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Is it correct to say: Would you like to start a cooperation (with us)? Or should it be: Would you like to cooperate (with us)? I feel like the first sentence is wrong, as it sounds to much like saying would you like to start a corporation (with us)? (with a dutch accent) but the second sentence suggests more aggressive...
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Colon or semicolon when because is omitted from a sentence e.g., I am sorry I disturbed you (;) (:) (because) it looked like you were having a lot of fun there. Because explains and clarifies a preceding clause so would it be correct to use a colon preceding the explanatory clause if because is omitted? Alternatively, ...
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Im taking a class in graduate probability. My background is in engineering (very used to math in an applied sense). I am also taking an undergraduate class in real analysis along side (should have taken it before, but I couldn't) I have a couple of questions: We're spending time looking at measurable functions on measu...
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The hyperreal number system adds infinities and infinitesimals, allowing Calculus to be done using these things instead of limits (sort of like when calculus was originally invented, but with rigor).This got me thinking, could this be done with topology to create hypertopology (an equivalent but perhaps more intuitive ...
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Imagine a cat jumping off a roof onto a sledge on ice. Model this as simply as possible, e.g. no resistive forces, perfectly rigid cat, sledge and floor. Moreover, the cat and sledge move in a straight line. The cat will have a vertical component to its momentum when it lands, but the sledge will - more or less - move ...
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I got confirmed from a graduate school starting from next year and I will major algebraic geometry. Until now, I have never thought that I study little things than others with my age. However, I heard that some of my colleagues already studied Hartshorne at least once and quite a few of them have read Rudin's RCA when ...
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While researching about lasers (it's my hobby), it suddenly hit me: there are lasers for every color of the visible spectrum, but there are no brown lasers. Brown isn't even on the rainbow. How is it possible that we can see it? Even stranger, brown as a color is produced with red and green, but when you mix red and gr...
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I am already fluent in portuguese and english, and I can also read spanish well. I have to read a text which is in french, and I'm having some difficulties. Knowing that there are a lot of people out there in the field of mathematics that are able readers of several languages, I would like to get the opinions of more e...
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In my notes I wrote that Rutherford's model of the atom could not explain spectral lines, because that is what my textbook says. I'm not really sure about the details of spectral lines though. I know that when electrons interact with photons of specific frequency, they transition between energy levels (ie they could in...
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After working on my oral skills in English for a couple of years, I know more interested in learning written English, specially by reading. I have been reading a couple of books over the last months (Game of Thrones, the whole Sherlock Holmes, Lord of the Rings, some Stephen King...) and articles (the Guardian, the New...
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I know this might not be an easy question, I've already read the wikipedia page, and there is an interesting view: Therefore, the main difference between chaotic systems and complex systems is their history. Chaotic systems do not rely on their history as complex ones do. Chaotic behaviour pushes a system in equilibriu...
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Generally speaking, by the well-known BCS theory, the more carrier density( density of state at Fermi surface) leads to higher critical temperature. However, in many researches, people fond that the relation between critical temperature and carrier density is not simple. There is a superconducting dome in phase diagram...
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Consider the sentence: While this assumption, on its own, is relatively innocuous, if implausible, in practice, it is supplemented by assumptions... The 'if' here really means something more like 'but perhaps also'. Another sentence: He appeared very happy, if not exuberant, at her arrival. 'if not' here means somethin...
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I'm facing a difficulty about referring to previously mentioned words. It's something that bothers me a lot about the English language. Please consider Mathematicians can use these theorems to their advantage. versus Mathematicians can, to their advantage, use these theorems. Which is more correct? The first sounds mor...
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I was suggested to use the term bullet-proofed by a colleague. Someone else now pointed out that bullet-proofed might not even exist, because we can't build the past tense of an adjective. Part one of the question is: can to bullet-proof be a verb which describes "making something bullet-proof"? And in consequence bull...
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I am not an expert on figure exports and, although I have been searching around quite a lot, I can't find the answer to my problem. During the writing of a journal article, I had the idea of using psfrag to replace text on my .eps figures generated with Matlab. That works fine, as long as the main text .tex file is com...
