From: mpd@netcom.com (Mike Duvos)
Date: Sun, 19 Jan 1997 14:55:22 -0800 (PST)
To: Cypherpunks@toad.com
Subject: Re: I beg you, PLEASE prove that 0.123456789101112131415 is IRRATIONAL (fwd)
In-Reply-To: <199701191919.NAA00377@einstein>
Message-ID: <199701192255.OAA05514@netcom23.netcom.com>
MIME-Version: 1.0
Content-Type: text/plain


Jim Choate writes:

> "If every segment is to have a numerical measure as its length, then a new
> domain of numbers is needed, an extension to the domain of rational numbers.
> This new domain can no longer be constructed, as in the previous case, by
> number pairs. But hints for its construction are provided by a theoretical
> analysis of the measuring process for segments."

> A mathematicaly rigorous defintion of the class of numbers called 'Real'
> is that which equates the members of that set to the possible lengths of an
> arbitrary line segment.

This seems a tad circular, as the real number line, from which line 
segments are constructed, is a copy of the set of real numbers. 

One can construct the reals from the rationals quite easily using any
of several well-known methods, such as equivalence classes of Cauchy 
sequences, or Dedikind cuts.  

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