From: Kent Crispin <kent@songbird.com>
Date: Mon, 20 Jan 1997 15:19:36 -0800 (PST)
To: ravage@EINSTEIN.ssz.com (Jim Choate)
Subject: Re: Dedikend Cut's and such (fwd)
In-Reply-To: <199701201626.IAA12828@toad.com>
Message-ID: <199701210021.QAA15476@songbird.com>
MIME-Version: 1.0
Content-Type: text


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