The rational numbers aren't physically real, because that would imply the ability to divide objects into exactly fractions, which generally isn't possible in a

The rational numbers aren't physically real, because that would imply the ability to divide objects into exactly fractions, which generally isn't possible in a verifiable way, which also must be consistent with the operations we want to perform. Fractions are a useful abstraction. The reality is just relations between natural numbers. The real numbers aren't invented to capture the square root of two. You can deal with that using a simpler set. The real numbers are necessary for common approaches to calculus and other forms of math that depend on a continuum of quantity. I would describe math as a tool for modeling reality, rather than understanding it. Because we really don't know much at all. All we've got are rules that are pretty damn good at predicting things under everyday conditions.