Decreasing sequence

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A sequence $\{x_n\}$ such that for each $n=1,2,\ldots,$ one has $x_n>x_{n+1}$. Sometimes such a sequence is called strictly decreasing, while the term "decreasing sequence" is applied to a sequence satisfying for all $n$ the condition $x_n\geq x_{n+1}$. Such a sequence is sometimes called non-increasing.

Every non-increasing sequence of real numbers that is bounded from below has a finite limit, while one that is not bounded from below has limit $-\infty$. See Continuity axiom.

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Decreasing sequence. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article