Product set/Arbitrary/Definition

Product set (family)

Let ${}I$ be a set, and let, for every ${}i\in I$, a set ${}M_{i}$ be given. Then the set

${}M=\prod _{i\in I}M_{i}=\{(x_{i})_{i\in I}:\,x_{i}\in M_{i}{\text{ for all }}i\in I\}\,$

is called the product set of the ${}M_{i}$.