Definition:Strictly 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 strictly increasing iff:


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

Real Sequences
The above definition for sequences is usually applied to real number sequences.

Let $\left \langle {x_n} \right \rangle$ be a sequence in $\R$.

Then $\left \langle {x_n} \right \rangle$ is strictly increasing if


 * $\forall n \in \N: x_n < x_{n+1}$

Also see

 * Increasing Sequence
 * Strictly Decreasing Sequence
 * Strictly Monotone Sequence