monotonically increasingMonotonicallyIncreasing2002-02-18 21:36:372005-08-16 00:41:05Definition\usepackage{amssymb}
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%\usepackage{xypic}A sequence $(s_n)$, $s_n \in \mathbb{R} $ is called \emph{monotonically increasing} if
$$ s_m > s_n \; \forall \; m > n $$
Similarly, a real function $f(x)$ is called monotonically increasing if
$$ f(x) > f(y) \; \forall \; x > y $$
Compare this to monotonically nondecreasing.
\textbf{Conflict note.} This condition is also sometimes called \emph{strictly increasing} \cite{NIST}. In such a context, ``monotonically increasing'' has the same meaning as monotonically nondecreasing.
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\bibitem{NIST} ``\PMlinkexternal{strictly increasing}{http://www.nist.gov/dads/HTML/strictlyIncreasing.html},'' from the NIST Dictionary of Algorithms and Data Structures, Paul E. Black, ed.
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