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Axiom
Examples
Examples
Axiom
Propositional logic
Propositional logic In propositional logic, it is common to take as logical axioms all formulae of the following forms, where , , and can be any formulae of the language and where the included primitive connectives are only "" for negation of the immediately following proposition and "" for implication from antecedent...
Axiom
First-order logic
First-order logic Axiom of Equality.Let be a first-order language. For each variable , the below formula is universally valid. This means that, for any variable symbol , the formula can be regarded as an axiom. Additionally, in this example, for this not to fall into vagueness and a never-ending series of "primitive...
Axiom
Non-logical axioms
Non-logical axioms Non-logical axioms are formulas that play the role of theory-specific assumptions. Reasoning about two different structures, for example, the natural numbers and the integers, may involve the same logical axioms; the non-logical axioms aim to capture what is special about a particular structure (or s...
Axiom
Examples
Examples This section gives examples of mathematical theories that are developed entirely from a set of non-logical axioms (axioms, henceforth). A rigorous treatment of any of these topics begins with a specification of these axioms. Basic theories, such as arithmetic, real analysis and complex analysis are often intr...
Axiom
Arithmetic
Arithmetic The Peano axioms are the most widely used axiomatization of first-order arithmetic. They are a set of axioms strong enough to prove many important facts about number theory and they allowed Gödel to establish his famous second incompleteness theorem.Mendelson, "5. The Fixed Point Theorem. Gödel's Incompleten...
Axiom
Euclidean geometry
Euclidean geometry Probably the oldest, and most famous, list of axioms are the 4 + 1 Euclid's postulates of plane geometry. The axioms are referred to as "4 + 1" because for nearly two millennia the fifth (parallel) postulate ("through a point outside a line there is exactly one parallel") was suspected of being deriv...
Axiom
Real analysis
Real analysis The objectives of the study are within the domain of real numbers. The real numbers are uniquely picked out (up to isomorphism) by the properties of a Dedekind complete ordered field, meaning that any nonempty set of real numbers with an upper bound has a least upper bound. However, expressing these prope...
Axiom
<span id="role">Role in mathematical logic</span>
Role in mathematical logic
Axiom
Deductive systems and completeness
Deductive systems and completeness A deductive system consists of a set of logical axioms, a set of non-logical axioms, and a set of rules of inference. A desirable property of a deductive system is that it be complete. A system is said to be complete if, for all formulas , that is, for any statement that is a lo...
Axiom
Further discussion
Further discussion Early mathematicians regarded axiomatic geometry as a model of physical space, implying, there could ultimately only be one such model. The idea that alternative mathematical systems might exist was very troubling to mathematicians of the 19th century and the developers of systems such as Boolean alg...
Axiom
See also
See also Axiomatic system Dogma First principle, axiom in science and philosophy List of axioms Model theory Regulæ Juris Theorem Presupposition Principle
Axiom
Notes
Notes
Axiom
References
References
Axiom
Further reading
Further reading Mendelson, Elliot (1987). Introduction to mathematical logic. Belmont, California: Wadsworth & Brooks.
Axiom
External links
External links Metamath axioms page Category:Concepts in logic
Axiom
Table of Content
short description, Etymology, Historical development, Early Greeks, Modern development, Other sciences, Mathematical logic, Logical axioms, Examples, Propositional logic, First-order logic, Non-logical axioms, Examples, Arithmetic, Euclidean geometry, Real analysis, <span id="role">Role in mathematical logic</span>, De...
Alpha
short description
Alpha (uppercase , lowercase ) is the first letter of the Greek alphabet. In the system of Greek numerals, it has a value of one. Alpha is derived from the Phoenician letter aleph , whose name comes from the West Semitic word for 'ox'. Letters that arose from alpha include the Latin letter and the Cyrillic letter .
Alpha
Uses
Uses
Alpha
Greek
Greek In Ancient Greek, alpha was pronounced and could be either phonemically long ([aː]) or short ([a]). Where there is ambiguity, long and short alpha are sometimes written with a macron and breve today: . = "a time" = "tongue" In Modern Greek, vowel length has been lost, and all instances of alpha simply r...
