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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 10081, alephsuc 10083, and alephlim 10082. 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 9951 | . 2 class ℵ | |
2 | char 9571 | . . 3 class har | |
3 | com 7864 | . . 3 class ω | |
4 | 2, 3 | crdg 8423 | . 2 class rec(har, ω) |
5 | 1, 4 | wceq 1534 | 1 wff ℵ = rec(har, ω) |
Colors of variables: wff setvar class |
This definition is referenced by: alephfnon 10080 aleph0 10081 alephlim 10082 alephsuc 10083 |
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