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Definition df-pnf 9173
Description: Define plus infinity. Note that the definition is arbitrary, requiring only that be a set not in and different from (df-mnf 9174). We use to make it independent of the construction of , and Cantor's Theorem will show that it is different from any member of and therefore . See pnfnre 9178, mnfnre 9179, and pnfnemnf 10768.

A simpler possibility is to define as and as , but that approach requires the Axiom of Regularity to show that and are different from each other and from all members of . (Contributed by NM, 13-Oct-2005.) (New usage is discouraged.)

Assertion
Ref Expression
df-pnf

Detailed syntax breakdown of Definition df-pnf
StepHypRef Expression
1 cpnf 9168 . 2
2 cc 9039 . . . 4
32cuni 4043 . . 3
43cpw 3826 . 2
51, 4wceq 1654 1
Colors of variables: wff set class
This definition is referenced by:  pnfnre  9178  mnfnre  9179  pnfxr  10764
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