# Definition:Sequence of Distinct Terms

## Definition

A sequence of distinct terms of $S$ is an injection from a subset of $\N$ into $S$.

Thus a sequence $\left \langle {a_k} \right \rangle_{k \in A}$ is a sequence of distinct terms iff:

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

Informally, a sequence of distinct terms is a sequence whose terms are pairwise distinct.