[theemathas]

The main reason that we use real numbers is because we need real numbers to do calculus, at least in the normal way. And to do physics, we need to do calculus. You can keep approximating integrals as sums of very large number of terms, but it gets unwieldy to handle symbolically.

[moloch-hai]

Real numbers almost always give the same result as more cumbersome methods, and we are mostly only interested in such results, so it is surprising when something wacky shows up to remind us of the tightrope we walk.