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  clickbait: 'Infinite sequences whose terms get arbitrarily close together.',
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  text: 'A **Cauchy sequence** is a sequence in which as the sequence progresses, all the terms get closer and closer together. It is closely related to the idea of a [-convergent_sequence].\n\n## Definition\n\nIn any [-metric_space] with a set $X$ and a distance function $d$, a sequence $(x_n)_{n=0}^\\infty$ is Cauchy if for every $\\varepsilon > 0$ there exists an $N$ such that for all $m, n > N$, we have that $d(x_m, x_n) < \\varepsilon$.\n\nIn the [4bc real numbers], the distance between two numbers is usually expressed as their difference, or $|x_m - x_n|$.\n\n## Complete metric space\n\nIn a [ complete metric space], every Cauchy sequence is convergent. In particular, the real numbers are a complete metric space.',
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