Alpha
Greek grammar
Greek grammar In the Attic–Ionic dialect of Ancient Greek, long alpha fronted to (eta). In Ionic, the shift took place in all positions. In Attic, the shift did not take place after epsilon, iota, and rho (; ). In Doric and Aeolic, long alpha is preserved in all positions.Herbert Weir Smyth. Greek grammar for college...
Alpha
Mathematics and science
Mathematics and science The letter alpha represents various concepts in physics and chemistry, including alpha radiation, angular acceleration, alpha particles, alpha carbon and strength of electromagnetic interaction (as fine-structure constant). Alpha also stands for thermal expansion coefficient of a compound in ph...
Alpha
International Phonetic Alphabet
International Phonetic Alphabet In the International Phonetic Alphabet, the letter ɑ, which looks similar to the lower-case alpha, represents the open back unrounded vowel.
Alpha
History and symbolism
History and symbolism
Alpha
Origin
Origin The Phoenician alphabet was adopted for Greek in the early 8th century BC, perhaps in Euboea.The date of the earliest inscribed objects; A.W. Johnston, "The alphabet", in N. Stampolidis and V. Karageorghis, eds, Sea Routes from Sidon to Huelva: Interconnections in the Mediterranean 2003:263-76, summarizes the pr...
Alpha
Plutarch
Plutarch Plutarch, in Moralia,Symposiacs, Book IX, questions II & III On-line text at Adelaide library presents a discussion on why the letter alpha stands first in the alphabet. Ammonius asks Plutarch what he, being a Boeotian, has to say for Cadmus, the Phoenician who reputedly settled in Thebes and introduced the a...
Alpha
Alpha and Omega
Alpha and Omega right|thumb|Stained glass featuring Alpha and Omega in the As the first letter of the alphabet, Alpha as a Greek numeral came to represent the number 1. Therefore, Alpha, both as a symbol and term, is used to refer to the "first", or "primary", or "principal" (most significant) occurrence or status of...
Alpha
Unicode
Unicode All code points with or but without (for accented Greek characters, see Greek diacritics: Computer encoding):
Alpha
Notes
Notes
Alpha
References
References Category:Greek letters Category:Vowel letters
Alpha
Table of Content
short description, Uses, Greek, Greek grammar, Mathematics and science, International Phonetic Alphabet, History and symbolism, Origin, Plutarch, Alpha and Omega, Unicode, Notes, References
Alvin Toffler
short description
Alvin Eugene Toffler (October 4, 1928 – June 27, 2016) was an American writer, futurist, and businessman known for his works discussing modern technologies, including the digital revolution and the communication revolution, with emphasis on their effects on cultures worldwide. He is regarded as one of the world's outst...
Alvin Toffler
Early life
Early life Alvin Toffler was born on October 4, 1928, in New York City, and raised in Brooklyn. He was the son of Rose (Albaum) and Sam Toffler, a furrier, both Polish Jews who had migrated to America. He had one younger sister. He was inspired to become a writer at the age of 7 by his aunt and uncle, who lived with th...
Alvin Toffler
Career
Career Seeking experiences to write about, Alvin and Heidi Toffler spent the next five years as blue collar workers on assembly lines while studying industrial mass production in their daily work. He compared his own desire for experience to other writers, such as Jack London, who in his quest for subjects to write ab...
Alvin Toffler
Ideas and opinions
Ideas and opinions Toffler stated many of his ideas during an interview with the Australian Broadcasting Corporation in 1998. "Society needs people who take care of the elderly and who know how to be compassionate and honest," he said. "Society needs people who work in hospitals. Society needs all kinds of skills that...
Alvin Toffler
Influences and popular culture
Influences and popular culture Toffler often visited with dignitaries in Asia, including China's Zhao Ziyang, Singapore's Lee Kuan Yew and South Korea's Kim Dae Jung, all of whom were influenced by his views as Asia's emerging markets increased in global significance during the 1980s and 1990s. Although they had origi...
Alvin Toffler
Critical assessment
Critical assessment Accenture, the management consultancy firm, identified Toffler in 2002 as being among the most influential voices in business leaders, along with Bill Gates and Peter Drucker. Toffler has also been described in a Financial Times interview as the "world's most famous futurologist". In 2006, the Peo...
