Date: Jul 13, 2013 7:37 PM
Author: Peter Duveen
Subject: Re: new tutor here
This is a phenomenally long thread, so the following approach may have been mentioned already. If the groundwork has been laid with integers, one introduces a new kind of number, 1/n, where n is an integer. The basic property of 1/n is that (1/n) x n = 1.

Let's now move to a specific example, say, 1/8. 1/8 x 8 = 1. Therefore 1/8 x 8 x 1/8 x 8 = 1 x 1 = 1

= 8 x 8 x 1/8 x 1/8 = 64 x 1/8 x 1/8 = 1. But 64 x 1/64 = 1. Therefore, 1/8 x 1/8 = 1/64, which is, of course, smaller than 1/8.