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Description: Define plus infinity.
Note that the definition is arbitrary, requiring
only that  be
a set not in  and
different from 
(df-mnf 6655). We use    to make it
independent of the
construction of ,
and Cantor's Theorem will show that it is
different from any member of and therefore . See pnfnre 6665,
mnfnre 6666, and pnfnemnf 6707.
A simpler possibility is to define |
| Ref | Expression |
|---|---|
| df-pnf |
  |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cpnf 6650 |
. 2
 | |
| 2 | cc 6384 |
. . . 4
| |
| 3 | 2 | cuni 3177 |
. . 3
|
| 4 | 3 | cpw 3032 |
. 2
|
| 5 | 1, 4 | wceq 1298 |
1
 |
| Colors of variables: wff set class |
| This definition is referenced by: pnfxr 6660 pnfxrOLD 6661 mnfxrOLD 6663 pnfnre 6665 mnfnre 6666 |
, but that approach requires the Axiom of
Regularity to show
that