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Definition df-aleph 7827
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 7947, alephsuc 7949, and alephlim 7948. 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 7823 . 2  class  aleph
2 char 7524 . . 3  class har
3 com 4845 . . 3  class  om
42, 3crdg 6667 . 2  class  rec (har ,  om )
51, 4wceq 1652 1  wff  aleph  =  rec (har ,  om )
Colors of variables: wff set class
This definition is referenced by:  alephfnon  7946  aleph0  7947  alephlim  7948  alephsuc  7949
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