We're so used to dealing with real numbers it's easy to forget they're terrible. These puppies are a particularly egregious example I like to point to - functions that preserve addition but literally black out the entire x-y plane when plotted. On rational numbers all additive functions are automatically linear, of the form mx+n. There's no nice in-between on the reals, either; it's the "curve" from hell or a line.

Hot take, but I really hope physics will turn out to work without them.