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  "body": "\n## Example\n\nLet $n$ be a positive integer.\nThe subgroup $n\\mathbb{Z}$ of the [[additive group of integers|0BSCJA5G53]] is normal, because $\\mathbb{Z}$ is abelian.\nThe [[quotient group|0KYX2N69J0]] $\\mathbb{Z}/n\\mathbb{Z}$ has the $n$ cosets $0 + n\\mathbb{Z}, 1 + n\\mathbb{Z}, \\ldots, (n-1) + n\\mathbb{Z}$.\nThe operation is $(a + n\\mathbb{Z}) + (b + n\\mathbb{Z}) = (a + b) + n\\mathbb{Z}$, which is addition modulo $n$.\n\n## Remarks\n\nThe coset $a + n\\mathbb{Z}$ is the set of integers with the same remainder as $a$ on division by $n$.\nThus $\\mathbb{Z}/n\\mathbb{Z}$ is the cyclic group of order $n$ of clock arithmetic.\nFor $n = 0$, the quotient $\\mathbb{Z}/0\\mathbb{Z}$ is isomorphic to $\\mathbb{Z}$.\n\n## Explanations\n\n### L1 human\n\nTwo integers are in the same coset of $n\\mathbb{Z}$ when their difference is a multiple of $n$.\nSo the quotient group keeps only the remainder modulo $n$.\nAdding cosets is the same as adding remainders and reducing modulo $n$.\n",
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