Set theory/Indexed family of sets/Definition

Let ${\displaystyle {}I}$ be a set, and let, for every ${\displaystyle {}i\in I}$, a set ${\displaystyle {}M_{i}}$ be given. Such a situation is called a family of sets

${\displaystyle M_{i}{\text{ , }}i\in I.}$

The set ${\displaystyle {}I}$ is called the index set of the family.