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

Similar definitions can be made for convergence of functions.

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