Definition:Strictly Decreasing/Sequence

Definition
Let $\left({S, \preceq}\right)$ be a totally ordered set.

Then a sequence $\left \langle {a_k} \right \rangle_{k \in A}$ of terms of $S$ is strictly decreasing iff:


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

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

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

Some sources refer to a strictly decreasing sequence as a decreasing sequence, and refer to a decreasing sequence which is not strictly decreasing 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:Decreasing Sequence
 * Definition:Strictly Increasing Sequence
 * Definition:Strictly Monotone Sequence