Category:Definitions/Increasing Sequences

This category contains definitions related to Increasing Sequences.
Related results can be found in Category:Increasing Sequences.

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 if and only if:

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