 Aleph number

The alephs enumerate the infinite initial ordinals: ${\aleph }_0=\omega$, successor indices select the next initial ordinal, and limit indices select the least initial ordinal above all earlier values.

Aleph numbers are a family of cardinal numbers used to represent the sizes of infinite sets in set theory. The first Aleph number, denoted as \( \aleph_0 \) (aleph-null or aleph-zero), represents the cardinality of the set of natural numbers, which is the smallest infinite cardinal number.