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 $\sequence {a_k}_{k \mathop \in A}$ is a sequence of distinct terms if and only if:

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

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

Sources

• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {III}$: The Natural Numbers: $\S 18$: Induced $N$-ary Operations