From: Michael Barr <barr@barrs.org>
To: "Stephen H. Schanuel" <schanuel@adelphia.net>
Cc: categories@mta.ca, Stephen H Schanuel <schanuel@ACSU.Buffalo.EDU>
Subject: Re: Reals a la Eudoxus (updated from re: Tate Reals)
Date: Wed, 19 Jan 2000 20:05:27 -0500 (EST) [thread overview]
Message-ID: <Pine.LNX.4.10.10001192001550.21007-100000@triples.math.mcgill.ca> (raw)
In-Reply-To: <000c01bf622e$0ddd7c60$80213018@buf.adelphia.net>
I don't want to be disagreeable, but it seems clear to me that this
construction gives Cauchy reals, not Dedekind reals and only the latter
can be said to go back to Eudoxus. Indeed, given a nearly function f,
with bound B on the near linearity, it is easy to see that |(fn/n) -
(fm/m)| =< B(1/n + 1/m) so that the sequence fn/n is Cauchy.
Michael
prev parent reply other threads:[~2000-01-20 1:05 UTC|newest]
Thread overview: 2+ messages / expand[flat|nested] mbox.gz Atom feed top
2000-01-19 3:34 Stephen H. Schanuel
2000-01-20 1:05 ` Michael Barr [this message]
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