I don't know if you're still reading this, but... Using Taylor series as a number system is just a hypothetical. Any systematic way of describing numbers could

I don't know if you're still reading this, but... Using Taylor series as a number system is just a hypothetical. Any systematic way of describing numbers could be a number system. Irrationals can't be represented as ratios, but beyond that, some have other finite representations, and others have none.