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In a metric space (X, d), a sequence $\text{[math]}$ in X is said to converge to a point $\text{[math]}$ if roughly speaking as $\text{[math]}$ goes to infinity $\text{[math]}$ gets closer and closer to $\text{[math]}$ and stays there. Rigorously, $\text{[math]}$ is said to converge to $\text{[math]}$ if for all $\text{[math]}$ there exists N such that for all n > N we have $\text{[math]}$ .

Similar definitions can be made for convergence of functions.

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