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  "body": "\n## Definition\n\nLet $(X, d)$ be a [[metric space|063W5JMY85]] and let $S$ be a nonempty subset of $X$.\nThe diameter of $S$ is\n$$\\operatorname{diam}(S) = \\sup \\{ d(x, y) : x, y \\in S \\},$$\nwhere the [[supremum|0BTMQ04556]] is taken in the [[extended real number line|0GSZ7B0CGR]], so that $\\operatorname{diam}(S) \\in [0, \\infty]$.\n\n## Remarks\n\nThe set $S$ is [[bounded|0P953MG05E]] if and only if $\\operatorname{diam}(S) \u003c \\infty$.\nFor the empty set, a common convention is $\\operatorname{diam}(\\emptyset) = 0$.\nIn $\\mathbb{R}$, the interval $(a, b)$ with $a \u003c b$ has diameter $b - a$, and so does $[a, b]$.\nIf $S \\subseteq T$, then $\\operatorname{diam}(S) \\le \\operatorname{diam}(T)$.\n\n## Explanations\n\n### L1 human\n\nThe diameter is the largest distance between two points of the set, or the limit of such distances.\nFor a disc of radius $r$ in the plane, the diameter is $2r$.\n",
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