On 2/5/2013 10:36 AM, WM wrote: > On 5 Feb., 16:53, fom <fomJ...@nyms.net> wrote: >> On 2/5/2013 4:11 AM, WM wrote: >> >>> On 5 Feb., 01:26, Virgil <vir...@ligriv.com> wrote: >> >>>> If, as WM claims, there are at most countably many ways of accessing >>>> reals and, as Cantor claimed, there are more than countably many reals, >>>> then ... >> >>> Then the axiom that every real can be put in trichotomy with every >>> rational number is contricted. Then ZFC contradicts analysis. >> >> In the logical type hierarchy that *defines* a real number, >> the order relation of the rationals is inherited. The >> rationals that are reals are distinct from the rationals >> from which the real numbers are defined. > > Please name a difference that can be proved to exist in mathematics.