> You’re only able to prove that ordering of the reals (and that it’s impossible to show) because you are computing the abstract structure underlying the reals (which is based on some lower level ideas etc.) Just because a problem is computationally hard with a step by step CPU doesn’t mean it isn’t computation.

The set of computable real numbers is countable and thus has measure zero. In other words, almost all real numbers are non-computable, and almost all has an exact definition.

So you can’t compute the real numbers unless you’re meaning something else by computing.