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Definition df-aleph 9973
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 10099, alephsuc 10101, and alephlim 10100. 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 9969 . 2 class
2 char 9589 . . 3 class har
3 com 7878 . . 3 class ω
42, 3crdg 8438 . 2 class rec(har, ω)
51, 4wceq 1533 1 wff ℵ = rec(har, ω)
Colors of variables: wff setvar class
This definition is referenced by:  alephfnon  10098  aleph0  10099  alephlim  10100  alephsuc  10101
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