Frank J. Lhota <NOSPAM.Lhota.firstname.lastname@example.org> wrote: > "Marc Olschok" <email@example.com> wrote in message > news:3cq077F6p2umuU1@news.dfncis.de... >> ... >> For 1 < |U| < 10 there seem to be only models with |U|=4 or |U|=9. >> However, I have no idea why this is so. > > Given that you have not solved the problem, I am amazed that you were able > to determine that the only values of |U| for which a # operator exists > within the range 1 < |U| < 10 was 4 and 9. Please post how you were able to > deduce this.
Among other things it reported the 4-element model you gave in a previous posting.
> > At any rate, this discovery does suggest a conjecture on the possible values > of |U|. The sequence of possible |U| values starts with > > 0, 1, 4, 9, ... > > One can easily guess the next number in this sequence.
Certainly. But right now I have no specific idea. Since x = (xx)(xx) for every x, it might help to investigate the possible choices for y and z such that x = (xx)(xx) = yz.