controversy over cantor's theory wikipedia - EAS
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See all on Wikipediahttps://en.wikipedia.org/wiki/Controversy_over_Cantor's_theoryIn mathematical logic, the theory of infinite sets was first developed by Georg Cantor. Although this work has become a thoroughly standard fixture of classical set theory, it has been criticized in several areas by mathematicians and philosophers. Cantor's theorem implies that there are sets having
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See moreCantor's first proof that infinite sets can have different cardinalities was published in 1874. This proof demonstrates that the set of natural numbers and the set of real numbers have different cardinalities. It uses the theorem that a
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See moreInitially, Cantor's theory was controversial among mathematicians and (later) philosophers. As Leopold Kronecker claimed: "I don't know
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See moreA common objection to Cantor's theory of infinite number involves the axiom of infinity (which is, indeed, an axiom and not a logical truth). Mayberry has noted that "... the set-theoretical axioms that sustain modern mathematics are self-evident in differing degrees. One of
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See moreWikipedia text under CC-BY-SA license- https://en.wikipedia.org/wiki/Talk:Controversy_over_Cantor's_theory
The article is "Controversy over Cantor's theory", and mostly covers serious philosophical arguments from respected mathematicians. It is not "Fringe views on Cantor's theory", where it might be appropriate to cite unreliable sources simply to remark on their existence.
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- https://en.wikipedia.org/wiki/Cantor's_theorem
Cantor's theorem and its proof are closely related to two paradoxes of set theory. Cantor's paradox is the name given to a contradiction following from Cantor's theorem together with the assumption that there is a set containing all sets, the universal set. In order to distinguish this paradox from the next one discussed below, it is important to note what this contradiction is.
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- https://en.wikipedia.org/wiki/Talk:Controversy_over_Cantor's_theory/Archive_1
1. Those that are naïve or silly (such as arguments that beg the question, plus Cantor's own comments on the question-begging nature of such arguments. Plus Hodges' comments. David, Wilfrid Hodges is a philosopher but he is also a respected mathematical logician who has written standard texts on model theory.
- https://en.wikipedia.org/wiki/Talk:Controversy_over_Cantor's_theory/Archive_2
- The very concept of a "countably infinite set" as employed by Cantor is suspect. What can be counted can not possibly be infinite, and what is infinite can not be counted. Karl Freidrich Gauss pointed this out when he wrote "I protest against the use of infinite magnitude as something completed, which is never permissible in mathematics". The flaw ...
- https://infogalactic.com/info/Controversy_over_Cantor's_theory
At the start, Cantor's theory was controversial among mathematicians and (later) philosophers. As Leopold Kronecker claimed: "I don't know what predominates in Cantor's theory – philosophy or theology, but I am sure that there is no mathematics there" [ citation needed ] .
- https://en.wikipedia.org/wiki/Georg_Cantor
Georg Ferdinand Ludwig Philipp Cantor (/ ˈ k æ n t ɔːr / KAN-tor, German: [ˈɡeːɔʁk ˈfɛʁdinant ˈluːtvɪç ˈfiːlɪp ˈkantɔʁ]; March 3 [O.S. February 19] 1845 – January 6, 1918) was a German mathematician.He played a pivotal role in the creation of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one …
- https://en.wikipedia.org/wiki/Cantor's_diagonal_argument
In set theory, Cantor's diagonal argument, also called the diagonalisation argument, the diagonal slash argument, the anti-diagonal argument, the diagonal method, and Cantor's diagonalization proof, was published in 1891 by Georg Cantor as a mathematical proof that there are infinite sets which cannot be put into one-to-one correspondence with the infinite set of natural numbers.: …
- https://en.wikipedia.org/wiki/Infinitesimal
Synthetic differential geometry or smooth infinitesimal analysis have roots in category theory.This approach departs from the classical logic used in conventional mathematics by denying the general applicability of the law of excluded middle – i.e., not (a ≠ b) does not have to mean a = b.A nilsquare or nilpotent infinitesimal can then be defined. This is a number x where x 2 = 0 is true ...
Controversy Over Cantor's Theory - Reception of The Argument
https://www.liquisearch.com/controversy_over...At the start, Cantor's theory was controversial among mathematicians and (later) philosophers. As Leopold Kronecker claimed: "I don't know what predominates in Cantor's theory – philosophy or theology, but I am sure that there is no mathematics there." Many mathematicians agreed with Kronecker that the completed infinite may be part of philosophy or theology, but that it has no …
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