I'll assume this a genuine question and give a genuine answer. > Why not groups? Because many things you would want to combine don't have inverses. Does the

I'll assume this a genuine question and give a genuine answer. > Why not groups? Because many things you would want to combine don't have inverses. Does the list [1,2,3] have an inverse? No. That's why lists form a monoid and not a group. > Why not vector spaces? Because all finite dimensional real vector spaces are isomorphic to R^n so we tend just to use the concrete instances of tuples of floating point numbers.