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Definition df-pnf 10666
Description: Define plus infinity. Note that the definition is arbitrary, requiring only that +∞ be a set not in and different from -∞ (df-mnf 10667). We use 𝒫 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 10671, mnfnre 10673, and pnfnemnf 10685.

A simpler possibility is to define +∞ as and -∞ as {ℂ}, 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 +∞ = 𝒫

Detailed syntax breakdown of Definition df-pnf
StepHypRef Expression
1 cpnf 10661 . 2 class +∞
2 cc 10524 . . . 4 class
32cuni 4832 . . 3 class
43cpw 4537 . 2 class 𝒫
51, 4wceq 1528 1 wff +∞ = 𝒫
Colors of variables: wff setvar class
This definition is referenced by:  pnfnre  10671  mnfnre  10673  pnfex  10683
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