[godelski]

I'm not sure how to answer because I'm not sure which question you're asking.

For infinity, neither can you calculate +/-inf but there also aren't an infinite set of representable numbers on [0,1]. You get more with fp64 and more with fp128 but it's still finite. This is what leads to that thing where you might add numbers and get something like 1.9999999998 (I did not count the number of 9s). Look at how numbers are represented on computers. It uses a system with mantissa and exponents. You'll see there are more representable numbers on [-1,1] than in other ranges. Makes that kind of normalization important when doing math work on computers.

This also causes breakdowns in seemingly ordinary math. Such as adding and multiplying not being associative. It doesn't work with finite precision, which means you don't want fields to with in. This is regardless of the precision level, which is why I made my previous comment.

For real numbers, we're talking about computers. Computers only use a finite subset of the real numbers. I'm not sure why you're bringing them up