Alvin Toffler
Selected awards
Selected awards Toffler has received several prestigious prizes and awards, including the McKinsey Foundation Book Award for Contributions to Management Literature, Officier de L'Ordre des Arts et Lettres, and appointments, including Fellow of the American Association for the Advancement of Science and the Internationa...
Alvin Toffler
Personal life
Personal life Toffler was married to Heidi Toffler (born Adelaide Elizabeth Farrell), also a writer and futurist. They lived in the Bel Air section of Los Angeles, California, and previously lived in Redding, Connecticut. The couple's only child, Karen Toffler (1954–2000), died at age 46 after more than a decade suffe...
Alvin Toffler
Bibliography
Bibliography Alvin Toffler co-wrote his books with his wife Heidi. The Culture Consumers (1964) St. Martin's Press, The Schoolhouse in the City (1968) Praeger (editors), Future Shock (1970) Bantam Books, The Futurists (1972) Random House (editors), Learning for Tomorrow (1974) Random House (editors), The Eco...
Alvin Toffler
See also
See also Daniel Bell Norman Swan Human nature John Naisbitt
Alvin Toffler
References
References
Alvin Toffler
External links
External links  – official Alvin Toffler site Toffler Associates Interview with Alvin Toffler by the World Affairs Council Discuss Alvin Toffler's Future Shock with other readers, BookTalk.org Future Shock Forum 2018 Finding aid to the Alvin and Heidi Toffler papers at Columbia University. Rare Book & Manusc...
Alvin Toffler
Table of Content
short description, Early life, Career, Ideas and opinions, Influences and popular culture, Critical assessment, Selected awards, Personal life, Bibliography, See also, References, External links
The Amazing Spider-Man
short description
The Amazing Spider-Man is an ongoing American superhero comic book series featuring the Marvel Comics superhero Spider-Man as its title character and main protagonist. Being in the mainstream continuity of the franchise, it was the character's first title, launching seven months after his introduction in the final issu...
The Amazing Spider-Man
Publication history
Publication history Writer-editor Stan Lee and artist/co-plotter Steve Ditko created the character of Spider-Man, and the pair produced 38 issues from March 1963 to July 1966. Ditko left after the 38th issue, while Lee remained as writer until issue 100. Since then, many writers and artists have taken over the monthly ...
The Amazing Spider-Man
1960s
1960s Due to strong sales on the character's first appearance in Amazing Fantasy No. 15, Spider-Man was given his own ongoing series in March 1963.DeFalco "1960s" in Gilbert (2008), p. 91: "Thanks to a flood of fan mail, Spider-Man was awarded his own title six months after his first appearance. Amazing Spider-Man bega...
The Amazing Spider-Man
1970s
1970s Several spin-off series debuted in the 1970s: Marvel Team-Up in 1972,Sanderson, Peter "1970s" in Gilbert (2008), p. 155: "Marvel Team-Up No. 1 inaugurated a new series in which Spider-Man teamed with a different hero in each issue."" and The Spectacular Spider-Man in 1976.Sanderson "1970s" in Gilbert (2008), p. ...
The Amazing Spider-Man
1980s
1980s thumb|The Amazing Spider-Man No. 252 (May 1984): Spider-Man's black costume debuts. Cover art by Ron Frenz and Klaus Janson. The Amazing Spider-Man #200 (Jan. 1980) featured the return and death of the burglar who killed Spider-Man's Uncle Ben. Writer Marv Wolfman and penciler Keith Pollard both left the title by...
The Amazing Spider-Man
1990s
1990s With a civilian life as a married man, the Spider-Man of the 1990s was different from the superhero of the previous three decades. McFarlane left the title in 1990 to write and draw a new series titled simply Spider-Man. His successor, Erik Larsen, penciled the book from early 1990 to mid-1991. After issue No. 35...
The Amazing Spider-Man
Relaunch and the 2000s
Relaunch and the 2000s Marvel began The Amazing Spider-Man relaunching the 'Amazing' comic book series with (vol. 2) #1 (Jan. 1999).Cowsill "1990s" in Gilbert (2012), p. 246: "This new series heralded a fresh start for the web-slinger's adventures." Howard Mackie wrote the first 29 issues. The relaunch included the San...
