# Non-increasing sequence

In mathematics a

**non-increasing sequence**is a typesequence , an ordered list of objects, with an additional property on thevalue s of its items. The property of being non-increasing is a local property in that if all adjacent items in the sequence have the property then the sequence over all has the property.The property of being a

decreasing sequence is a stronger requirement since any "decreasing sequence" is a "non-increasing sequence", but the converse is not true. A special example of a non-increasing sequence is the constant sequence where all items in the sequence have identical value.**Definition**Let "X" be a set, and "⊆" a

partial order on "X". Let α be asequence of ordinals. We say that a sequence of elements "x"_{α}of "X" is**non-increasing**if for each ordinal α and each ordinal β>α, we have "x"_{β}⊆"x"_{α}.Algebraically speaking, a sequence $(a\_n)\_\{n=1\}^\{infty\}$ is non-increasing if $forall\; ninmathbb\; N:a\_ngeq\; a\_\{n+1\}$.

**See also***

Monotonic function

*decreasing sequence

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