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Definition df-pnf 7766
Description: Define plus infinity. Note that the definition is arbitrary, requiring only that +oo be a set not in  RR and different from -oo (df-mnf 7767). We use  ~P
U. CC to make it independent of the construction of  CC, and Cantor's Theorem will show that it is different from any member of 
CC and therefore  RR. See pnfnre 7771 and mnfnre 7772, and we'll also be able to prove +oo  =/= -oo.

A simpler possibility is to define +oo as  CC and -oo as  { CC }, but that approach requires the Axiom of Regularity to show that +oo and -oo are different from each other and from all members of  RR. (Contributed by NM, 13-Oct-2005.) (New usage is discouraged.)

Ref Expression
df-pnf  |- +oo  =  ~P U. CC

Detailed syntax breakdown of Definition df-pnf
StepHypRef Expression
1 cpnf 7761 . 2  class +oo
2 cc 7582 . . . 4  class  CC
32cuni 3704 . . 3  class  U. CC
43cpw 3478 . 2  class  ~P U. CC
51, 4wceq 1314 1  wff +oo  =  ~P U. CC
Colors of variables: wff set class
This definition is referenced by:  pnfnre  7771  mnfnre  7772  pnfxr  7782
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