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In mathematics, a sequence <math> a_n</math> is generally said to '''converge''' to <math>x</math> if roughly speaking as <math> n </math> goes to infinity <math> a_n</math> gets closer and closer to <math>x</math> and stays there.  Rigorously, <math> a_n</math> is said to converge to <math>x</math> if for all <math>\epsilon>0</math> there exists N such that for all n > N we have <math>|a_n -x| < \epsilon </math>.

In a [[metric space]] (X, d), a [[sequence]] <math> a_n</math> in X is said to '''converge''' to a point <math>x</math> if roughly speaking as <math> n </math> goes to infinity <math> a_n</math> gets closer and closer to <math>x</math> and stays there.  Rigorously, <math> a_n</math> is said to converge to <math>x</math> if for all <math>\epsilon>0</math> there exists N such that for all n > N we have <math>d\left (a_n, x\right ) < \epsilon </math>.

Similar definitions can be made for convergence of functions.

Similar definitions can be made for convergence of [[function]]s.

[[Category:Mathematics]]

[[Category:Topology]]