monotonically decreasingMonotonicallyDecreasing2002-02-18 21:33:392005-08-16 00:49:23Definition\usepackage{amssymb}
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%\usepackage{xypic}A sequence $(s_n)$ is \emph{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.
\textbf{Conflict note.} In other context, such as \cite{NIST}, this is called \emph{strictly decreasing}. When this is the case, ``monotonically nonincreasing'' is instead called ``monotonically decreasing.''
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\bibitem{NIST} ``\PMlinkexternal{strictly decreasing}{http://www.nist.gov/dads/HTML/strictlyDecreasing.html},'' from the NIST Dictionary of Algorithms and Data Structures, Paul E. Black, ed.
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