The Amazing Spider-Man
2010s and temporary end of publication
2010s and temporary end of publication Mark Waid scripted the opening of "The Gauntlet" storyline in issue No. 612 (Jan. 2010).Cowsill "2010s" in Gilbert (2012), p. 327: "Written by Mark Waid and drawn by Paul Azaceta, the two-part opening mixed the real-world drama of the economic meltdown with some Spidey action." Th...
The Amazing Spider-Man
2014 relaunch
2014 relaunch In January 2014, Marvel confirmed that The Amazing Spider-Man would be relaunched on April 30, 2014, starting from issue No. 1, with Peter Parker as Spider-Man once again. The first issue of this new version of The Amazing Spider-Man was, according to Diamond Comics Distributors, the "best-selling comic b...
The Amazing Spider-Man
The Amazing Spider-Man: Renew Your Vows
The Amazing Spider-Man: Renew Your Vows In 2015, Marvel started the universe wide Secret Wars event where the core and several other Marvel universes were combined into one big planet called Battleworld. Battleworld was divided into sections with most of them being self-contained universes. Marvel announced that severa...
The Amazing Spider-Man
2015 relaunch
2015 relaunch Following the 2015 Secret Wars event, a number of Spider-Man-related titles were either relaunched or created as part of the "All-New, All-Different Marvel" event. Among them, The Amazing Spider-Man was relaunched as well and primarily focused on Peter Parker continuing to run Parker Industries and becomi...
The Amazing Spider-Man
2018 relaunch
2018 relaunch In March 2018, it was announced that writer Nick Spencer would be writing the main semi-monthly The Amazing Spider-Man series beginning with a new No. 1, replacing long-time writer Dan Slott, as part of the Fresh Start relaunch that July. The first five-issue story arc was titled 'Back to Basics.' During ...
The Amazing Spider-Man
2020s
2020s Issue 45 kicked off the Sins Rising story which saw the resurrected Sin-Eater carry out the plans of Kindred to cleanse the world of sin, particularly that of Norman Osborn. The story concluded with issue 49, issue 850 in legacy numbering, seeing Spider-Man and Green Goblin team up to defeat Sin-Eater. Last Rema...
The Amazing Spider-Man
2022 relaunch
2022 relaunch In January 2022, it was announced that writer Zeb Wells and John Romita Jr. would be working on a relaunched The Amazing Spider-Man, bringing the number of volumes for the title to its sixth, with the series beginning in April 2022 as a semi-monthly publication. The relaunch encompasses both a legacy numb...
The Amazing Spider-Man
2025 relaunch
2025 relaunch In December 2024, it was announced that Kelly would become the writer of a new volume of ASM that will launch after 8 Deaths of Spider-Man in April 2025, with John Romita Jr. and Pepe Larraz providing the work on the art.
The Amazing Spider-Man
Contributors
Contributors
The Amazing Spider-Man
Vol. 1 (1963–1998, 2003–2014, 2017–2018)
Vol. 1 (1963–1998, 2003–2014, 2017–2018)
The Amazing Spider-Man
Writers
Writers Years Writer Issues 1963–1972, 1973, 1980, 1984Stan Lee #1-100, #105-110, #116-118, #200 (epilogue), Annual #1-5, #18 1971–1972 Roy Thomas #101-104 1972–1975 Gerry Conway #111-149, Giant-Size Super-Heroes #1 1975–1978 Archie Goodwin #150, #181, Annual #11 1975–1978 Len Wein #151-181, Annual #10 1976–1978, 1981...
The Amazing Spider-Man
Pencilers
Pencilers Years Penciler Issues 1963–1966 Steve Ditko #1–38, Annual #1-2 1966–1974, 1992, 2003 John Romita Sr. #39-75, #82-88, #93–95, #106–119, #132, #365, #500, Annual #3-4 1968 Larry Lieber Annual #5 1968 Don Heck #57, #59-63, #66 1969–1970, 1980 Jim Mooney #68-69, #71, #80, #84-87, #207 1969–1970 John Buscema #72-...
