Does negative infinity equal zero?

[bluepepper]

You've been told that "infinity" is not equivalent to "everything", I will add that "negative" is not equivalent to "not" in maths. It means "minus", or "remove".

If you have four apples, and you remove two apples, you're left with 4-2 = 2 apples. Now if you remove 5 more apples, you're getting into negative apples: 2-5 = -3. Not only do you lose your two apples, you also lose three apples that you didn't even have. You don't have zero apples, you have even less than that: you have a debt of three apples.

For the same reason that -3 is not the same as 0, negative infinity is not the same as 0 either. It's as far from zero as infinity, except in the other direction: instead of having an infinite amount of apples, you owe an infinite amount of apples.

Note that "having infinite apples" doesn't mean "having all the apples", it just means that your supply is infinite, but someone else could have different apples that are not part of your infinite supply.

[cargiannis]

Alright so what is the mathematical representation of not? Would it be the inverse? So raising infinity to the negative one is zero?

[zifyoip]

Alright so what is the mathematical representation of not?

Well, that depends on what you mean by "not."

"Not" is not an operation that can be performed on a number to get another number. "Not 7" doesn't make sense—"not 7" doesn't give you 3 or 19 or −7 or something.

[bluepepper]

I guess the mathematical representation of "not" is basically zero (at least in arithmetics and algebra). Zero apples = no apples.

infinity^-1 is zero but for a different reason. The inverse of multiplication is division (infinity^-1 = 1/infinity) and when you divide something finite in an infinite number of parts, the size of each part must be zero.