# Aleph one

smallest uncountable cardinal number

Aleph one, written as ${\displaystyle \aleph _{1}}$, is an infinite cardinal number following aleph null (${\displaystyle \aleph _{0}}$).[1] It is the cardinality (size) of the set of numbers of possible arrangements for all countably infinite sets. Under continuum hypothesis, it is also the cardinality of the real numbers.[2] Aleph one is followed by aleph two, ${\displaystyle \aleph _{2}}$.

## References

1. "Comprehensive List of Set Theory Symbols". Math Vault. 2020-04-11. Retrieved 2020-09-05.
2. Weisstein, Eric W. "Aleph-1". mathworld.wolfram.com. Retrieved 2020-09-05.