In article <firstname.lastname@example.org>, email@example.com wrote:
> On Monday, 24 June 2013 00:44:20 UTC+2, Virgil wrote: > > > Nothing in any standard axiom system for the reals requires that there be > > any numeral for any number, except possibly those named by 0 and 1. > > Ever real number must be in trichotomy with every rational number. Without > digits this is very hard to prove. Without knowing and without being able to > address the real at all, it is impossible to prove.
But since it is assumed as a part of the definition of any ordered field of reals, it does not require proof. --