 From Cantor’s proof, however, set theorists erroneously conclude that “the set of irrational numbers” is greater in multiplicity than any enumeration of irrationals (or the set of rationals), when the only conclusion to draw is that there is no such thing as the set of all the irrational numbers. The truly dangerous aspect to ‘propositions’ such as “The real numbers cannot be arranged in a series” and “The set… is not denumerable” is that they make concept formation [i.e., our invention] “look like a fact of nature” (i.e., something we discover) (RFM II §§16, 37). At best, we have a vague idea of the concept of “real number”, but only if we restrict this idea to “recursive real number” and only if we recognize that having the concept does not mean having a set of all recursive real numbers.