Exactly. I was trying to avoid any mathematical jargon while describing monoids because they are such general and pervasive structures in programming. Further, being able to construct useful new monoids is crucial for making full use of a finger tree and I didn't want to have someone find an interesting structure unapproachable because they had to walk through an abstract algebra jargon storm in order to understand it. I realize I referenced associativity without describing it, so I didn't quite achieve my goal, but hopefully the examples got the idea across to someone who might otherwise have dismissed it due to the perception that it was too academic and unapproachable.

As an aside, trying to remove the jargon from a definition like this is surprisingly hard and really expands the size of the definition. I think it is still worthwhile to try when writing for a general audience because algebraic structure is everywhere and very useful to recognize for people who are interested in rigorously manipulating abstraction, i.e. programmers.