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  "body": "\n## Definition\n\nLet $a \u003c b$ be real numbers.\nA partition of $[a, b]$ is a finite sequence of real numbers $P = (x_0, x_1, \\dots, x_n)$ with\n$$a = x_0 \u003c x_1 \u003c \\cdots \u003c x_n = b.$$\nThe intervals $[x_{i-1}, x_i]$ for $i = 1, \\dots, n$ are the subintervals of $P$.\n\n## Remarks\n\nPartitions are the basis of [[Darboux sums|0QRQVH0CRW]] and [[Riemann sums|0HBY48G8G1]].\nA [[refinement|0EEKF7YFBW]] of $P$ adds more points. The [[mesh|04GM4NYXJB]] of $P$ is the length of its longest subinterval.\nA tagged partition also chooses a point $t_i$ in each subinterval $[x_{i-1}, x_i]$.\n\n## Explanations\n\n### L1 human\n\nA partition cuts the interval $[a, b]$ into finitely many pieces.\nThe cut points are listed from left to right.\n",
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