Date: Nov 28, 2012 1:07 PM
Author: Paul A. Tanner III
Subject: Re: Some important demonstrations on negative numbers
On Wed, Nov 28, 2012 at 11:45 AM, Joe Niederberger

<niederberger@comcast.net> wrote:

...

> Let's look at negative numbers again. "Formally" we may write -1 < 0, and -1/1 = 1/-1. This perplexes mathematicians for a long time:

>

> http://www.ma.utexas.edu/users/mks/326K/Negnos.html

>

> One can say "just accept it, because it makes other things work out nicely". That's the "formal" approach.

>

Not to some of us. The formal approach is to prove it.

>

> Or one can attempt to understand it another way that grounds it in the everyday.

Or one can prove it (where "it" could be the more general -(a/b) =

a/(-b) for all elements in the set even if the set contains no

identity element).