Definition:Decreasing/Sequence

Definition
Let $\struct {S, \preceq}$ be a totally ordered set.

Then a sequence $\sequence {a_k}_{k \mathop \in A}$ of terms of $S$ is decreasing :


 * $\forall j, k \in A: j < k \implies a_k \preceq a_j$

Real Sequence
The above definition for sequences is usually applied to real number sequences:

Also known as
A decreasing sequence is also referred to as order-reversing.

Some sources refer to a decreasing sequence as a monotonic decreasing sequence to distinguish it from a strictly decreasing sequence.

That is, such that monotonic is being used to mean a decreasing sequence in which consecutive terms may be equal.

does not endorse this viewpoint.

Also see

 * Definition:Strictly Decreasing Sequence
 * Definition:Increasing Sequence
 * Definition:Monotone Sequence