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Definition df-pnf 8914
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 8915). 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 8919, mnfnre 8920, and pnfnemnf 10506.

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 8909 . 2  class  +oo
2 cc 8780 . . . 4  class  CC
32cuni 3864 . . 3  class  U. CC
43cpw 3659 . 2  class  ~P U. CC
51, 4wceq 1633 1  wff  +oo  =  ~P U. CC
Colors of variables: wff set class
This definition is referenced by:  pnfnre  8919  mnfnre  8920  pnfxr  10502
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