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:

$\mathbf a \mathbf b := \map \Card {A \times B}$

where:

$A \times B$ denotes the Cartesian product of $A$ and $B$
$\map \Card {A \times B}$ denotes the cardinal associated with $A \times B$.