From: Peter Hickman <peter@...>
Date: 2004-01-26T21:06:51+09:00
Subject: Re: ruby-math and "why is ** not abelian?"

Van Jacques wrote:

>I was reading the 1st thread in the ruby-math discussion at
>
>http://blade.nagaokaut.ac.jp/cgi-bin/scat.rb/ruby/ruby-math/
>
>(it in Japanese, but Excite has an auto translater--its interesting to
>see
>how it translates Japanese to English).
>
>If anyone cares, what I got was basically this.
>
>If + is commutative, and the successor operation to + is *, which is
>also commutative;
>(a*b = b*a), then why isn't a**b = b**a since ** is successor
>operation to * ?
>
>Some discussion of induction and Peano axioms, which I didn't think
>through.
>
>Van
>
>
>  
>
The problem is that ** is the 'raise to the power of' operator

so 2**3 = 8
but 3**2 = 9

So a**b != b**a except when a=b.

What operation did you think that ** would actually do?