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Definition df-pnf 9124
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 9125). 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 9129, mnfnre 9130, and pnfnemnf 10719.

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.)

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

Detailed syntax breakdown of Definition df-pnf
StepHypRef Expression
1 cpnf 9119 . 2  class  +oo
2 cc 8990 . . . 4  class  CC
32cuni 4017 . . 3  class  U. CC
43cpw 3801 . 2  class  ~P U. CC
51, 4wceq 1653 1  wff  +oo  =  ~P U. CC
Colors of variables: wff set class
This definition is referenced by:  pnfnre  9129  mnfnre  9130  pnfxr  10715
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