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Definition df-pnf 8869
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 8870). 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 8874, mnfnre 8875, and pnfnemnf 10459.

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 8864 . 2  class  +oo
2 cc 8735 . . . 4  class  CC
32cuni 3827 . . 3  class  U. CC
43cpw 3625 . 2  class  ~P U. CC
51, 4wceq 1623 1  wff  +oo  =  ~P U. CC
Colors of variables: wff set class
This definition is referenced by:  pnfnre  8874  mnfnre  8875  pnfxr  10455
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