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The # Operation
Posted:
Apr 20, 2005 9:49 AM


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 associative. What is known is that # satifies the following axioms:
Axiom 1: For all x, y in U, x # ( x # y ) = x # ( x # x ) Axiom 2: For all x, y, z in U, ( x # y ) # ( y # z )
Give a simple characterization of U and the # operation. Also, if U is a finite set, what can we say about the cardinality of U?



