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  "body": "\n## Definition\n\nLet $A$ and $B$ be [[sets|0SJ3RX9TXA]].\nThe sets $A$ and $B$ are equinumerous, written $A \\approx B$, when there is a [[bijective function|0SNQEF7Z53]] $f \\colon A \\to B$.\n\n## Remarks\n\nEquinumerosity is reflexive, symmetric and transitive. The identity, the inverse and the composition of bijections give the three properties.\nThe set $\\mathbb{N}$ is equinumerous with the set of even natural numbers, by $n \\mapsto 2n$. So an infinite set can be equinumerous with a proper subset.\nOther names are \"equipotent\" and \"have the same [[cardinality|0JTGRV4WT4]]\".\n\n## Explanations\n\n### L1 human\n\nYou do not need to count to compare sizes.\nIf each chair in a room has one person and each person has one chair, there are as many people as chairs.\nEquinumerosity applies the same idea to infinite sets.\n",
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