>>11575130>Nobody uses real numbers on a daily basis.For fuck's sake, natural numbers and rational numbers are (subsets of the) real numbers.
Don't tell me you don't use those on a daily basis.(*)
There are ways to represent (certain) irrational numbers in computers - not approximating them using floats or doubles, but actually directly working with them. (Naturally not all of them.) That's not what any sane person would ever do for non-scientific purposes, though. Use a double and you'll probably be fine. (For currency use integers.)
Most of the problems you list are due to limitations in variable size.
You may just as well say: All numbers are the same for computers, since practically all of them are past the largest representable number.
And you don't need the Reals for all those problems. The whole numbers already do that.
>The volume of the (observable) universe is 4.6×10^185 cubic Planck lengths.FTFY, and thanks for that number. I'll believe that for now without checking.
Seems in the right ballpark, though.
>This has been done at least three times:I wasn't claiming it had not been done. I was merely saying that we are talking about the Reals.
(*): I do realize one could make the same argument with complex numbers ("The Reals are the complex numbers with b=0."), but I'd argue those are a slightly different beast.
