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Mirrors > Home > MPE Home > Th. List > df-aleph | Structured version Visualization version GIF version |
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 9099, alephsuc 9101, and alephlim 9100. 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.) |
Ref | Expression |
---|---|
df-aleph | ⊢ ℵ = rec(har, ω) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cale 8972 | . 2 class ℵ | |
2 | char 8628 | . . 3 class har | |
3 | com 7231 | . . 3 class ω | |
4 | 2, 3 | crdg 7675 | . 2 class rec(har, ω) |
5 | 1, 4 | wceq 1632 | 1 wff ℵ = rec(har, ω) |
Colors of variables: wff setvar class |
This definition is referenced by: alephfnon 9098 aleph0 9099 alephlim 9100 alephsuc 9101 |
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