NODE 644f9569Re: Dedikend Cut's and such (fwd)
Jim Choate <ravage@EINSTEIN.ssz.com>Mon, 20 Jan 1997 08:26:15 -0800 (PST)
Forwarded message:
> > Did a little research, Dedekind Cut's and such use Integers to define a
> > SPECIFIC Real to a arbitrary BUT FIXED resolution. They do not define the
> > set of Reals.
>
> They do. The set of all numbers representable by a DC is precisely
> the set of reals.
Then you are saying that using Dedekind Cut's it is possible to define the
ENTIRE set of Reals? I am assuming that entire includes all those Reals
which aren't representable by any algorithm and of which we can't even speak
(even though we are).
Another pretty nifty trick.
Jim Choate
CyberTects
ravage@ssz.com
NODE 7a9961afRe: Dedikend Cut's and such (fwd)
Kent Crispin <kent@songbird.com>Mon, 20 Jan 1997 15:19:36 -0800 (PST)
Jim Choate allegedly said:
>
>
> Forwarded message:
>
> > > Did a little research, Dedekind Cut's and such use Integers to define a
> > > SPECIFIC Real to a arbitrary BUT FIXED resolution. They do not define the
> > > set of Reals.
> >
> > They do. The set of all numbers representable by a DC is precisely
> > the set of reals.
>
> Then you are saying that using Dedekind Cut's it is possible to define the
> ENTIRE set of Reals? I am assuming that entire includes all those Reals
> which aren't representable by any algorithm and of which we can't even speak
> (even though we are).
>
> Another pretty nifty trick.
Yep. "Define" is not the same as "generate". Algorithms "generate".
--
Kent Crispin "No reason to get excited",
kent@songbird.com,kc@llnl.gov the thief he kindly spoke...
PGP fingerprint: 5A 16 DA 04 31 33 40 1E 87 DA 29 02 97 A3 46 2F