Re: The # Operator

"Frank J. Lhota" <NOSPAM.lhota@xxxxxxxxxxx> writes in article <W%5he.43$E05.31@trndny09> dated Fri, 13 May 2005 18:05:42 GMT:
>I recall seeing this problem used as a means of testing software that does
>Mathematical deductions. I though it might also make for an entertaining
>recreational algebra problem.
>
>We have a set U with a binary operation #. It is not known if # is
>commutatve, or if # is associative. What is known is that # satifies the
>following
>axioms:
>
>Axiom 1: For all x, y in U, x # ( x # y ) = x # ( x # x )

So you can calculate x # ( x # y ) without knowning the value of y.

>Axiom 2: For all x, y, z in U, ( x # y ) # ( y # z ) = y

Again, you can calculate ( x # y ) # ( y # z ) without knowing x or z.

>if U is a finite set, what can we say about the cardinality of U?

I'd say it's finite. :^) (What did you really mean to ask?)

--Keith Lewis klewis {at} mitre.org
The above may not (yet) represent the opinions of my employer.
.