On 9 Dez., 22:29, Virgil <vir...@ligriv.com> wrote:
> > With respect to real numbers we need not only the answer to the > > question whether x is a real number, but we need trichotomy with > > respect to every real number. Undefinable numbers cannot satisfy this > > need. > > WM may need it, but if the issue is only whether something is or is not > a real number, there are definitions of what is a real number that does > need not establish its trichotomy with anything. > > Trichotomy is a derived property not a definitional one of some > definitions of the reals.
Then you have another idea of real number. Be happy with it. For doing mathematics including real calculations trichotomy is indispensable.