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Definition df-aleph 8110
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 8236, alephsuc 8238, and alephlim 8237. 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 8106 . 2  class  aleph
2 char 7771 . . 3  class har
3 com 6476 . . 3  class  om
42, 3crdg 6865 . 2  class  rec (har ,  om )
51, 4wceq 1369 1  wff  aleph  =  rec (har ,  om )
Colors of variables: wff setvar class
This definition is referenced by:  alephfnon  8235  aleph0  8236  alephlim  8237  alephsuc  8238
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