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Definition df-aleph 8383
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 8505, alephsuc 8507, and alephlim 8506. 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 8379 . 2  class  aleph
2 char 8081 . . 3  class har
3 com 6707 . . 3  class  om
42, 3crdg 7139 . 2  class  rec (har ,  om )
51, 4wceq 1437 1  wff  aleph  =  rec (har ,  om )
Colors of variables: wff setvar class
This definition is referenced by:  alephfnon  8504  aleph0  8505  alephlim  8506  alephsuc  8507
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