Well building the reals from rationals is not easy at all. It took a few decades to get a reasonable definiton. And in constructive mathematics, there are sever

Well building the reals from rationals is not easy at all. It took a few decades to get a reasonable definiton. And in constructive mathematics, there are several competing (non equivalent) definitions of the reals. It's a very deep topic, yet we seem to understand (at least in calculus) what real numbers are.