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).