On Monday, 24 June 2013 21:16:36 UTC+2, Virgil wrote:
> > 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.
That is true matheology: "Since it is assumed, it does not require proof." Why don't you assume everything you desire?