March 2008 (UTC) 

 :::Interesting thoughts. But still, in order to show associativity, using this example, one would have to define what a function composition is. That sort of defeats the original purpose of the example: explaining a group while avoiding a formal definition. The definition of a*b by (a*b)(x) = a(b(x)) would look awfully circular to the layman in the context of associativity. −  08:57, 17