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  "body": "\n## Definition\n\nLet $f \\colon A \\to B$ be a [[function|0XHDTE5YMZ]].\nThe function $f$ is surjective when, for each $b \\in B$, there is an $a \\in A$ with $f(a) = b$.\n\n## Remarks\n\nOther names are onto function and surjection.\nEquivalently, the [[range|0E9GTAV478]] of $f$ is the whole [[codomain|0F9JHP8AJN]] $B$.\nThe function $x \\mapsto x^3$ on $\\mathbb{R}$ is surjective, and $x \\mapsto x^2$ on $\\mathbb{R}$ is not, because $-1$ is not a value.\n\n## Explanations\n\n### L1 human\n\nA surjective function hits every element of the codomain at least once.\nTo prove surjectivity, take an arbitrary $b \\in B$ and find an input $a$ with $f(a) = b$.\n",
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