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  "body": "\n## Definition\n\nLet $D \\subseteq \\mathbb{R}$, let $f \\colon D \\to \\mathbb{R}$, and let $a$ be a limit point of $D \\cap (a, \\infty)$.\nA real number $L$ is the right limit of $f$ at $a$ if the following holds.\nFor each $\\varepsilon \u003e 0$ there is $\\delta \u003e 0$ with $|f(x) - L| \u003c \\varepsilon$ for all $x \\in D$ with $a \u003c x \u003c a + \\delta$.\nThe notation is $\\lim_{x \\to a^+} f(x) = L$.\nThe left limit $\\lim_{x \\to a^-} f(x)$ is defined in the same way, with $a - \\delta \u003c x \u003c a$.\n\n## Remarks\n\nThe right limit is the [[limit|0TXTSEMHR5]] of the restriction of $f$ to $D \\cap (a, \\infty)$.\nIf $a$ is a limit point of points on both sides, then $\\lim_{x \\to a} f(x) = L$ if and only if both one-sided limits exist and equal $L$.\nFor the sign function at $0$, the right limit is $1$ and the left limit is $-1$.\n\n## Explanations\n\n### L1 human\n\nA one-sided limit only looks at points on one side of $a$.\nA function with a jump at $a$ has two different one-sided limits there.\n",
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