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Increasing sequences

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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}. \,

See also




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