Convergence

Two items are said to be convergent if in time they become increasingly like each other. Equally they are divergent if they keep moving apart. However, the word convergent is often used with the second item left implicit.

For example, in mathematics, convergence describes limiting behaviour, particularly of an infinite sequence or series (mathematics) toward some unknown limit. To assert convergence is to claim the existence of an unknown limit, such that for any degree of accuracy required you can always be sure to be that accurate provided you have gone far enough. In particular cases the definitions of 'far enough' metric and the other terms vary. In maths the opposite of convergence is divergence, which may be some kind of oscillation of values, or unrestricted growth (recognised as the case of an infinite limit). An infinite series that is divergent does not a priori have any mathematical value. That is, it cannot be used for meaningful computations of its value. Such series are indeed applied: as generating functions, as asymptotic series, or via some summation method.

In general, an infinite sequence of points of a topological space is said to converge to a point x if every neighborhood of x contains all but a finite number of points of the sequence. See also net (topology), uniform convergence.

One question of interest is whether WikiPedia is in broad terms a convergent or divergent phenomenon. Will the number of pages grow without limit (which is possible given arbitrarily long phrases can be used for page names) or will WikiPedia start evolving toward a finished work, or a work where limits exist to changes (with news and topical issues only changing)?