About mathematics and the physical world Suppose it is proven that in the physical universe all magnitudes are finite:


*

*there are no infinitely long magnitudes.

*there are no infinitely small magnitudes.
Then:
Would we get a mathematic contradiction?
If we assume this to be true, then: would all the notions of infinite, and consequently, integrals, derivatives, limits, etc will have to be rewritten using finite operations?, e.g., sums instead of integrals?
Under this assumption, what kind of applicability would have (lets say) the concept of infinite and maths with infinite magnitudes?
Well, one can say, what's the problem, we can preserve math as it is, however, the implications of doing this seems to be risky...

No. I think you have a fundamental misconception of the relationship between physics and mathematics. Mathematics can be very useful in physics, and the development of mathematics has very often been guided by what might be useful in physics, but it doesn't rely on physics. You can't get a mathematical contradiction by showing anything about the physical world. That's not specific to infinity, but a very general consequence of the relationship between the two disciplines. Many branches of mathematics that make use of infinite sets are tremendously useful in physics, and that wouldn't change if it turned out that this is due to some approximation to an even more successful finite model.
