# Definition:Family

## Disambiguation

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**Family** may refer to:

**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.