Mathematicians pay a lot of attention to real numbers simply because ones runs into them everywhere. If rational numbers were enough to make analysis, calculus,

Mathematicians pay a lot of attention to real numbers simply because ones runs into them everywhere. If rational numbers were enough to make analysis, calculus, and ultimately physics work out, we would certainly stick with those simpler objects. Real numbers are strange fellas for sure, but nature being describable by rational numbers alone ought to be testable.