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Definition df-pnf 7062
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 7063). 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 7067 and mnfnre 7068, 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 7057 . 2  class +oo
2 cc 6887 . . . 4  class  CC
32cuni 3580 . . 3  class  U. CC
43cpw 3359 . 2  class  ~P U. CC
51, 4wceq 1243 1  wff +oo  =  ~P U. CC
Colors of variables: wff set class
This definition is referenced by:  pnfnre  7067  mnfnre  7068  pnfxr  8692
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