The set of computable numbers is actually countable (see ref. linked above). It has to be by definition because the set of finite computer-programs is itself co

The set of computable numbers is actually countable (see ref. linked above). It has to be by definition because the set of finite computer-programs is itself countable. This is the whole point of the un-reality of "real" numbers: "all" of it (= measure 1) is uncomputable except a "tiny" measure-0 set.