 In sum, because a mathematical extension is necessarily a finite sequence of symbols, an infinite mathematical extension is a contradiction-in-terms. This is the foundation of Wittgenstein’s finitism. Thus, when we say, e.g., that “there are infinitely many even numbers”, we are not saying “there are an infinite number of even numbers” in the same sense as we can say “there are 27 people in this house”; the infinite series of natural numbers is nothing but “the infinite possibility of finite series of numbers”—“[i]t is senseless to speak of the whole infinite number series, as if it, too, were an extension” (PR §144). The infinite is understood rightly when it is understood, not as a quantity, but as an “infinite possibility” (PR §138).