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A sequence $x_0, x_1, x_2, \dots$ in a [[metric space]] $(X,d)$ is called a ''convergent'' if there exists a point $a \in X$ such that, for every real number $\epsilon > 0$, there exists a natural number $N$ such that $d(a,x_n) < \epsilon$ for all $n > N$. If such a number doesn't exist, the sequence is called ''divergent''. The point $a$, if it exists, is unique. Then we say that this point is the ''[[limit]] of the sequence'' and that the sequence $x_0, x_1, x_2, \dots$ ''converges'' to $a$. [[category:topology]]

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