5. Products

Info

In this section we deal only with sets. No proper classes are involved.

Definition 5.1 笛卡儿积

Let \(\{ A_i | i \in I\}\) be a family of sets indexed by a (nonempty) set \(I\). The (Cartesian) product of the sets \(A_i\) is the set of all functions \(f:I \rightarrow \bigcup_{i \in I} A_i\) such that \(f(i) \in A_i\) for all \(i \in I\). It is denoted \(\prod_{i \in I}A_i\).