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Definition df-aleph 9358
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 9481, alephsuc 9483, and alephlim 9482. 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 9354 . 2 class
2 char 9009 . . 3 class har
3 com 7568 . . 3 class ω
42, 3crdg 8036 . 2 class rec(har, ω)
51, 4wceq 1530 1 wff ℵ = rec(har, ω)
Colors of variables: wff setvar class
This definition is referenced by:  alephfnon  9480  aleph0  9481  alephlim  9482  alephsuc  9483
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