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.