Definition 3

Let $(\mathfrak{a}_\iota)_{\iota \in I}$ be a family of cardinals. The cardinal of the product (resp. sum) of the sets $\mathfrak{a}_\iota$ is called the cardinal product (resp. cardinal sum) of the cardinals $\mathfrak{a}_\iota$ and is denoted by $\mathop{\mathbf{P}}_{\iota \in I} \mathfrak{a}_\iota$ $\left(\text{resp. } \sum_{\iota \in I} \mathfrak{a}_\iota\right)$.

Whenever there is no risk of confusion we shall say simply "product" and "sum" in place of "cardinal product" and "cardinal sum", and we shall write $\prod_{\iota \in I} \mathfrak{a}_\iota$ in place of $\mathop{\mathbf{P}}_{\iota \in I} \mathfrak{a}_\iota$ (cf. Exercise 2).