Difference between revisions of "Monotone sequence"
From Encyclopedia of Mathematics
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− | A sequence | + | {{TEX|done}} |
+ | A sequence $\{x_n\}$ such that for all $n=1,2,\dots,$ either | ||
− | < | + | $x_n<x_{n+1}$ (a strictly-increasing sequence); |
− | + | $x_n\leq x_{n+1}$ (a non-decreasing sequence); | |
− | + | $x_n>x_{n+1}$ (a strictly-decreasing sequence); or | |
− | + | $x_n\geq x_{n+1}$ (a non-increasing sequence). | |
====Comments==== | ====Comments==== | ||
See also [[Increasing sequence|Increasing sequence]]; [[Decreasing sequence|Decreasing sequence]]. | See also [[Increasing sequence|Increasing sequence]]; [[Decreasing sequence|Decreasing sequence]]. |
Latest revision as of 22:33, 30 November 2018
A sequence $\{x_n\}$ such that for all $n=1,2,\dots,$ either
$x_n<x_{n+1}$ (a strictly-increasing sequence);
$x_n\leq x_{n+1}$ (a non-decreasing sequence);
$x_n>x_{n+1}$ (a strictly-decreasing sequence); or
$x_n\geq x_{n+1}$ (a non-increasing sequence).
Comments
See also Increasing sequence; Decreasing sequence.
How to Cite This Entry:
Monotone sequence. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Monotone_sequence&oldid=11301
Monotone sequence. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Monotone_sequence&oldid=11301