Definition: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 decreasing iff:


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

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.

Also see

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