CentralNotice Cantor's diagonal argument From Wikipedia, the free encyclopedia Jump to: navigation , search An illustration of Cantor's diagonal argument (in base 2) for the existence of uncountable sets . The sequence at the bottom cannot occur anywhere in the enumeration of sequences above. An infinite set may have the same cardinality as a proper subset of itself, as the depicted bijection f ( x )=2 x from the natural to the even numbers demonstrates. Nevertheless, infinite sets of different cardinalities exist, as Cantor's diagonal argument shows. In set theory , Cantor's diagonal argument , also called the diagonalisation argument , the diagonal slash argument or the diagonal method , 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 nat...