Aleph number

Infinite cardinal number

In mathematics, particularly in set theory, the aleph numbers are a sequence of numbers used to represent the cardinality (or size) of infinite sets. They were introduced by the mathematician Georg Cantor and are named after the symbol he used to denote them, the Hebrew letter aleph (ℵ). The smallest cardinality of an infinite set is that of the natural numbers, denoted by ℵ 0 {\displaystyle \aleph _{0}} (read aleph-nought, aleph-zero, or aleph-null); the next larger cardinality of a well-ordered set is ℵ 1 , {\displaystyle \aleph _{1},} then ℵ 2 , {\displaystyle \aleph _{2},} then ℵ 3 , {\displaystyle \aleph _{3},} and so on.

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