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Definition df-pnf 7120
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 7121). 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 7125 and mnfnre 7126, 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 7115 . 2  class +oo
2 cc 6944 . . . 4  class  CC
32cuni 3607 . . 3  class  U. CC
43cpw 3386 . 2  class  ~P U. CC
51, 4wceq 1259 1  wff +oo  =  ~P U. CC
Colors of variables: wff set class
This definition is referenced by:  pnfnre  7125  mnfnre  7126  pnfxr  8792
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