View source for Monotone sequence

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

<img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/m/m064/m064860/m0648603.png" /> (a strictly-increasing sequence);

<img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/m/m064/m064860/m0648604.png" /> (a non-decreasing sequence);

<img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/m/m064/m064860/m0648605.png" /> (a strictly-decreasing sequence); or

<img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/m/m064/m064860/m0648606.png" /> (a non-increasing sequence).

====Comments====
See also [[Increasing sequence|Increasing sequence]]; [[Decreasing sequence|Decreasing sequence]].