one thing to keep in mind, is that infinity as a physical entity may not even exist. we have constructed infinity from ZFC, and deduced consequences of those a

one thing to keep in mind, is that infinity as a physical entity may not even exist. we have constructed infinity from ZFC, and deduced consequences of those axioms. Many many examples in Math go against natural intuition but they are still useful for example, you say that the real number isn't "self-contradictory". Look at the banach-tarski paradox, that certainly contradicts intuition. A large part of mathematics is foregoing natural intuitive, and just follow the logical deductions of axioms. That is how we got hyperbolic geometry, which is essential to special relativity.