# Aleph null

cardinal of the set of all natural numbers, and more generally of any well-ordered and countable infinite set

Aleph null (also aleph naught or aleph 0) is the smallest infinite number. It is the cardinality (size) of the set of natural numbers (there are aleph null natural numbers). Georg Cantor invented and named the concept. The symbol for aleph null is ${\displaystyle \aleph _{0}}$.[1]

It is the first infinite number in a series of infinite cardinal numbers. In fact, it is the size of any set which can be matched one-to-one with the natural numbers.[2] The set of algebraic numbers, for example, has cardinality ${\displaystyle \aleph _{0}}$.[3]

Aleph null is followed by aleph one, an infinite number represented by the symbol ${\displaystyle \aleph _{1}}$.[3]

## References

1. "Compendium of Mathematical Symbols". Math Vault. 2020-03-01. Retrieved 2020-08-12.
2. "Transfinite number | mathematics". Encyclopedia Britannica. Retrieved 2020-08-12.
3. Weisstein, Eric W. "Aleph-0". mathworld.wolfram.com. Retrieved 2020-08-12.