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  "body": "\n## Description\n\nThe extended real number line is the set $\\overline{\\mathbb{R}} = \\mathbb{R} \\cup \\{-\\infty, +\\infty\\}$.\nIt has two new elements, $-\\infty$ and $+\\infty$, that are not [[real numbers|08J2M1JYAG]].\nIts order extends the order of $\\mathbb{R}$, with $-\\infty \u003c x \u003c +\\infty$ for each real number $x$.\n\n## Remarks\n\nIn $\\overline{\\mathbb{R}}$, each subset has a [[supremum|0BTMQ04556]] and an infimum. For example, $\\sup \\mathbb{N} = +\\infty$ and $\\sup \\emptyset = -\\infty$.\nSome operations extend: $x + \\infty = +\\infty$ for each real $x$. Other expressions, such as $\\infty - \\infty$, stay undefined.\nThe set $\\overline{\\mathbb{R}}$ is not a field.\n\n## Explanations\n\n### L1 human\n\nThe extended real line adds two end points to the number line, one at each end.\nThis lets you write $\\lim_{x \\to \\infty}$ and $\\sup$ of unbounded sets with symbols instead of words.\n",
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