\beth

The \beth symbol is used in set theory to denote a certain sequence of cardinal numbers, known as the Beth numbers. These numbers are used to explore the sizes of infinite sets and are related to the concept of power sets.

Examples

The first Beth number is equal to the first infinite cardinal, aleph-null.

\beth_0 = \aleph_0

The second Beth number represents the cardinality of the power set of the natural numbers.

\beth_1 = 2^{\aleph_0}

The Beth number at the first infinite ordinal, representing a union of all smaller Beth numbers.

\beth_\omega = \bigcup_{n < \omega} \beth_n