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  "body": "\n## Statement\n\nLet $(a_n)$ be a real sequence and let $L$ and $L'$ be real numbers.\nIf $(a_n)$ converges to $L$ and $(a_n)$ converges to $L'$, then $L = L'$.\n\n## Remarks\n\nThe proof takes $\\varepsilon = |L - L'|/2$ in the [[epsilon-N definition|09G6KHS6GY]]. If $L \\ne L'$, then for large $n$ the term $a_n$ would be closer than $\\varepsilon$ to both numbers, which is impossible.\nThe statement holds in each metric space and, more generally, in each Hausdorff topological space.\nThe statement fails in some spaces that are not Hausdorff. In a set with the trivial topology, each sequence converges to each point.\n\n## Explanations\n\n### L1 human\n\nA sequence cannot approach two different numbers at the same time.\nIf the two numbers are a distance $d$ apart, the terms cannot be within $d/2$ of both of them.\n",
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