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  "body": "\n## Example\n\nLet $n \\ge 1$ be an integer.\nFor $x = (x_1, \\ldots, x_n)$ and $y = (y_1, \\ldots, y_n)$ in $\\mathbb{R}^n$, let\n$$d_\\infty(x, y) = \\max_{1 \\le i \\le n} |x_i - y_i|.$$\nThen $d_\\infty$ is a [[metric|063W5JMY85]] on $\\mathbb{R}^n$, the sup metric.\n\n## Remarks\n\nIt is also called the Chebyshev distance or the maximum metric.\nFor all $x, y$ in $\\mathbb{R}^n$, $d_\\infty(x, y) \\le d_2(x, y) \\le d_1(x, y) \\le n \\, d_\\infty(x, y)$, where $d_2$ is the [[Euclidean metric|0E1MMCAY5B]] and $d_1$ is the [[taxicab metric|07CJNE6ZAQ]].\nIt is the limit of the [[p-metric|0TFDZN6AXP]] $d_p$ as $p \\to \\infty$.\n\n## Explanations\n\n### L1 human\n\nThe sup metric takes only the largest difference of the coordinates.\nOn a chessboard, it is the number of moves that a king needs to go from one square to another.\n",
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