Beth number

In mathematics, particularly in set theory, the beth numbers form a certain (unset) sequence of infinite cardinal numbers (also known as transfinite numbers), conventionally written ${\displaystyle \beth _{0},\beth _{1},\beth _{2},\beth _{3},\dots }$, where ${\displaystyle \beth }$ is the Hebrew letter beth. The beth numbers are related to the aleph numbers (${\displaystyle \aleph _{0},\aleph _{1},\dots }$), but unless the generalized continuum hypothesis is true, there are numbers indexed by ${\displaystyle \aleph }$ that are not indexed by ${\displaystyle \beth }$. On the other hand, beth numbers are cofinal (every cardinal number is less than a beth number) in plain Zermelo-Fraenkel set theory.