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# Decreasing sequences

(Redirected from Nonstrictly decreasing sequences)

Sequences ${\displaystyle \scriptstyle \{a(n)\}_{n=i_{\rm {min}}}^{i_{\rm {max}}}\,}$ for which the terms belong to a totally ordered set (or linearly ordered set) and such that

${\displaystyle a(n+1)\leq a(n),\quad i_{\rm {min}}\leq n

where

${\displaystyle \exists k\,|\,a(k+1)

## Nonstrictly decreasing sequences

Sequences ${\displaystyle \scriptstyle \{a(n)\}_{n=i_{\rm {min}}}^{i_{\rm {max}}}\,}$ for which the terms belong to a totally ordered set (or linearly ordered set) and such that

${\displaystyle a(n+1)\leq a(n),\quad i_{\rm {min}}\leq n

## Strictly decreasing sequences

Sequences ${\displaystyle \scriptstyle \{a(n)\}_{n=i_{\rm {min}}}^{i_{\rm {max}}}\,}$ for which the terms belong to a totally ordered set (or linearly ordered set) and such that

${\displaystyle a(n+1)