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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 – informally, that there are sets which in some sense contain more elements than there are positive integers.
6 days ago · The Cantor diagonal method, also called the Cantor diagonal argument or Cantor's diagonal slash, is a clever technique used by Georg Cantor to show that the integers and reals cannot be put into a one-to-one correspondence (i.e., the uncountably infinite set of real numbers is "larger" than the countably infinite set of integers ).
George's most famous discovery - one of many by the way - was the diagonal argument. Although George used it mostly to talk about infinity, it's proven useful for a lot of other things as well, including the famous undecidability theorems of Kurt Gödel. George's interest was not infinity per se.
Jul 6, 2020 · The diagonal helps us construct a number b ∈ ℝ that is unequal to any f(n). Just let the nth decimal place of b differ from the nth entry of the diagonal. Then the nth decimal place of b differs from the nth decimal place of f(n). - Excerpt, Book of Proof* by Richard Hammock (2013)
- Jørgen Veisdal
Jul 6, 2020 · In addition to his inventions of set theory and transfinite numbers, Georg Cantor (1845–1918) is remembered as the brilliant inventor of the popular diagonalization argument later employed by both Kurt Gödel (1906–1978) and Alan Turing (1912–1954) in their most famous papers.
- Jørgen Veisdal
May 21, 2024 · Quick Reference. The method first used by Cantor to show that there cannot be an enumeration of the real numbers. Any real number can be written as an infinite decimal. So we imagine a correspondence with the natural numbers, giving us some real as the first, another as the second, and so on.
Diagonalization is a method discovered by Georg Cantor in 1873. This method is integral in the proof of the halting problem. Diagonalization is also used in Sipser to describe countable and uncountable sets, and to prove the countability or uncountability of sets.
