Forget Flat Earth Theory, now we have Flat Universe Theory!

[TheDarkestOfAngels]

The surface of a sphere is infinite. You can keep going on it and never reach an end.

The surface of a sphere is not infinate in any respect to volume or space.

It is possible to have different degrees of infinity. Imagine two infinities. One is an ordered collection of all real numbers (..... -1.000000, -0.999999999, ....etc) from negative infinity to positive infinity, the other an ordered collection of all integers (... -1, 0, 1.....) from negative infinity to positive infinity. The infinite number of all real numbers is definitely larger than the infinite number of all integers. You can prove this to yourself by seeing that you can map every one of the infinite number of integers onto a unique real number, ( 1 to 1.00000, 2 to 2.00000, etc) and you still have an infinite number of unmapped real numbers left (0.9999999, 1.0000001, 1.0000002, etc)

You are indeed correct that mathmatical infinities are quite possible.
This cannot and never does apply to reality. You cannot have an infinate amount of space in a box just because you can keep moving indefinately in one direction due to being able to continuously slow down enough to never actually impact one side of the box.
This is a major stretch.

But you can make the smaller infinity that is the count of integers larger by also including a count of all numbers divisible by 0.5, So something infinite can still expand (......-1, -0.5, 0, 0.5, 1......) This is what is happening when infinite universe expands.

You certainly can - mathmatially - it just doesn't apply to reality due to a number of huge problems it can create.
For example, a 'smaller infinity' expanding into a 'larger infinity' is problematic because they 're both infinate in space and volume and therefore must expand into the larger universe using other sets of infinities - the 'dark' energy responsible for the expansion of the universe would have to be infinate as well, for example.
... eh. The short of it is that an infinity in one dimension essentilaly requires infinities in others that would ultimately result in a reality that we know of that couldn't exist.

The universe can be infinite and still expand because just like expansion of the infinite count of integers, you can take each discreet subpart of the infinite universe, say a 1 light year length analogous to say part of count of integers between 2 and 3, and expand it to 2 light years, analogous to inserting 2.5 between 2 and 3.

So the universe can be infinite, and still expand. It doesn't expand into anything, each part of it just expands.

I don't think it can be without serious problems of a mathmatically-relevant system that's supposed to correspond to reality. Every infinity that I've seen apply to reality has had serious problems in actually making a model that's consistent with reality-based predictions - which is the main reason why all of the physics that I know slightly better behind the mathmatical models of the universe all list it as finite in size and only go up so far in describing reality, with possibilities and theories that go steps above. I've never seen a model of any kind that's relevant today that has an infinity in any respect that doesn't cause serious problems in generating an accurate model of reality.