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Definition df-pnf 6819
Description: Define plus infinity. Note that the definition is arbitrary, requiring only that +∞ be a set not in and different from -∞ (df-mnf 6820). 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 6824 and mnfnre 6825, and we'll also be able to prove +∞ ≠ -∞.

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 6814 . 2 class +∞
2 cc 6669 . . . 4 class
32cuni 3571 . . 3 class
43cpw 3351 . 2 class 𝒫
51, 4wceq 1242 1 wff +∞ = 𝒫
Colors of variables: wff set class
This definition is referenced by:  pnfnre  6824  mnfnre  6825  pnfxr  8422
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