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Definition df-pnf 9651
Description: Define plus infinity. Note that the definition is arbitrary, requiring only that be a set not in and different from (df-mnf 9652). 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 9656, mnfnre 9657, and pnfnemnf 11355.

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 9646 . 2
2 cc 9511 . . . 4
32cuni 4249 . . 3
43cpw 4012 . 2
51, 4wceq 1395 1
Colors of variables: wff setvar class
This definition is referenced by:  pnfnre  9656  mnfnre  9657  pnfxr  11350
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