Cantor's diagonal argument is a proof technique Georg Cantor published in 1891 to show that the real numbers cannot be placed in one-to-one correspondence with the natural numbers: given any proposed complete listing of real numbers, a new number can always be constructed, digit by digit down the list's own diagonal, that differs from every listed number and so cannot appear on it. Cantor later generalised the same technique to prove Cantor's theorem, that a set's power set is always strictly larger than the set itself. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
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Cantor's diagonal argument (among various similar names) is a mathematical proof that there are infinite sets which cannot be put into one-to-one correspondence with the infinite set of natural numbers.
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Georg Cantor published this proof in 1891.
In Category: Concepts, lead paragraph, opening definition
Cantor's diagonal argument (among various similar names) is a mathematical proof that there are infinite sets which cannot be put into one-to-one correspondence with the infinite set of natural numbers
Associated With: Georg Cantor, lead paragraph, publication date
Georg Cantor published this proof in 1891
Associated With: Cantor's Theorem, General sets
A generalized form of the diagonal argument was used by Cantor to prove Cantor's theorem: for every set S, the power set of S-that is, the set of all subsets of S (here written as P(S))-cannot be in bijection with S itself.
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