Cantor’s Diagonal method

Cantor’s diagonal method is a mathematical proof of the existence of Uncountable sets, sets which cannot be put into one-to-one correspondence with Infinite set of Natural numbers. The size of Infinite sets are now treated with theory of cardinal numbers which Cantor began.

It demonstrates a powerful and general technique that has since been used in a wide range of proofs, including Russell’s paradox, the first of Gödel’s incompleteness theorems, and Turing’s answer to the Entscheidungsproblem.