We shall call the "transreal line" the union of the real line, and the three points, infinity, -infinity and ? (which he denotes as phi). Having gone over his papers with a friend (during the brief cessations from hysterical laughter) we deciphered the exact content of his "discovery". Essentially he has formulated a weak and useless version of real analysis with a horrendous number of axioms and added on a point ? which is disconnected from the real line unioned with infinity and -infinity. All of the objections I have seen to his system are not valid manipulations in it for example, you are not permitted to use >, = or ?" is not allowed. I have briefly scanned his list but I don't see where he addresses the question of whether he allows 1/(-x) = -1/x as permitting such a thing within his system would immediately cause infinity = -infinity which is not allowed by an earlier axiom (i.e. that it is internally inconsistant).