@jeffcliff @plotinusgroyper >If ease of construction is more important than truth connectiveness to reality. It's more of a preference thing.

Well, the way we think of it is like this:

Let's say, hypothetically, that ZFC is completely fucked somehow and we find out that we can't *actually* construct the Reals. Then what would happen is all of Real Analysis and Complex Analysis becomes fucking dust overnight, but we'd still have quite a lot of useful math lying around.

If we do it your way and Complex Numbers become just fucking dust, then *all* of our math becomes garbage and we're totally fucked.

The thing is that it is *entirely possible* that we're just completely fucking wrong about our axioms - they're *axioms* after all. We'd like very much for as much math to stay intact if we have to give up on an axiom, and we build it the way we do because we're more willing to accept "Real Numbers are garbage" than "no there aren't actually Natural Numbers."