Definition:Increasing/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 increasing iff:


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

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

Also known as
An increasing sequence is also known as an ascending sequence.

Also see

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