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  "body": "\n## Definition\n\nLet $(a_n)$ be a [[real sequence|0CTV783HYT]].\nThe sequence is increasing if $a_n \\le a_{n+1}$ for all $n \\in \\mathbb{N}$.\nThe sequence is decreasing if $a_n \\ge a_{n+1}$ for all $n \\in \\mathbb{N}$.\nThe sequence is monotone if it is increasing or decreasing.\nThe sequence is strictly increasing if $a_n \u003c a_{n+1}$ for all $n$, and strictly decreasing if $a_n \u003e a_{n+1}$ for all $n$.\n\n## Remarks\n\nSome texts say non-decreasing for increasing in this sense, and they keep the word increasing for strictly increasing.\nBy induction, $(a_n)$ is increasing if and only if $a_m \\le a_n$ for all $m \\le n$. This is the definition of a monotone function on $\\mathbb{N}$.\nThe sequence $1/n$ is strictly decreasing. The sequence $(-1)^n$ is not monotone.\n\n## Explanations\n\n### L1 human\n\nA monotone sequence always moves in one direction.\nAn increasing sequence never goes down, and a decreasing sequence never goes up.\n",
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