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  "body": "\n## Example\n\nLet $\\mathbb{Z} = \\{\\ldots, -2, -1, 0, 1, 2, \\ldots\\}$ be the set of integers, with the usual addition $+$.\nThen $(\\mathbb{Z}, +)$ is an [[abelian group|082GHNPJ53]].\nIts identity element is $0$, and the inverse of $n$ is $-n$.\n\n## Remarks\n\nThe group $(\\mathbb{Z}, +)$ is infinite, and each element $n$ is the $n$-fold sum of $1$ or of $-1$.\nThus the element $1$ generates the group.\nThe integers with multiplication are not a group, because $2$ has no multiplicative inverse in $\\mathbb{Z}$.\n\n## Explanations\n\n### L1 human\n\nThe integers with addition are the first example of a group for most students.\nAdding is associative, $0$ changes nothing, and $-n$ undoes $n$.\nEach element of the group is a sum of copies of $1$ or of $-1$.\n",
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