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Mirrors > Home > MPE Home > Th. List > df-mnf | Structured version Visualization version GIF version |
Description: Define minus infinity as the power set of plus infinity. Note that the definition is arbitrary, requiring only that -∞ be a set not in ℝ and different from +∞ (see mnfnre 11254 and pnfnemnf 11266). (Contributed by NM, 13-Oct-2005.) (New usage is discouraged.) |
Ref | Expression |
---|---|
df-mnf | ⊢ -∞ = 𝒫 +∞ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cmnf 11243 | . 2 class -∞ | |
2 | cpnf 11242 | . . 3 class +∞ | |
3 | 2 | cpw 4602 | . 2 class 𝒫 +∞ |
4 | 1, 3 | wceq 1542 | 1 wff -∞ = 𝒫 +∞ |
Colors of variables: wff setvar class |
This definition is referenced by: mnfnre 11254 pnfnemnf 11266 mnfxr 11268 |
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