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An associative binary operation 
20080908 

From Skye: Suppose that * is an associative binary operation on a set S. Show that the set H={a E S such that a*x=x*a for all x E S} is closed under *. (We think of H as consisting of all elements of S that commute with every element in S.)
Thanks! Answered by Harley Weston. 





Binary operations 
20070730 

From jim: prove or disprove:
Every binary operation on a set consisting of a single element is both commutative and associative.
Answered by Penny Nom. 


