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Difference between revisions of "Monotone sequence"

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A sequence <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/m/m064/m064860/m0648601.png" /> such that for all <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/m/m064/m064860/m0648602.png" /> either
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A sequence $\{x_n\}$ such that for all $n=1,2,\dots,$ either
  
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<img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/m/m064/m064860/m0648603.png" /> (a strictly-increasing sequence);
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$x_n<x_{n+1}$ (a strictly-increasing sequence);
  
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<img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/m/m064/m064860/m0648604.png" /> (a non-decreasing sequence);
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$x_n\leq x_{n+1}$ (a non-decreasing sequence);
  
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<img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/m/m064/m064860/m0648605.png" /> (a strictly-decreasing sequence); or
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$x_n>x_{n+1}$ (a strictly-decreasing sequence); or
  
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<img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/m/m064/m064860/m0648606.png" /> (a non-increasing sequence).
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$x_n\geq x_{n+1}$ (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=43515
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