I can't seem to make head or tail of the description of direct and inverse limits of abelian groups in problems 8 and 10 of the attached excerpt from Dummitt and Foote. Does anyone have a simpler or more intuitive definition of these two notions, or just an explanation of Dummit and Foote's definitions? Perhaps the definition would simplify considerably if instead of an arbitrary partially ordered indexing set, we had a sequence of abelian groups indexed by the natural numbers? Any help would be greatly appreciated. Thank You in Advance.