420994", "178409", "991620", "598508", "992760", "1047488", "701838", "449282", "1260589", "1162194", "1073525", "396397", "640779", "68938", "816503", "1208824", "1226614", "923447", "808229"], "answers": ["because one expression is equivalent to another except right at that hole"]} | |
| {"q_id": "science-forum-test-145", "query": "why dont miners get boiled to death at $4$ km deep?", "doc_id": ["1563897", "1564385", "1563888"], "answers": ["because the mines use suitable cooling and ventilation equipment", "they cool the mine actively"]} | |
| {"q_id": "science-forum-test-321", "query": "what is the result of $\\infty - \\infty$?", "doc_id": ["797660", "44431", "32240", "196973", "218343", "32254", "724353", "32248", "635170", "369257", "482177", "15718", "193483", "32246", "19966", "895217", "878006", "226635", "774945", "1402208"], "answers": ["Indeterminate", "indeterminate", "there is no reasonable way to define $\\infty - \\infty$", "it is indeterminate", "The answer is undefined"]} | |
| {"q_id": "science-forum-test-1807", "query": "is every lebesgue measurable function on $\\mathbb{r}$ the pointwise limit of continuous functions?", "doc_id": ["1249729", "1343814", "1019817", "1131810", "1134067", "892398", "73163", "35541", "8446", "1035003", "833654", "8444", "435006", "751797", "282444", "1075764", "1242901", "777384", "44196", "246726", "1052454", "169952", "35440"], "answers": ["No"]} | |
| {"q_id": "science-forum-test-666", "query": "fastest way to meet, without communication, on a sphere?", "doc_id": ["491214"], "answers": ["one of you stays still", "stay put"]} | |
| {"q_id": "science-search-test-569", "query": "is atp synthase a channel protein?", "doc_id": ["1679994", "1690300", "1686887", "1689982", "1681242", "1668605", "1678221", "1677574", "1672592", "1681170", "1684269", "1684754", "1689764"], "answers": ["ATP synthase is an enzyme, a molecular motor, and an ion channel"]} | |
| {"q_id": "science-search-test-615", "query": "what are some differences between insects and spiders?", "doc_id": ["1690539"], "answers": ["spiders and insects have different forms of respiration, different mouthparts, and different exoskeletons"]} | |
| {"q_id": "science-forum-test-1257", "query": "what is exponentiation?", "doc_id": ["590399", "1247838", "567935", "116761", "934855", "1161502", "111429", "1345882", "250821", "426447", "1302872", "807140", "309177", "308093", "613425", "125575", "613610", "149312", "600344", "356498", "935090", "309089", "832256", "281803", "740472", "109659", "315056"], "answers": ["repeated multiplication"]} | |
| {"q_id": "science-forum-test-644", "query": "more than 99% of groups of order less than 2000 are of order 1024?", "doc_id": ["117438", "117439", "678171", "628125", "455008", "132320"], "answers": ["assertion is true"]} | |
| {"q_id": "science-search-test-257", "query": "how to calculate difference between two dates in maths?", "doc_id": ["745618", "302015", "309226"], "answers": ["go through Julian day numbers and perform substraction"]} | |
| {"q_id": "science-search-test-115", "query": "are all triangular matrices invertible?", "doc_id": ["317806", "1080604", "12341", "1052514", "830256", "275958", "594333", "794474", "36813", "655275", "1129750", "925904", "160416", "594335", "1265799", "1106839"], "answers": ["only if it has no zeros on the main diagonal"]} | |
| {"q_id": "science-forum-test-421", "query": "why is the penrose triangle impossible?", "doc_id": ["1328758"], "answers": ["You would end up with a triangle with three $90^{\\circ}$ angles"]} | |
| {"q_id": "science-forum-test-514", "query": "can you raise a number to an irrational exponent?", "doc_id": ["778", "47752", "214108", "794345", "1472380", "144924", "1322952", "29261", "510648", "424270", "723068", "325422", "1209002", "1146880", "514956", "388846", "690181", "716272", "1328090", "1053869", "1412997", "1425321", "53687", "1022118"], "answers": ["Yes"]} | |
| {"q_id": "science-search-test-48", "query": "are all diagonalizable matrices invertible?", "doc_id": ["123256", "264822", "12341", "339140", "1388439", "940832", "29872", "943580", "711443", "1087566", "1377961", "1111185", "802229", "955688", "827361", "744619"], "answers": ["No. For instance, the zero matrix is diagonalizable, but isn't invertible"]} | |
| {"q_id": "science-forum-test-1990", "query": "how does the brains energy consumption depend on mental activity?", "doc_id": ["1668624", "1680124", "1668967", "1687032", "1677341", "1673440", "1693640", "1668621"], "answers": ["The energy consumption doesn't vary that much between resting and performing tasks"]} | |
| {"q_id": "science-forum-test-1618", "query": "what does e mean in 9.0122222900391e-5?", "doc_id": ["51710", "3687", "3688", "156479", "682664", "381110", "1181486", "1190672", "314742", "221411", "72173", "636592", "144381", "1390614", "450458", "443209", "206502", "1156351", "723131", "407236", "1088837", "1103737", "498599", "315246"], "answers": ["exponent of 10"]} | |