Re: No positive integers less than on

From: Bill Dubuque (wgd_at_nestle.csail.mit.edu)
Date: 01/19/05 

Date: 18 Jan 2005 23:35:29 -0500

Alejandra <Sigma1023@hotmail.com> wrote:
>
> I have been assigned to prove that there are no positive integers less
> than one. My teacher gave the hint to use the well-ordering principle.

HINT 0 < n < 1 => 0 < nn < n < 1

The same type of descent can be used in irrationality proofs, e.g.
see my prior post [1]. One is essentially exploiting the fact that
rings of (algebraic) integers are DISCRETE, whereas the corresponding
rings of (algebraic) fractions are DENSE. For much more see [1].

--Bill Dubuque

[1] http://google.com/groups?selm=y8zptmfj7im.fsf@nestle.ai.mit.edu
    http://groups-beta.google.com/group/sci.math/msg/6556056f3621d4c1

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