From: mpd@netcom.com (Mike Duvos)
Date: Sun, 19 Jan 1997 18:23:19 -0800 (PST)
To: cypherpunks@toad.com
Subject: [Math Noise]
Message-ID: <199701200223.SAA17184@netcom19.netcom.com>
MIME-Version: 1.0
Content-Type: text/plain


Jim Choate <ravage@EINSTEIN.ssz.com> writes:

 > In reference to numbers which you can't describe, if you
 > examine the work they are ALL in the Complex domain, none of
 > them are Real's.

Only countably many real numbers, or members of any uncountable
set, are denumerable. It is the property of being uncountable,
rather than of being real or complex, which is important here.

In general, only countably many members of any uncountable set
can be precisely specified within any formal system, given names
comprised of strings of symbols, or other similar things.

 > Complex numbers deal with areas, not with lengths.

It is often convenient, such as when drawing contour maps, to
consider the complex numbers to be in 1-1 correspondence with the
points of the plane.  However, I wouldn't necessarily consider
regions of the complex plane to have "area" in the Euclidian
sense.

 > If there existed a Real for which we could not describe
 > this would imply that we could not draw a line of that
 > length.

We can't physically draw a line segment to arbitrary high
precision. We can conceive of the notion of line segments being
in 1-1 correspondence with the reals, but we can specify at most
countably many "finitely denumerable" line segments if we wish to
discuss their lengths individually.

--
     Mike Duvos         $    PGP 2.6 Public Key available     $
     mpd@netcom.com     $    via Finger.                      $