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text: 'The order $|G|$ of a [3gd group] $G$ is the size of its [3gz underlying set]. For example, if $G=(X,\\bullet)$ and $X$ has nine elements, we say that $G$ has order $9$. If $X$ is infinite, we say $G$ is infinite; if $X$ is finite, we say $G$ is finite.\n\nThe [4cq order of an element] $g \\in G$ of a group is the smallest nonnegative integer $n$ such that $g^n = e$, or $\\infty$ if there is no such integer. The relationship between this usage of order and the above usage of order is that the order of $g \\in G$ in this sense is the order of the [subgroup] $\\langle g \\rangle = \\{ 1, g, g^2, \\dots \\}$ of $G$ [generating_set generated by] $g$ in the above sense. ',
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