Page "Georg Cantor" Paragraph 21

Cantor introduced fundamental constructions in set theory, such as the power set of a set A, which is the set of all possible subsets of A.

He later proved that the size of the power set of A is strictly larger than the size of A, even when A is an infinite set ; this result soon became known as Cantor's theorem.

Cantor developed an entire theory and arithmetic of infinite sets, called cardinals and ordinals, which extended the arithmetic of the natural numbers.

His notation for the cardinal numbers was the Hebrew letter ( aleph ) with a natural number subscript ; for the ordinals he employed the Greek letter ω ( omega ).

This notation is still in use today.