molesgallus said:
It occurs to me that there is a fundamental flaw with the concept of infinity; I can't understand it.
And you'd likely be right to do that, especially if you are a mathematician. If you are, please explain why 'infinity' and 'nothing' are not synonms. And don't read on, because the rest of my argument relies on that fact ebing accepted.
First of all, your inability to understand something does not mean it is flawed - it suggests that your comprehension is flawed. Not necessarily your fault, since infinity is rather hard to explain, and a lot of people use the term incorrectly.
Infinity = undefined = unknown.
Infinity from the root finite, as in a specific number. Infinity means an unknown number.
If I grab a handful of sand, I have grabbed an "infinite" number of grains - that is, I have no idea how many there are, and no way to count them. If I then invent a device that tells me I actually have 503,205 grains of sand, then that handful is no longer infinite - it has become finite.
There are an infinite number of stars - because we have no way to count them.
There is an infinite amount of space - because we have no way to measure it.
Is there an edge or end to the empty space beyond the edge of the known universe? We have no idea. We don't think so, but that's a best guess. Mostly we don't have any reason to believe that there's anything else out there, so we assume that nothing is. There is no way for us to get there, and no way to measure it if we did, so it remains unknown.
When people talk about infinity in math, they mean a very large, but non-specific number. For instance, numbers are infinite - you can always add 1 to the biggest number, and get a bigger number yet. So the total "number" of whole numbers is infinity - that is, an unknown (and unknowable) number that is very large.
However, if you instead said the number of numbers up to the first decimal place (ie 1.0, 1.1, 1.2, 1.3, etc) then you'd get a number ten times larger than the other infinity. The number is still infinite, but for every single number in the above infinity, there are ten numbers in this infinity.
The point of that is that infinity really just means "unknown" - and usually "unknowable" - at least by current science. Sure, there are a finite number of stars, but that number is insanely huge and there's no possible way to measure that number (because some stars are dark, some are behind others, and some are just so damn far away that their light can't reasonably reach us). Is there something beyond the "edge" of the universe? We have no idea - because we can't see that far.
tl;dr: infinity doesn't mean "nothing" - it means unknown.
