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  "body": "\n## Statement\n\nLet $D \\subseteq \\mathbb{R}$ and let $f \\colon D \\to \\mathbb{R}$ be a function.\nThen $f$ is [[continuous|0P27W9RW0G]] if and only if $f$ is [[sequentially continuous|0MVDQEAB60]].\n\n## Remarks\n\nThe forward direction follows from the [[epsilon-delta form|0W8YHHGCJG]] of continuity.\nFor the converse, suppose that $f$ is not continuous at $a$. Then there is $\\varepsilon \u003e 0$ and for each $n$ a point $x_n$ with $|x_n - a| \u003c 1/n$ and $|f(x_n) - f(a)| \\ge \\varepsilon$.\nThe equivalence holds in all metric spaces. Mathlib states it for sequential spaces, as `continuous_iff_seqContinuous`.\n\n## Explanations\n\n### L1 human\n\nWe can test continuity with sequences.\nA function is continuous exactly when it sends every convergent sequence to a convergent sequence with the right limit.\n",
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