On Sat, 15 Jul 2006 21:32:38 -0500, "Robert J. Kolker" <email@example.com> wrote:
>Virgil wrote: >> >> >> That may be your definition, but it is no one else's. >> >> According to the Harper Collins Dictionary of mathematics, for example, >> >> irrational: not expressible as a ratio of integers, >> >> transcendental: not the root of any polynomial equation with >> rational coefficients. >> >> Unless you can show that your "definitions" are at least compatible with >> these, yours are wrong. > >You are wasting your time. Lester neither knows nor understands >mathematics. If one insists on modeling the real numbers as the set of >points on a Euclidean straight line, one will find the transcendentals >side by side with the other real numbers.
Yes, well, of course, if one insists on saying there is a real number line then one insists on saying there is a real number line. That is not exactly true as Bob has admitted in the past. Bob acknowedged there is no one real number line in formal terms. If Bob wishes to maintain there is one real number line and there is no real number line perhaps Bob represents the epitome of a modern mathematiker.