
Re: 1 x 1 ?
Posted:
Sep 16, 1999 5:47 PM


Using juxtaposition for multiplication, by association: [ab + a(b)] + (a)(b) = ab + [a(b) + (a)(b)] Then by distribution, the definition of "", a0=0a=0, a+0=0: above = ab + [a + (a)](b) = ab + 0(b) = ab. Likewise: [ab + a(b)] + (a)(b) = a[b + (b)] + (a)(b) = a0 + (a)(b) = (a)(b). A fortiori the result follows.
So, it's not "the fundamental reason" but lots of fundamental reasons. Can a simpler proof be given? Perhaps the special case (1)(1) = 1 can be proved more simply. A supplementary: is there an interesting algebraic system in which it's false?
Guillermo Phillips wrote:
> Hello All, > > Here's something I've always wondered (perhaps in my naivety). Why > should 1 x 1 = 1? > I appreciate that lots of nice things come from this, but what's the > fundamental reason for it? > > Guillermo.