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I'm trying to fill out a survey that asks me about features that should or should not be included in a smartphone app. The actual questions are confidential, but it's in the style of a sentence like this: "You can control the temperature of the room you're in" followed by these options (of which you can choose one) Ass...
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A video shows two spherical objects (made up of particles) collide. The title refers to them as two planets colliding. When the objects are indeed as large is planets (however large that might be), the video seems sped up. What if the objects are smaller than that, like the size of marbles? Would they still move as slo...
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I'm spending too much time thinking about this problem : I need to show that the shrinking wedge of circles which is path connected, locally path connected ,doesn't have a simply connected covering space . hatcher gives a condition for a space to be semi locally connected it's about the induced injection between the fu...
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This is something probably very basic but I was led back to this issue while listening to a recent seminar by Allan Adams on holographic superconductors. He seemed very worried to have a theory at hand where the chemical potential is negative. (why?) For fermions, isn't the sign of the chemical potential a matter of de...
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Is there a way to selectively disable a specific ligature in XeLaTex? I cannot see how. The selnolig package seems to do what I need but I don't even know how to use Lualatex with my Texshop setup on Mac. Specifics: I am using XeLaTex, new to it and trying to figure my way around and set up some standard templates for ...
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If a body becomes charged by losing electrons for example, it will experience a braking force when it is accelerated due to radiation called Bremsstrahlung radiation. Part of the energy used to accelerate the charged body will be emitted as radiation. It should therefore take more energy to accelerate the charged mass ...
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Why can't you create energy out of nowhere For me it's not enough that a smart guy for hundreds of years said so. Some scientists and religious people said that the earth was flat - untill someone said it wasn't. And we know that it isn't flat, we can prove it. I can prove it. Do we just say we can't create energy out ...
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Below is a review by music critic Robert Christgau of a Flaming Lips album. I've pasted the entire review, but my focus is on the first two sentences. Primarily, is it idiomatic to use "couldn't" here? Because unless I'm wrong, isn't the point of what he's saying that you don't have to hate Sgt. Pepper to think it "cou...
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M-W has the following definition for mixed metaphor: a figure of speech combining inconsistent or incongruous metaphors Hence a requirement is that a 'mixed metaphor' contains more than one metaphor. Eric Lippert comments in another thread: "mixed metaphor" is more commonly used to describe the result of accidentally c...
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Else-site, I got into a discussion with a member where the thread turned accusatory and defensive because I said a programming language had tricky details that you learned over time. I did not mean that it was a bad thing, only that there were features less traveled that really enhance the effectiveness of code. One of...
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I came across a question where i was asked to find the force exerted by the walls of a frustum shaped bucket on a liquid inside it . I found the force exerted by the liquid on the walls of the bucket by concepts of hydrostatic force and thought that by newton's third law both the forces will be equal and opposite . But...
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How do you see non-academic mathematics? I have an impression that the academy has still a quite significant prestige and is thought to be the safe-guard for "real science". That is, to verify that those that have the most experience in science, can produce science and have the "blessing" of the academy, in order to de...
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So basically, I was trying to find a good answer to the question of how light interacts matter. Namely on the quantum level what causes matter to appear transparent, reflective, opaque, etc I came upon the answer with respect to transparency here, but I feel that the concept isn't fully explored here and that something...
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I live by Internet, as both a user and a developer. This dual role gives me a chance to observe. Every time I try to ask something in communities like StackOverflow, I always pick words carefully and provide sufficient information, hoping that my questions will be answered in a short time. But even so, sometimes my que...
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I've been reading the book "Geometric Mechancis" by Darryl Holm and the in the first chapter he treats geometric optics. There the author talks about light rays and those light rays looks like trajectories as of particles as we consider in Classical Mechanics. The first thing that the author state is Fermat's principle...
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This question stems from a disagreement between me and my girlfriend. During the hot summer months, we like to open up the windows during the early morning to cool down our flat a bit. One of us thinks that every window should be opened fully, since that will ensure maximum airflow, the oter swears that the actual area...
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Let imagine a tunnel that connect two distant places at the globe (eastern-western or north-south) There are a lot of posible "distances" or metrics, defined by maps, routes, "as the crow flies", etc.. but none of those distance can be shorter than the distance of the tunel. So if two trains travels at same speed, one ...
