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


Re: Joel David Hamkins on definable real numbers in analysis
Posted:
Jun 23, 2013 6:18 PM


In article <9bbd8a08dd03472bbdda9da7da5cc1a2@googlegroups.com>, mueckenh@rz.fhaugsburg.de wrote:
> On Sunday, 23 June 2013 18:10:30 UTC+2, Zeit Geist wrote: > > > First, no one can just wellorder the real numbers. > > > Correct. But Zermelo has "proved" that someone *can*.
That proof says that if one assumes ZFC then a well ordering of the reals is possible, but does not prove that anyone in particular capable of producing that possibility.
The Reimann hypothesis is generally thought to be provable, but no one has as et managed to prove it.
Fermat's last theorem was for a long time unproven though provable, and its proof, when found, was of considerable length and difficulty.
So in the mathematics outside of WMytheology, there is a considerable difference between something being doable and its having been done.
While in ZFC well ordering the reals may have been proven theoretically doable, it has certainly not yet been done there or in any other axiom system.
> And Fraenkle has been > sceptical about that, because, although there have been great efforts, nobody > "up to now" has accomplished it.
FLT took from 1537, when it was first conjectured until 1995 to be finally proven.
The Reimann hypothesis, first proposed in 1859, while generally accepted as true, has yet to be proven true. > > > The fact is that given certain assumptions about the real numbers, then one > > can show that a well ordering of them is logical necessity. > > In fact it is a logical necessity, even without any assumptions. Not for any but finite sets, so that "Every set is well ordered" can only hold in such backwaters of mathematics such as WM's wild weird world of WMytheology that are limited to only actually finite sets. NOte that every finite ordered set is wellordered, so that in WM's wild weird world of WMytheology every ordered set is automatically wellordered. Thus, among other things, in WM's wild weird world of WMytheology, neither the set of all rationals nor the set of all reals can be densely ordered since dense sets cannot be finite and all sets in WMytheology are required to be finite.
> > > We already Know that you reject the axioms of ZFC, > > Not even that. I reject only the erroneous interpretation of the axiom of > infinity.
WH also rejects the axiom of union,
For every set A there exists the set {A} is obviously true > > > Is Euclidean Geometry the absolute truth? > > In Euclidean space Euclidean geometry is the absolute truth.
In the wild weird world of WMytheology, WM's insanity is claimed to be sane. 

