MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-aleph Unicode version

Definition df-aleph 7573
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 7693, alephsuc 7695, and alephlim 7694. 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  |-  aleph  =  rec (har ,  om )

Detailed syntax breakdown of Definition df-aleph
StepHypRef Expression
1 cale 7569 . 2  class  aleph
2 char 7270 . . 3  class har
3 com 4656 . . 3  class  om
42, 3crdg 6422 . 2  class  rec (har ,  om )
51, 4wceq 1623 1  wff  aleph  =  rec (har ,  om )
Colors of variables: wff set class
This definition is referenced by:  alephfnon  7692  aleph0  7693  alephlim  7694  alephsuc  7695
  Copyright terms: Public domain W3C validator