>>13896942You will never be a real number system. You have no complete system of inference rules, you have no elegant construction, you are not computable. You are an ordered field twisted by second order logic into a crude mockery of nature’s perfection.
All the “validation” you get is two-faced and half-hearted. Behind your back people mock you. Mathematicians are disgusted and ashamed of you, your “friends” laugh at your ghoulish, unintuitive properties behind your back.
Students are utterly repulsed by you. Hundreds of years of teaching have not allowed anyone to understand limits. Even First order models which “look countable” look uncanny and unnatural to a man. The indeterminate cardinalities of your subsets are a dead giveaway. And even if you manage to get an impressionable mathematician home with you, he’ll turn tail and bolt the second he gets a whiff of your continuous, non-differentiable functions.
