`S = {str -> bool}` is actually uncountable. `S` is isomorphic to the power set (set of all subsets) of `str`, and `2^str` is at least as big as the set of real numbers, as any real number (like π) can be mapped to the set of string prefixes (like `{"3", "3.1", "3.14", ...}`). Since the reals are uncountable, so is `2^str` and `S`.