About a previous incorrect claim that MinusInfinity was itself real, Bobacus asked:
In what sense is it a real number? All my real numbers are > x for some real x, so MinusInfinity as defined above is not real. Is there a DeepAndMeaningfulReason? from SetTheory? or limit theory? --Bobacus
Minus infinity is, indeed, not a number in R, though it is a number in C which has been added in order to make C work. And it's put in a place where it would be in R, if R were just a little big bigger. Its reality is fluffy. --Vitenka
Mmm, I wouldn't say it's in C either. The standard phrases as I recall were "the ComplexPlane" C for { x + y i: x, y in R}, and the ExtendedComplexPlane being C plus the PointAtInfinity, which is viewed as the same thing as the PointAtMinusInfinity. So MinusInfinity is no more a complex number than it is a real one. It is however a perfectly good SurrealNumber? in Cantor's sense. --AlexChurchill
For people with some concepts of infinity, the idea of MinusInfinity is very counterintuitive. AlexChurchill has never found it so. He can, however, understand how people can find MinusZero hard to understand.