In reply to ajsteele:
> I think I am coming at this wrong, it started as a facetious question but I'm now really intrigued by the concept of infinity. I think I was imagining a massive number earlier, 1 so long it is currently incomprehensible but after thinking for a bit I'm now thinking it's more likely to be a language construct
Yes, sort of. Insofar as a lot of maths doesn't talk about "infinity" as a number, but as part of a concept, like "f(x) does this as x tends to infinity" meaning roughly "you can find some X such that f(x) does this for all x > X".
Other times, in a computation, you might use "infinity" as a shorthand for "something that's automatically bigger than anything except another infinity".
Meanwhile, set theory, and other areas of maths that are closely linked to it, start from the definition of an infinite collection of objects. Specifically, an infinite collection of objects is the one that can be put into one-to-one correspondence with "itself minus some stuff" - eg the set of natural numbers (1, 2, 3, 4...) is in one to one correspondence with the set of multiples of ten (10, 20, 30, 40...), even though intuitively the set of natural numbers includes "more stuff". The fact that you can keep mapping 70 -> 700, 1,000,000 -> 10,000,000, Graham's number -> Graham's number * 10 etc without running out of stuff is basically what we mean by it being infinite. "Infinite numbers" are then defined to be (roughly) the sizes of infinite sets.
Algebraic geometry uses infinity to mean something like "the point that you add beyond both ends of a number line so you can think of it as looping around into a circle." Although done properly it uses a slightly more rigorous definition than that!
> What I mean by that is, infinite can mean different things at different times depending on the context,
Yes, sort of.
> I'm thinking a low type of "infinity" could be -275 celcius as that is below absolute zero so is infinitely colder than anything we know possible. Am I on the right lines here?
Not in a mathematical sense for that one - "infinitely cold" doesn't really mean anything, and I can't really see why it would mean "colder than is physically possible".
One normal situation where "infinite" comes into play in talking about reality is probably when you pretend something's infinitely big or far away because it's big enough or far enough away to make no difference - so if you're doing calculations on the trajectory of a cricket ball, you can treat alpha-centauri as being infinitely far away, because it's so far away that its gravitational pull is irrelevant.
Similarly when calculating how a sardine propels itself, you can treat the ocean as infinite (because the effects on the sardine caused by the precise size and shape of the ocean are negligible) whereas when calculating the likely fluctuations in the gulf stream this summer you can't because they aren't.