Index Sets

Definition: Indexing

Let $S$ be a set.

An indexing on $S$ is a surjection $f:I\to S$ from some set $I$ onto $S$.

Definition: Index Set

Let $S$ be a set.

An index set for $S$ is any set $I$ for which there exists an indexing from $I$ to $S$.

NOTATION

We use $s_i$ to denote the element in $s\in S$ such that $f(i)=s$.