 The second problem with interpreting the infinite division as a repeated division of all parts is that it does not divide an object into distinct parts, if objects are composed in the natural way. To see this, let’s ask the question of what parts are obtained by this division into 1/2s, 1/4s, 1/8s, …. Since the division is repeated without end there is no last piece we can give as an answer, and so we need to think about the question in a different way. If we suppose that an object can be represented by a line segment of unit length, then the division produces collections of segments, where the first is either the first or second half of the whole segment, the second is the first or second quarter, or third or fourth quarter, and in general the segment produced by \(N\) divisions is either the first or second half of the previous segment. For instance, writing the segment with endpoints \(a\) and \(b\) as \([a,b]\), some of these collections (technically known as ‘chains’ since the elements of the collection are ordered by size) would start \(\{[0,1], [0,1/2], [1/4,1/2], [1/4,3/8], \ldots \}\). (When we argued before that Zeno’s division produced uncountably many pieces of the object, what we should have said more carefully is that it produces uncountably many chains like this.)