 To focus our inquiry, consider the case of a complex object and its proper parts. Some metaphysicians have considered the possibility that there are gunky objects: objects such that every part of them itself has proper parts. If \(A\) is gunky then it is composed of some things, the \(X\)s, such that there is more than one of the \(X\)s, and \(A\) is not amongst the \(X\)s. Pick one of those \(X\)s, \(X_1\). \(X_1\) is composed of some things, the \(Y\)s, such that there is more than one of the \(Y\)s, and neither \(A\) nor \(X_1\) is amongst the  \(Y\)s.[8]  Pick one of those \(Y\)s, \(Y_1\). \(Y_1\) is composed of some things, the \(Z\)s, such that there is more than one of the \(Z\)s, and neither \(A\), nor \(X_1\), nor \(Y_1\) is amongst the \(Z\)s. And so on. This process will never end: each item in the series is a collection of entities (a collection containing just one thing in the first case, and more than one thing in every subsequent case), and given the transitivity of parthood each thing in each collection will be a part of \(A\) and hence—since \(A\) is ex hypothesi gunky—will itself be composed of a collection of proper parts, and so we can therefore pick any member from any collection to generate the next item on the list. (Of course, a thing need not—and if it is gunky, will not—have a unique decomposition: there can be two collections of things, the \(X\)s and the \(Y\)s, each of which compose \(A\), where none of the \(X\)s is amongst the \(Y\)s and vice versa. But all we need is that there are some such collections, from which we can pick arbitrarily to get the next collection in the sequence.) Now take the infinite series that consists of \(A\) as its first element, \(X_1\) as its second element, \(Y_1\) as its third, etc. So we form this infinite sequence by taking one item from each collection that formed the previous infinite sequence: namely that item which was used to give us the collection of things that came next in the series.