Rather, I habitually confuse the countable with countably infinite. For example, I said the set of computer programs is countable when I really meant countably

Rather, I habitually confuse the countable with countably infinite. For example, I said the set of computer programs is countable when I really meant countably infinite. Moreover, the set of inputs (which are also finite strings over a finite alphabet) is similarly countably infinite. So we can't write programs for every possible function from strings to strings.