The problem is that under the hood calculus is all about limits (or methods with a certain equivalence, we won't get into that). Take a derivative? that's a li

The problem is that under the hood calculus is all about limits (or methods with a certain equivalence, we won't get into that). Take a derivative? that's a limit. Take an integral? That's a limit. And limits of seemingly rational expressions are sometimes irrational, case and point the limit of (1 + 1/n)^n as n approaches infinity is euler's constant, e. So if you're taking limits with rationals you're going to find yourself with undefined limits (because irrational numbers are no longer defined) breaking things constantly. Formally, the irrationals are dense but not complete.