
Re: 1 x 1 ?
Posted:
May 12, 2009 12:37 PM


hagman <google@voneitzen.de> wrote: > On 12 Mai, 06:59, Kayama <yano...@earth.ocn.ne.jp> wrote: >> >> If we can use the expression 1=e^{i\pi}, we can show >> 1*1=e^{i\pi}*e^{i\pi}=1 readily: >> >> if we rotate once 1 (the vector 01) by \pi rad around the origin anticlockwise on the complex plane, we obtain >> 1. Further likewise if we rotate 1 by \pi rad once more, we can obtain 1*1=1. >> >> At least I understand 1*1=1 in this way. >> >> In that way we can obtain i (imaginary unit), if we rotate 1 by \pi/2 around the origin anticlockwise. >> >> If we cannnot allow to use the expression 1=e^[i\pi}, I don't understand 1*1=1 vividly. > > Well, (1)*(1) = 1 holds in all rings, not just in the field C. > And I doubt you can prove a lot about the exponential function > without making use of (1)*(1) = 1 somewhere ...
More generally, the Law of Signs is simply the special linear case of the composition of odd functions in nearrings, see my 08 Feb 2008 post http://google.com/groups?selm=y8z1w7nf41w.fsf%40nestle.csail.mit.edu
Bill Dubuque

