Decreasing sequence

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.