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  "body": "\n## Definition\n\nLet $f \\colon A \\to B$ be a [[function|0XHDTE5YMZ]].\nThe function $f$ is bijective when it is [[injective|0PVG1CRAJN]] and [[surjective|0XKH881BZ7]].\nEquivalently, for each $b \\in B$, there is exactly one $a \\in A$ with $f(a) = b$.\n\n## Remarks\n\nOther names are bijection and one-to-one correspondence.\nThe function $x \\mapsto 2x + 1$ on $\\mathbb{R}$ is bijective.\nA function is bijective if and only if it has an [[inverse function|0W766JAPSN]]. See [[bijective iff it has a two-sided inverse|01VG2A0BHW]].\nTwo finite sets have the same number of elements exactly when there is a bijection between them.\n\n## Explanations\n\n### L1 human\n\nA bijection pairs the elements of $A$ and the elements of $B$ perfectly.\nEach element of $A$ has one partner in $B$, and each element of $B$ has one partner in $A$.\n",
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