The cardinal numbers defined by , , and at limit ordinals are the beth numbers. In particular , the cardinality of the continuum. This notation distinguishes iterated power sets from the enumeration by Aleph numbers of well-orderable infinite cardinal numbers.
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In set theory, a **Beth number** is a hierarchy of infinite cardinal numbers that are used to describe the sizes of infinite sets. They are denoted by the symbol \( \beth \) followed by a subscript indicating the ordinal number in the sequence. The definition of Beth numbers is as follows: 1. \( \beth_0 \) is defined to be \( \aleph_0 \), the cardinality of the set of natural numbers, which is the smallest infinite cardinal.