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  "body": "\n## Definition\n\nLet $\\sim$ be an [[equivalence relation|0SGTMBEWRF]] on a set $A$.\nThe quotient set of $A$ by $\\sim$ is the set\n$$A/{\\sim} = \\{[a] \\mid a \\in A\\}$$\nof all [[equivalence classes|082RMRSY26]].\nThe canonical projection is the [[function|0XHDTE5YMZ]] $\\pi \\colon A \\to A/{\\sim}$ with $\\pi(a) = [a]$.\n\n## Remarks\n\nFor congruence modulo $n$ on $\\mathbb{Z}$, the quotient set $\\mathbb{Z}/n\\mathbb{Z}$ has the $n$ elements $[0], [1], \\dots, [n-1]$.\nThe canonical projection is [[surjective|0XKH881BZ7]].\nA function on $A/{\\sim}$ is often defined by a formula on representatives. The formula must give the same value for equivalent representatives.\n\n## Explanations\n\n### L1 human\n\nIn the quotient set, each class becomes a single point.\nFrom $\\mathbb{Z}$ with congruence modulo $2$ you get a set with two elements: \"even\" and \"odd\".\n",
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