>Here, if any function f applied to x and y produces the same answer, x=y. x and y are indistinguishable, and in mathematics, that implies they are identical.

>Here, if any function f applied to x and y produces the same answer, x=y. x and y are indistinguishable, and in mathematics, that implies they are identical. That is an error. They are only indistinguishable with respect to f, but it does not preclude the existence of a `g` where (exists f, g, x, y f(x) = f(y), g(x) != g(y)). >Any new function must be a composition of existing functions Based on what? This might apply for limited sets like natural numbers, but I imagine an argument similar to Cantor's diagonal can be made for others.