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  "body": "\n## Definition\n\nLet $\\sim$ be an [[equivalence relation|0SGTMBEWRF]] on a set $A$ and let $a \\in A$.\nThe equivalence class of $a$ is the set\n$$[a] = \\{x \\in A \\mid x \\sim a\\}.$$\nEach element of $[a]$ is a representative of the class.\n\n## Remarks\n\nFor congruence modulo $3$ on $\\mathbb{Z}$, the class of $1$ is $[1] = \\{\\dots, -5, -2, 1, 4, 7, \\dots\\}$.\nFor $a, b \\in A$, $[a] = [b]$ if and only if $a \\sim b$. Otherwise, $[a]$ and $[b]$ are disjoint.\nThe set of all classes is the [[quotient set|0ZVHXDSZC7]].\n\n## Explanations\n\n### L1 human\n\nAn equivalence class collects all the objects that the relation treats as the same.\nFor \"has the same birthday as\", the class of a person is the group of all people born on the same day of the year.\n",
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