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Definition df-aleph 7457
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 7577, alephsuc 7579, and alephlim 7578. 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 7453 . 2  class  aleph
2 char 7154 . . 3  class har
3 com 4547 . . 3  class  om
42, 3crdg 6308 . 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  7576  aleph0  7577  alephlim  7578  alephsuc  7579
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