Re: Well Ordering the Reals

Virgil said:
> In article <MPG.1ddc18dcd6f3c38e98a6a2@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> Tony Orlow <aeo6@xxxxxxxxxxx> wrote:
>
> > Daryl McCullough said:
> > > Tony Orlow says...
> > >
> > > >Well, that is what I am asking. How does one prove that such an ordered
> > > >subset
> > > >actually includes ALL the reals, rather than just the rationals or some
> > > >other
> > > >type of real? I don't think this enumeration misses one point on the line,
> > > >but
> > > >how do I prove this?
> > >
> > > How do you prove something that is provably false? Well, first
> > > you prove a contradiction. Everything follows from a contradiction.
> > >
> > > --
> > > Daryl McCullough
> > > Ithaca, NY
> > >
> > >
> > No one has proven this false. If you think you can, then please show the
> > proof.
>
> What has been proved is that, regardless of whether it includes all
> reals, is ti not a well ordering of all reals.
>
Okay, perhaps it does not qualify as a well ordering. I wouldn't mind proving
it contains all the reals. Then again, deductive proof isn't as much fun as
pattern derivation and the development of solutions to problems. I think this
set is worth playing with.
--
Smiles,

Tony
http://www.people.cornell.edu/pages/aeo6/WellOrder/
.

Relevant Pages