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Definition df-aleph 7506
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 7626, alephsuc 7628, and alephlim 7627. 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  |-  aleph  =  rec (har ,  om )

Detailed syntax breakdown of Definition df-aleph
StepHypRef Expression
1 cale 7502 . 2  class  aleph
2 char 7203 . . 3  class har
3 com 4593 . . 3  class  om
42, 3crdg 6355 . 2  class  rec (har ,  om )
51, 4wceq 1619 1  wff  aleph  =  rec (har ,  om )
Colors of variables: wff set class
This definition is referenced by:  alephfnon  7625  aleph0  7626  alephlim  7627  alephsuc  7628
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