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The hippopede is historically famous because Eudoxus used its properties in the first mathematical model of planetary motion. He nested concentric spheres rotating at different inclinations to each other, and had the motion transfer from outer ones inward, the planet was attached to the equator of the innermost sphere....
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I was reading G.I.Taylor's Single - Photon Double Slit experiment. Now, at a time only a single photon gets emitted. What is the probability of it at a certain point of the screen to hit? The answer is written rather abruptly: Although the photon can hit anywhere, the probability is more, where the brightness(bright fr...
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Let's define a "hand-incalculable problem" as a mathematical problem that can not be solved by available human calculation power (using only writing materials and utensils) at a specific date and geography, during lifetime of the person who posed the problem. Given a specific date and problem can we strictly label the ...
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I'd like to know if there have been attempts in solving the full problem of the dynamics of a classical hydrogen atom. Taking into account Newton equations for the electron and the proton and Maxwell equations for the electromagnetic field produced by these charges one obtains a higly non-linear set of coupled equation...
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He was born and brought up in this village, but after staying and studying abroad his childhood friends seem backwards to him; he _ this place now. Or He had lived in this city all his life but whenever he gets a chance he starts counting the flaws. He thanklessly _ his homeland. It might even apply to a situation like...
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Whenever I write TeX/LaTeX documents, I always find that annoying because I can't really focus on the content, It's not that I don't like TeX or what it does for me, it's just the fact that the document quickly becomes something way too verbose. I was thinking about adopting an intermediate syntax, something more "dry"...
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First and foremost I want to say that by no means am I a physics guru, but I still ponder this question. While I can understand from my current understanding of physics that a perpetual machine is yet,by current understanding, unattainable, does that mean that there is no hope for a free source of energy? Confined to t...
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So I decide to self-study the real analysis (measure theory, Banach space, etc.). Surprisingly, I found that Rudin-RCA is quite readable; it is less terse than his PMA. Although the required text for my introductory analysis course was PMA, I mostly studied from Hairer/Wanner's Analysis by Its History (I did not like P...
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I have the following sentence: Increase your rating as you develop your coding skills while you evaluate the skills of other developers. However, I now realize that this sentence is a bit off since it doesn't communicate properly. Some feel that this sentence sounds challenging since some imply that you're competing an...
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If an angle is the measure of distance between to points (Edit: Ok, admittedly bad phrasing. A measure of rotation between two intersecting lines, or points, etc.), is there such a thing as a zero degree angle? I asked a math nerd friend about this years ago and he still hates me for it but couldn't prove it either way...
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Suppose someone comes up with a great original idea. Some time later, someone else comes up with exactly the same idea without knowing that idea been conceived already and even without being influenced in any way by the other person's thought. In other words, both of them make the discovery totally independently and no...
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Specifically, I am referring to the traditional gesture some female service staff members seem to do, when demonstrating their work or their readiness to receive orders. Also, this is the gesture Alice Cullen performs in Twilight movies on several occasions (if I remember correctly). I could not find a photo with this ...
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I have a circle moving on a spherical surface. If the camera angle is fixed, is there a way to calculate the original circle's offset from the centre given the distorted ellipse formed when the circle moves to the edge of the sphere(as seen from the camera)? I've looked into Listing's plane and the Tissot directrix(bec...
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Reading the wikipedia article about the particle in the box, there is this image: Animations from B to F show wave function of a particle in a box starting from ground state up to excited states. The animation C shows wave function behavior in the first excited state and at the middle point both real part (blue) and im...
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I've seen nice graph showing relative activity of each isotope in Chernobyl fallout: Could anyone suggest similar graph or raw data but for absolute isotope activity for the case of nuclear explosion fallout? (for some boosted fission bomb) So that one could see how much gamma, beta and alpha-active particles one shoul...
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What's a word that can be used to describe an author's portrayal of a scene as normal even though the content of what is described is innately disturbing/unnatural? He cut open the dog's underbelly and we all took turns examining its insides, which were just as we had expected them to be. To get over the disappointment...
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I have a question about a Quantum Mechanics machine that should interact with the past, I can't find any flaws with it, but I just want to make sure. The machine has a lot of facts about history, some true and some false, and the machine knows which one each fact is. It measures the spin of an electron, and if it has a...
