Definition:Product of Cardinals

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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 $A \times B$.


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