From: Jim Choate <ravage@EINSTEIN.ssz.com>
Date: Sun, 19 Jan 1997 15:33:48 -0800 (PST)
To: cypherpunks@toad.com
Subject: Re: I beg you, PLEASE prove that 0.123456789101112131415 is IRRATIONAL (fwd)
Message-ID: <199701192340.RAA00844@einstein>
MIME-Version: 1.0
Content-Type: text



Forwarded message:

> 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.  

So you are saying that the Reals are a subset (ie can be constructed from)
of the Rationals?

I can create a number which is not representable by the ratio of two
integers from two numbers which are representable by ratios of two integers?

That's a nifty trick indeed, I am really impressed.

Cauchy produced a test for testing convergence. I fail to see the relevance
here, but please expound...

Dedekind Cut:

"Thus a nested sequence of rational intervals give rise to a seperation of
all rational numbers into three classes."

Just exactly where does this allow us to create Reals?


                                                   Jim Choate
                                                   CyberTects
                                                   ravage@ssz.com