Now, as in the case of sequences, we are interested in the "limit" of a directed set. According to what was said above, this would be an element that is the most general piece of information that extends the information of all elements of the directed set, i.e. the unique element that contains "exactly" the information that was present in the directed set, and nothing more. In the formalization of order theory, this is just the least upper bound of the directed set. As in the case of limits of sequences, least upper bounds of directed sets do not always exist.