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Definition df-aleph 8342
 Description: Define the aleph function. Our definition expresses Definition 12 of [Suppes] p. 229 in a closed form, from which we derive the recursive definition as theorems aleph0 8468, alephsuc 8470, and alephlim 8469. The aleph function provides a one-to-one, onto mapping from the ordinal numbers to the infinite cardinal numbers. Roughly, any aleph is the smallest infinite cardinal number whose size is strictly greater than any aleph before it. (Contributed by NM, 21-Oct-2003.)
Assertion
Ref Expression
df-aleph

Detailed syntax breakdown of Definition df-aleph
StepHypRef Expression
1 cale 8338 . 2
2 char 8003 . . 3
3 com 6700 . . 3
42, 3crdg 7094 . 2
51, 4wceq 1395 1
 Colors of variables: wff setvar class This definition is referenced by:  alephfnon  8467  aleph0  8468  alephlim  8469  alephsuc  8470
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