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