Definition:Aleph Number

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Definition

An aleph number is an infinite cardinal.


Symbol

The symbol used to denote an aleph number is the first letter of the Hebrew alphabet aleph: $\aleph$.


Aleph-Null: $\aleph_0$

Aleph-null is the cardinal number of a set which is in one-to-one correspondence with the natural numbers $\N$.


Also known as

An aleph number is also known as an aleph.


Also see

  • Results about aleph numbers can be found here.


Historical Note

The concept and notation of aleph numbers are due to Georg Cantor.

He defined the notion of cardinality.

He was the first to realize that infinite sets can have different cardinalities.


Linguistic Note

Aleph, $\aleph$, is the first letter of the Hebrew alphabet.

It is pronounced al-eph, with the stress on the first syllable.


Sources