Decreasing 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

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

where

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

Nonstrictly decreasing 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

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

Strictly decreasing 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

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

See also

• Increasing sequences
  • Nonstrictly increasing sequences
  • Strictly increasing sequences

• Decreasing sequences
  • Nonstrictly decreasing sequences
  • Strictly decreasing sequences

• Strictly monotonic sequences
  • Strictly increasing sequences
  • Constant sequences
  • Strictly decreasing sequences

• Nonstrictly monotonic sequences
  • Nonstrictly increasing sequences
  • Nonstrictly decreasing sequences