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in Dire Straits "Sultans of Swing" what is the meaning of these two lines: In the first verse: You get a shiver in the dark It's been raining in the park but meantime South of the river you stop and you hold everything A band is blowing Dixie double four time You feel all right when you hear that music ring As I unders...
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As is the case with most students (I suppose), I seem to have lost touch with the do doing some "basic" math -- calculating integrals, playing around with matrices and doing some linear algebra etc. -- as I have proceeded through my undergraduate program. To be honest, I didn't practice a whole lost of questions when I...
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Is there a way to tell TeX to avoid breaking the page after the first word of a sentence? ... ... He was quite dead. Apparently his neck had been broken. The lightning flashed for a third time, and his face leaped upon me. I sprang to my feet. It (text continues on next page) And then you have to turn the page for the ...
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I got a question about the usage of generalization of collocations. There is a word such as "bird of prey" to refer to birds eating animal flesh. And one way to generalize reference of a noun is to put "the" in front of the word, especially for animals, plants, recent inventions; the lion is the king of the animal worl...
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I am not very familiar with the quirkiness of relativity, and I was wondering how to explain this situation. If a beam of light is shining at some object at some distance from the origin of the beam, does relativity imply that photons in the beam lack time flow and, thereby, never actually experience contact with the o...
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The closest description I can think of is a "drama queen/king", except that tends to describe people who like being in a drama. Instead, I want a phrase describing people who like to pick up on stories such as the following: questionable decisions of others controversies immoral acts and then they get on their soapbox ...
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The area/arc-length is given by an integral or the integral defines the area/arc-length is one the first things we learn in Calculus, but that is done in the Cartesian coordinates, next one moves to polar coordinates and the area is transformed/redefined by a new integral using the Jacobian. My question is : Since area...
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I have a pair of shoes, which seem to isolate me from the ground. In effect I'm gathering static charge and every time i grab an aluminum door handle, that current discharges and that hurts. Ouch. I invented a way to workaround that: when I'm going to touch door handle, first I take my Skeletool (a stainless steel mult...
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Please refer to the figure attached. Consider a normal force is acting on the top of sphere. A constant coefficient of friction causes frictional force throughout the sliding. I want to know after this sphere slides (pure sliding no rolling) for sometime and assuming that it wears as it slides, what should be the shape...
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This question pertains to programing but is really a math question. I am building an application that draws a line graph, similar to a stock line graph. The problem is I am not starting with a known set of numbers. The values will come in based on an altitude value. So, when I start the graph I have no idea what the ma...
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I want to discuss with my boss a part of this code - so I need a name for it. items = array.map(function(item){ return item.item; }); I want to say "This usage of the same identifier twice is _______________ and confusing." They might respond "No this is _________ which is fine". Is tautology an accurate word to use th...
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In several articles and books, I have read that "the magnetic force on or due to a small element of a circuit is equivalent to two or more of its component elements, provided that the current remains same". i.e. the magnetic force on or due to AB(in red) is the same as the magnetic force on or due to its component curr...
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I don't know why, but since recently my Emacs is behaving strangely. As usual I compiled using C-c C-c to call LaTeX, then there were errors and it asked me to type (as usual) C-c '. but when I did it just commented out the whole paragraph, which is the same effect as C-c %. C-c % still works the same and typing ' prod...
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Dictionary definitions of `bonny' admit to chiefly British (or even Scots), but give no further hint of the possible tinges of this word. Bonny (adj.) means attractive, fair; fine, excellent [M-W]. Perhaps I perceive it as slightly archaic, hence this post. Is this word (still) functioning in the meaning given, and wha...
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I am creating a program but facing problem with proper language for comment string in program. My program performs some operation. This operation typically always generates some data. (meaningful data if operation went as expected or error data if operation didn't go well). Now this program returns these two things to ...
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I got into a discussion with my physics teacher about the speed of light and I asked What if an object with mass was to lose mass as it gained speed-- would that allow for an object to eventually reach the speed of light or surpass it if possible through that thinking? My teacher didn't really have an answer to that an...
