What is "limit point"

n. (context mathematics analysis of a set English) a point which lies in the closure of ''A''{''x''} of a set ''A''.

n. the mathematical value toward which a function goes as the independent variable approaches infinity [syn: limit, point of accumulation]

In mathematics, a limit point of a set S in a topological space X is a point x (which is in X, but not necessarily in S) that can be "approximated" by points of S in the sense that every neighbourhood of x with respect to the topology on X also contains a point of S other than x itself. Note that x does not have to be an element of S. This concept profitably generalizes the notion of a limit and is the underpinning of concepts such as closed set and topological closure. Indeed, a set is closed if and only if it contains all of its limit points, and the topological closure operation can be thought of as an operation that enriches a set by uniting it with its limit points.