I'm fully aware of the complexities of real numbers. But I also know they are essential to derive any advanced mathematics. All the normal derivations and defin

I'm fully aware of the complexities of real numbers. But I also know they are essential to derive any advanced mathematics. All the normal derivations and definitions of calculus depend on properties unique to the reals. And while it might be possible to re-derive calculus using computable numbers (I'm fairly sure it is, but not completely), a great many results using topology absolutely depend on the properties of the reals that the domain of computable numbers simply don't have.