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> It very well could be an infinite number of atoms and then what?

Where I get stuck with this is how might we measure that? Continuous measurements and infinite measurements are not something we can make. We fit continuous theories to discrete measurements--and the good ones fit really well!--but until we can measure it how can we actually know? I concluded we just can't, and we have to be OK with that.

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> We fit continuous theories to discrete measurements--and the good ones fit really well!--but until we can measure it how can we actually know?

Well, physicists came up with quantum mechanics because they found a way to distinguish a genuinely discrete phenomenon.

Understanding the physical universe overlaps with a subset of math. It shouldn't constrain the abstract tools which may or may not one day be useful for that understanding.

I agree that continuity (and therefore infinity) are really useful tools. But it may also be useful to develop mathematical formalism that hews more closely to that which we can actually observe. Or not! But if nobody investigates we'll never know.

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