# 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.

## Sources

- 1965: Seth Warner:
*Modern Algebra*... (previous) ... (next): $\S 18$