 One way to visualize there being an “end” that could have more elements beyond it is to consider the rationals of the form \(1/n\) for all nonzero integers \(n\), in increasing order. This list starts out \(-1/1, -1/2, -1/3,\ldots\) and after listing infinitely many negative rationals of that form, with no greatest such, switches over to positive rationals, with no first such, finally ending with 1/3, 1/2, 1/1. The entire list is discrete in the sense that every rational except the endpoints \(-1/1\) and 1/1 has a well-defined predecessor and successor in this subset of the rationals, unlike the situation for the set of all rationals between \(-1/1\) and \(1/1\). This would no longer be the case were we to introduce the rational 0 “in the middle”, which would have neither a predecessor nor a successor.)