If you give it the up-front caveat “this can represent all rational numbers and at least some algebraic irrationals”, I think that rules out the polynomial appromixation approach, since you can’t give arbitrary arguments and get intermediate values by continuity. But I’m not certain of that.
If you give it the up-front caveat “this can represent all rational numbers and at least some algebraic irrationals”, I think that rules out the polynomial appromixation approach, since you can’t give arbitrary arguments and get intermediate values by continuity. But I’m not certain of that.