Definition:Product of Cardinals

Definition
Let $A$ and $B$ be sets.

Let $\mathbf a$ and $\mathbf b$ be the cardinals associated respectively with $A$ and $B$.

Then the product of $\mathbf a$ and $\mathbf b$ is defined as:
 * $\mathbf a \mathbf b := \operatorname{Card} \left({A \times B}\right)$

where:
 * $A \times B$ denotes the Cartesian product of $A$ and $B$
 * $\operatorname{Card} \left({A \times B}\right)$ denotes the cardinal associated with $A \times B$.