Definition:Increasing/Sequence

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

Let $A$ be a subset of the natural numbers $\N$.

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


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

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

Also see

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