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# Increasing sequences

(Redirected from Strictly increasing sequences)

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

$a(n+1) \ge a(n),\quad i_{\rm min} \le n < i_{\rm max}, \,$

where

$\exists k \,|\, a(k+1) > a(k),\quad i_{\rm min} \le k < i_{\rm max}. \,$

## Nonstrictly increasing sequences

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

$a(n+1) \ge a(n),\quad i_{\rm min} \le n < i_{\rm max}. \,$

## Strictly increasing sequences

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

$a(n+1) > a(n),\quad i_{\rm min} \le n < i_{\rm max}. \,$