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Definition df-aleph 7569
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 7689, alephsuc 7691, and alephlim 7690. 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 7565 . 2  class  aleph
2 char 7266 . . 3  class har
3 com 4656 . . 3  class  om
42, 3crdg 6418 . 2  class  rec (har ,  om )
51, 4wceq 1624 1  wff  aleph  =  rec (har ,  om )
Colors of variables: wff set class
This definition is referenced by:  alephfnon  7688  aleph0  7689  alephlim  7690  alephsuc  7691
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