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Definition df-aleph 9881
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 10007, alephsuc 10009, and alephlim 10008. 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 ℵ = rec(har, ω)

Detailed syntax breakdown of Definition df-aleph
StepHypRef Expression
1 cale 9877 . 2 class
2 char 9497 . . 3 class har
3 com 7803 . . 3 class ω
42, 3crdg 8356 . 2 class rec(har, ω)
51, 4wceq 1542 1 wff ℵ = rec(har, ω)
Colors of variables: wff setvar class
This definition is referenced by:  alephfnon  10006  aleph0  10007  alephlim  10008  alephsuc  10009
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