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Definition df-aleph 8320
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 8446, alephsuc 8448, and alephlim 8447. 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 8316 . 2  class  aleph
2 char 7981 . . 3  class har
3 com 6679 . . 3  class  om
42, 3crdg 7075 . 2  class  rec (har ,  om )
51, 4wceq 1379 1  wff  aleph  =  rec (har ,  om )
Colors of variables: wff setvar class
This definition is referenced by:  alephfnon  8445  aleph0  8446  alephlim  8447  alephsuc  8448
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