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
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): aleph
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): aleph
- 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): aleph