Virgil
Posts:
9,012
Registered:
1/6/11


Re: Joel David Hamkins on definable real numbers in analysis
Posted:
Jun 25, 2013 5:32 PM


In article <a4e85bdfb597425e90423d83cf43831a@googlegroups.com>, mueckenh@rz.fhaugsburg.de wrote:
> 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
Then what WM calls matheology is the true mathematiccs, and what WM does is a mere useless corruption of it.
It is standard practice, at least in pure mathematics, to start with an interesting list of assumptions or axioms TAKEN WITHOUT PROOF to see what conclusions can be derived from them. And the set of conclusions one can draw from some given set of assumptions quite regularly leads to a reconsideration of and modification of that original set of assumptions.
For example, the axiom sets for ZF and ZFC are the results of long sequences of creating axiom lists and seeing where they led.
Anyone, like WM, who claims to be a mathematician, but denies this, does not have any idea how pure mathematics works.
And, judging by his posts, WM does not have much of an idea how applied mathematics works either. 

