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Definition df-pnf 6839
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 6840). 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 6844 and mnfnre 6845, 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.)

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

Detailed syntax breakdown of Definition df-pnf
StepHypRef Expression
1 cpnf 6834 . 2 +oo
2 cc 6689 . . . 4  CC
32cuni 3571 . . 3  U. CC
43cpw 3351 . 2  ~P U. CC
51, 4wceq 1242 1 +oo  ~P U. CC
Colors of variables: wff set class
This definition is referenced by:  pnfnre  6844  mnfnre  6845  pnfxr  8442
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