I know of one mathematician who thinks the real numbers are a peculiar construction in the context of topology because of the pathological things you can do with them — continuous nowhere-differentiable curves, space-filling curves, and so on. That’s why she studies motivic/A1 homotopy theory instead of classical homotopy theory; only polynomial functions are allowed.
I know of one mathematician who thinks the real numbers are a peculiar construction in the context of topology because of the pathological things you can do with them — continuous nowhere-differentiable curves, space-filling curves, and so on. That’s why she studies motivic/A1 homotopy theory instead of classical homotopy theory; only polynomial functions are allowed.