Definition df-aleph 9992

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 10116, alephsuc 10118, and alephlim 10117. 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

Step	Hyp	Ref	Expression
1		cale 9988	. 2 class ℵ
2		char 9528	. . 3 class har
3		com 7860	. . 3 class ω
4	2, 3	crdg 8395	. 2 class rec(har, ω)
5	1, 4	wceq 1570	1 wff ℵ = rec(har, ω)

This definition is used by:  alephfnon  10115  aleph0  10116  alephlim  10117  alephsuc  10118