40-00-MonotonicallyIncreasing.tex

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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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