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  "body": "\n## Definition\n\nLet $P = (x_0, \\dots, x_n)$ be a [[partition|069P20KYQT]] of $[a, b]$.\nThe mesh of $P$ is\n$$\\| P \\| = \\max_{1 \\le i \\le n} (x_i - x_{i-1}),$$\nthe length of the longest subinterval of $P$.\n\n## Remarks\n\nRefining a partition does not increase its mesh.\nThe [[Riemann integral|0QM4TXT3DR]] is a limit of Riemann sums as the mesh tends to $0$.\nFor the partition of $[0, 1]$ into $n$ equal pieces, the mesh is $1/n$.\n\n## Explanations\n\n### L1 human\n\nThe mesh measures how fine a partition is.\nA small mesh means that all the pieces are short.\n",
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