Comment by freehorse

> I believe real numbers to be completely natural

Are real numbers not just "a convenience" in a sense? I do not see anything "fundamental" or "natural" about dedekind cuts or any other construction of the real numbers. If anything real numbers, to me, are more built out of the convenience of having a complete field extension of the rational numbers. We could do just fine with computable numbers and avoid a lot of problems that this line of convenience leads to.