Definition:Family


 * Family is used by some authors as a synonym for set.

However, the general underststanding of the term family is as follows:


 * Indexed family: a mapping $x: I \to S$ from an indexing set $I$ to a set $S$, usually denoted $\left\langle{x_i}\right)_{i \mathop \in I}$
 * Indexed family of sets: when $S$ is a set of sets
 * Indexed family of subsets: when $S$ is a set of subsets of another set.