Definition:Indexing Set/Notation

Definition
The family of elements $x$ of $S$ indexed by $I$ is often seen with one of the following notations:


 * $\left \langle {x_i} \right \rangle_{i \mathop \in I}$


 * $\left({x_i}\right)_{i \mathop \in I}$


 * $\left\{{x_i}\right\}_{i \mathop \in I}$

There is little consistency in the literature, but $\left({x_i}\right)_{i \mathop \in I}$ is perhaps most common.

The subscripted $i \in I$ is often left out, if it is obvious in the particular context.