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Definition df-pnf 9955
 Description: Define plus infinity. Note that the definition is arbitrary, requiring only that +∞ be a set not in ℝ and different from -∞ (df-mnf 9956). We use 𝒫 ∪ ℂ to make it independent of the construction of ℂ, and Cantor's Theorem will show that it is different from any member of ℂ and therefore ℝ. See pnfnre 9960, mnfnre 9961, and pnfnemnf 9973. A simpler possibility is to define +∞ as ℂ 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 ℝ. (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 9950 . 2 class +∞
2 cc 9813 . . . 4 class
32cuni 4372 . . 3 class
43cpw 4108 . 2 class 𝒫
51, 4wceq 1475 1 wff +∞ = 𝒫
 Colors of variables: wff setvar class This definition is referenced by:  pnfnre  9960  mnfnre  9961  pnfxr  9971
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