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Hey, I feel you, my first thought was that continuously differentiable functions aren't physical :)

The first order theories of the real numbers using addition and multiplication are decidable [0], while FO theories of the integers under the same operations are not.

[0] https://en.wikipedia.org/wiki/Decidability_of_first-order_th...

Wikipedia can be confusing..

https://mathoverflow.net/questions/134259/is-the-first-order...

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