On Wed, Nov 28, 2012 at 11:45 AM, Joe Niederberger <firstname.lastname@example.org> 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).