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What cases can "y'all" work in? A prior question asks about the 'proper' usage of "y'all", but it and its answers only address nominative case (all examples are nominative). I think that there are some cases where "y'all" doesn't work as is. For example, nominative: "Y'all come back now, ya hear?" accusative: "I'll rin...
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What word best describes the experience of starting something, and ending up, before you know it, far deeper into it than you had ever intended, or far more embroiled, involved, or even having finished or done it irreversibly. An example might be, say, opening a book out of curiosity, and finding yourself, the next thi...
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I watched this video: popped water balloons And as you see when the needle pops the balloons the water stays in the same shape as the balloon for a few fragments of a second. The force impacting the water after the balloon has been popped must be gravity, and since the water stays in the same shape for a while must mea...
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I've just got wondering if this sentence is grammatically correct: You are who I love. This is what I am thinking: Let's focus on the who clause, then you can find that the missing element from this clause is actually an object after the verb love. Therefore, who should be changed to whom, which is an object relative p...
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I will greatly appreciate your help with this question. I use beamerposter and want all the blocks (across various columns) to be of the same height (= max height of among all other blocks). I came across your solution here: How to modify columns/column environments so they resize automatically to the largest column ? ...
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i have problem to determine if the word bake is transitive or intransitive verb from the Phrase "Samantha can bake at any time of the day." i am reading from a book called English grammar understanding the basic it say Action verbs that act upon something are called transitive verbs. Action verbs that do not act upon s...
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Since we have working models for forces "combining" or being describable via a single framework at higher energies (such as the "electroweak" force and the aim of GUTs), does electromagnetism split into an "electric" force and a "magnetic" force at lower energies, or is this simply a misnomer in the English language bo...
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Looking around trying to find questions concerning the intuition behind discrete/indiscrete topologies, I haven't found much towards the essence of what these particular topologies imply about the space (and why it is meaningful). I realize that in a discrete topology, every set is both closed and open, as is the case ...
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If I fill a plastic ziploc-shaped bag with water, the cross section profile should be sort of teardrop shaped (assuming we ignore the edge effects of the bag being sealed on the sides as well as the top and bottom). The bag should "sag"/get wider until to get the center of gravity as low as possible. Initially, getting...
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Are the slang usages of "bud" (mainly meaning cannabis, and occasionally clitoris, from what I understood) prevalent enough that I should avoid using them in a product intended for international availability? Example sentences which could be printed: "John has created a bud here!" "Share this bud!" (ouch) "Create bud" ...
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Is there a logical story behind this phrase? Because when looked at from a naive perspective, giving somebody their own medicine sounds like a kind thing to do as it would only treat their illness. The phrase only makes sense in the context of someone who knowingly sells poison as medicine, which is a rather rare thing...
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The smallest possible cardinality of a base is called the weight of the topological space. I was wondering if all minimal bases have the same cardinality, and if every base contains a subset whose cardinality is the weight of the topological space? What aspects are common between a (smallest) base of a topology and a b...
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My daughter said to me this morning (the context is irrelevant): Er, it's all wet! The interjection I have written here as Er was synonymous with Yuck. Its wetness did not cause great happiness. But what's the right way to write it? The problem with the way I've formulated it above is that it looks like the Er of (genu...
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Let us suppose I am running on a street. When my eyes are open, I can see many things moving backward, and thus it gives me an idea that I am moving wrt those things. Not even this, even if I close my eyes during the run, I can really feel that I am moving. Now assume that I reach a world where there is absolutely noth...
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Or, I guess it could be worded, since when and why was it counted as part of a formal writing style to capitalize many general nouns? (After all, it's not German ...) This is also a trend in legal documents, however, I believe, attributable to the fact that certain terms (e.g. "Company") can have very specific definiti...
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One formulation of Dilworth's theorem(for finite partially ordered sets) states that : There exists an antichain A, and a partition of the order into a family P of chains, such that the number of chains in the partition equals the cardinality of A. The above is an extract from this wiki page. However, I don't understan...
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I'm looking for the name of the logical fallacy where intent or agency is assumed when in fact there is none. It's a common fallacy in my experience, but I can't seem to find it described specifically on any site that discusses logical fallacies. It seems to be a special case of apophenia, but Wikipedia and Google turn...