The Amazing Spider-Man
Vol. 2 (1999–2003)
Vol. 2 (1999–2003)
The Amazing Spider-Man
Writers
Writers Years Writer Issues 1999–2001 Howard Mackie (vol. 2) #1-13, #15-29 2000 John Byrne #13-14 2001–2003 J. Michael Straczynski #30-58
The Amazing Spider-Man
Pencilers
Pencilers Years Penciler Issues 1999–2000 John Byrne (vol. 2) #1-18 2000 Erik Larsen (vol. 2) #19-21 2000–2003 John Romita Jr. (vol. 2) #22-27, #30-58 2001 Joe Bennett (vol. 2) #28 2001 Lee Weeks (vol. 2) #29
The Amazing Spider-Man
Vol. 3 (2014–2015)
Vol. 3 (2014–2015)
The Amazing Spider-Man
Writers
Writers Years Writer Issues 2014–2015 Dan Slott #1-18 2015 Gerry Conway #16.1-20.1
The Amazing Spider-Man
Pencilers
Pencilers Years Penciler Issues 2014–2015 Humberto Ramos (vol. 3) #1-6, #8, #16-18 2014–2015 Giuseppe Camuncoli (vol. 3) #1, #7-9, #12–15 2015 Olivier Coipel (vol. 3) #9-11 2015 Carlo Barberi #16.1-20.1
The Amazing Spider-Man
Vol. 4 (2015–2017)
Vol. 4 (2015–2017)
The Amazing Spider-Man
Writers
Writers Years Writer Issues 2015–2017 Dan Slott #1-32
The Amazing Spider-Man
Pencilers
Pencilers Years Penciler Issues 2015–2017 Giuseppe Camuncoli #1–5, #9–16, #19–24 2016 Matteo Buffagni #6-8 2016 R.B. Silva #17-18 2017 Stuart Immonen #25-31 2017 Greg Smallwood #32
The Amazing Spider-Man
Vol. 5 (2018–2022)
Vol. 5 (2018–2022)
The Amazing Spider-Man
Writers
Writers Years Writer Issues 2018–2021 Nick Spencer #1-74; #18.HU-20.HU; #50.LR-54.LR 2020–2021 Matthew Rosenberg #50.LR-54.LR 2021 Ed Brisson #68-69 2021 Christos Gage #74 2021–2022 Zeb Wells #75-76, #86, #93; #92.BEY 2021–2022 Kelly Thompson #77-78, #91-92 2022 Jed MacKay #87-88, #92; #78.BEY, #92.BEY 2022 Cody Zigla...
The Amazing Spider-Man
Pencilers
Pencilers Years Penciler Issues 2018–2020 Ryan Ottley #1-5, #11-13, #16, #23-25, #30-31, #37, #41-43, #49 2018–2021 Humberto Ramos #6-10, #17-18, #20, #22, #25, #49, #74 2018 Steve Lieber #6-7 2019 Michele Bandini #9-10 2019 Chris Bachalo #14-15 2019 Alberto Jimenez Alburquerque #16 2019 Gerardo Sandoval #19, #21 2019...
The Amazing Spider-Man
Vol. 6 (2022–2025)
Vol. 6 (2022–2025)
The Amazing Spider-Man
Writers
Writers Years Writer Issues 2022–present Zeb Wells #1-18, #21-60 2022–2023 Dan Slott #6, #31 2022 Daniel Kibblesmith #6 2022 Jeff Loveness #6 2023-2025 Joe Kelly #19-20, #61-62, #65, #69-70 2023 Celeste Bronfman #31 2023 Cale Atkinson #31 2023 Albert Monteys #31 2023 Steve Foxe #312024-2025Justina Ireland#63-64, #66-...
The Amazing Spider-Man
Pencilers
Pencilers Years Penciler Issues 2022–2024 John Romita Jr. #1-5, #7-8, #11-13, #21-26, #31, #39-44, #49, #55-60 2022–2025 Ed McGuinness #6, #15-18, #27-30, #37-38, #50-54, #60-62, #69-70 2022–2023 Patrick Gleason #9, #32-36, #60 2022 Nick Dragotta #10 2023 Michael Dowling #14 2023 Kyle Hotz #14 2023 Terry Dodson #14, #...
The Amazing Spider-Man
Collected editions
Collected editions See: Spider-Man Collected Editions
The Amazing Spider-Man
See also
See also
The Amazing Spider-Man
References
References
The Amazing Spider-Man
External links
External links The Amazing Spider-Man comic book sales figures from 1966–present at The Comics Chronicles The Amazing Spider-Man cover gallery Spiderman Videos Category:1963 comics debuts Category:Comics by Archie Goodwin (comics) Category:Comics by Dennis O'Neil Category:Comics by Gerry Conway Category:Comic...
