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A sequence $(s_n)$ is monotonically decreasing if
$$ s_m < s_n \;\forall\; m > n $$
Similarly, a real function $f(x)$ is monotonically decreasing if
$$ f(x) < f(y) \;\forall\; x > y$$
Compare this to monotonically nonincreasing.
Conflict note. In other context, such as [1], this is called strictly decreasing. When this is the case, ``monotonically nonincreasing'' is instead called ``monotonically decreasing.''
- 1
- ``strictly decreasing,'' from the NIST Dictionary of Algorithms and Data Structures, Paul E. Black, ed.
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