MinusInfinity

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

Ooops, quite right.  It's in C+, not C.  --Vitenka