The Amazing Spider-Man
Table of Content
short description, Publication history, 1960s, 1970s, 1980s, 1990s, Relaunch and the 2000s, 2010s and temporary end of publication, 2014 relaunch, The Amazing Spider-Man: Renew Your Vows, 2015 relaunch, 2018 relaunch, 2020s, 2022 relaunch, 2025 relaunch, Contributors, Vol. 1 (1963–1998, 2003–2014, 2017–2018), Writers, ...
AM
Wiktionary
AM or Am may refer to:
AM
Arts and entertainment
Arts and entertainment
AM
Music
Music A minor, a minor scale in music A.M. (Chris Young album) A.M. (Wilco album) AM (Abraham Mateo album) AM (Arctic Monkeys album) AM (musician), American musician Am, the A minor chord symbol Armeemarschsammlung (Army March Collection), catalog of German military march music Andrew Moore (musician), Canadi...
AM
Television and radio
Television and radio AM (radio program), Australian current affairs radio program American Morning, American morning television news program Am, Antes del Mediodía, Argentine current affairs television program Am, a character in the anthology Star Wars: Visions @fter Midnight (TV series) (logo: @m), American late ...
AM
Other media
Other media Allied Mastercomputer, the antagonist of the short story "I Have No Mouth, and I Must Scream"
AM
Business
Business Aston Martin, a British sportscar manufacturer
AM
Education
Education Active Minds, a mental health awareness charity Arts et Métiers ParisTech, a French engineering school Australian Museum, a museum in Australia Master of Arts, an academic degree
AM
Military
Military A US Navy hull classification symbol: Minesweeper (AM) Air marshal, a senior air officer rank used in Commonwealth countries Anti-materiel rifle, rifle designed for use against military equipment Aviation structural mechanic, a U.S. Navy occupational rating
AM
Science
Science AM, a complexity class related to Arthur–Merlin protocol Adrenomedullin, a protein Air mass (astronomy), measure of the amount of air along the line of sight in astronomical observations Am, tropical monsoon climate in the Köppen climate classification Americium, symbol Am, a chemical element Attometre, a...
AM
Technology
Technology Amplitude modulation, an electronic communication technique AM broadcasting, radio broadcasting using amplitude modulation Additive manufacturing, or 3-D printing, a process of making a three-dimensional solid object of virtually any shape from a digital model. Agile modeling, a software engineering meth...
AM
Timekeeping
Timekeeping a.m., ante meridiem, the time period from midnight to noon, written e.g., 6a.m. Anno Mundi, a calendar era based on the biblical creation of the world
AM
Transportation
Transportation A.M. (automobile), a 1906 French car Aeroméxico (IATA airline code AM), airline in Mexico All-mountain, a discipline of mountain biking Arkansas and Missouri Railroad
AM
Other uses
Other uses First-person singular present of the copula verb to be Am (cuneiform), a written syllable Member of the Order of Australia, postnominal letters which can be used by a Member of the Order Assembly Member (disambiguation), a political office formerly a Member of the National Assembly for Wales, now Member...
AM
See also
See also Pro–am `am (disambiguation) A&M (disambiguation) AM2 (disambiguation) AMS (disambiguation)
AM
Table of Content
Wiktionary, Arts and entertainment, Music, Television and radio, Other media, Business, Education, Military, Science, Technology, Timekeeping, Transportation, Other uses, See also
Antigua and Barbuda
Short description
Antigua and Barbuda is a sovereign archipelagic country composed of Antigua, Barbuda, and numerous other small islands. Antigua and Barbuda has a total area of 440 km2 (170 sq mi), making it one of the smallest countries in the Caribbean. The country is mostly flat, with the highest points on Antigua being in the Sheke...
Antigua and Barbuda
Etymology
Etymology is Spanish for 'ancient' and is Spanish for 'bearded'. The island of Antigua was originally called by the Arawaks, and the Caribs possibly called Barbuda . Christopher Columbus, while sailing by in 1493, may have named it , after an icon in the Spanish Seville Cathedral. The "bearded" of Barbuda is thoug...