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I was given the following question for comprehension pasted below: What does John mean when he says that he would only win his own money? And I answered that John meant that Marry won't be betting any money, so he will be winning only his own money. Professor marked it incorrect. Can you please what exactly is the prob...
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What are some good ways to motivate the material on infinite series that appears at the end of a typical American Calculus II course? My students in this course are generally from biochemistry, computer science, economics, business, and physics (with a few humanities folks taking the course for fun) - not just math maj...
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I am a pre-engineering student currently taking a Single Variable Calculus course at a community college. I recognize that my future success (or not so much) as an engineer will be based, in large part, on my capabilities with and understanding of Calculus. Therefore, I really, really want to master it like I've never ...
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I am new to the world of stochastic processes and Brownian motion, and am having a hard time finding easily digestible reference material (especially ones with well-worked out examples). So, in a way this question is more of a request for sources/references than a specific answer. To give a little context to where I am...
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There are easy methods for discrete simulations of gas dispersion in two dimensions. If you take a large square lattice, each cell of which is assumed to contain at most one gas molecule, and you move the molecules from cell to adjacent cell at random, the large-scale results are in many ways a good simulation of gas b...
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British English often employs mass nouns where American English would only employ count nouns. Count nouns are nouns which take pluralization and numerical quantifiers like 'many'. Mass nouns can't be pluralized and take volume quantifiers like 'a bit of'. For example: I like sport. I like drink. I pay tax. I've got to...
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An elementary fact that people learn about mirrors is the law of reflection, that the angle of incidence of a light beam striking the mirror (as measured with respect to a normal) equals the angle of reflection. Does this law also hold for a mirror that is moving? Consider a square mirror that is moving at speed v in a...
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"You do research in mathematics! Can you explain your research to me?" If you're a research mathematician, and you have any contact with people outside of the mathematics community, I'm sure you've been asked this question many times. For years now, I've struggled to find a satisfying answer. I think an ideal answer to...
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So I am reading the essay "On Some Verses of Virgil" by Michel de Montaigne (translation by Donald M. Frame) and I came across this particular sentence. Is there any ugliness in doing wrong that can dispense us from the duty of confessing it? The choice of vocabulary here is, honestly, quite confusing to me. Here is th...
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I am writing a formal document. It is a petition to appeal an administrative law decision. The decision is jam-packed full of sloppy mistakes of every kind imaginable. (The guy who wrote it couldn't even manage to spell the name of my town correctly in the title of the document.) I list all the errors and inaccuracies ...
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I have used classical Lagrangian mechanics for quite a while, and what I like about it is that everything can be derived from a very small number of geometric principles. There are just three things you need to "take on faith": That configuration space should be endowed with a Riemannian metric given by mass; That forc...
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For instance, "A politician must be able to think quickly on the spot. He or she must also have no qualms about lying." I know some people who use "they", but as that both sounds and is ungrammatical, I'm wondering if there is any other concise and non-awkward alternative. Edit: Apparently many do consider "they" as co...
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I'm writing some copy for a marketing campaign that promotes the use of a software testing tool by demonstrating how the results of the tool provide you with a greater wealth of information on which to make business decisions. In relation to this, I'm using the term "informed decisions" and my initial wording included ...
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I was reading this interpretation from this site, where these lines are noteworthy enough to talk for the fact that this interpretation doesn't actually talk about many-worlds: These are the "many worlds" in question, although it should be clear that the label is somewhat misleading. People sometimes raise the objectio...
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Firstly I'm not saying that I don't believe in Cantor's diagonalization arguments, I know that there is a deficiency in my knowledge so I'm asking this question to patch those gaps in my understanding. From my understanding of Cantor's Diagonalization argument, if you apply diagonalization to a mapping from one set of ...
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According to path integral theory, it can be assumed that a particle travelling from a point A to B (in an experiment that has not been designed to detect the path) takes all the possible paths from A to B. (Please note that I use the words 'can be assumed' because I know that there is a debate whether the particle rea...
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I was looking up how to find relationships between Sobolev spaces and I came across this post on MO in which the first comment talks about a scaling procedure for understanding the relationships: To find the right values of k,p,r,a, I was taught to use scaling arguments. Take a nice enough singularity for the function ...
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