I'm not sure that it could be, actually. You can't use a finite amount of evidence to verify that something is infinite, so any infinity can always be replaced with a huge (or minuscule) number and the theory would make the same measurable predictions.
Sure, but calculus makes infinity sufficient, but not necessary for describing the physical world. Integers, rationals, and apparently complex numbers (presumably those with rational components) are actually necessary for describing the physical world, given our current understanding. Irrational numbers and infinities are extremely useful, but not strictly necessary.
Sorry, I'm not getting it. A large use case for complex numbers is describing things that rotate, literally or not, like oscillations, waves etc. Trigonometry lies deeply in that math and the irrational number pi pops out left and right. An approximation of pi wouldn't cut it, would it?
