 Devaney’s definition has the virtues of being precise and compact. However, objections have been raised against it. Since the time he proposed his definition, it has been shown that (2) and (3) imply (1) if the set \(K\) has an infinite number of elements (see Banks et al. 1992), although this result does not hold for sets with finite elements. More to the point, the definition seems counterintuitive in that it emphasizes periodic orbits rather than aperiodicity, but the latter seems a much better characterization of chaos. After all, it is precisely the lack of periodicity that is characteristic of chaos. To be fair to Devany, however, he casts his definition in terms of unstable periodic points, the kind of points where trajectories issuing forth from neighboring points would exhibit WSD. If the set of unstable periodic points is dense in \(K\), then we have a guarantee that the kinds of aperiodic orbits characteristic of chaos will be abundant. Some have argued that (2) is not even necessary for characterizing chaos (e.g., Robinson 1995, pp. 83–4). Furthermore, nothing in Devaney’s definition hints at the stretching and folding of trajectories, which appears to be a necessary condition for chaos from a qualitative perspective. Peter Smith (1998, pp. 176–7) suggests that Chaos\(_{d}\) is, perhaps, a consequence rather than a mark of chaos. 