monotonic
Monotonic
2002-02-18 21:43:08
2005-08-16 01:03:45
Definition
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A sequence or function is said to be \emph{monotonic} if it is
\begin{itemize}
\item monotonically increasing
\item monotonically decreasing
\item monotonically nondecreasing
\item monotonically nonincreasing
\end{itemize}
Intuitively, this means that a monotone sequence can be thought of a ``staircase'' going either only up, or only down, with the stairs any height and any depth. The same goes for step functions. Smooth (analytic) monotone functions are like ``slopes,'' either up or down at potentially varying steepnesess.