# Definition:Exponentiation 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 exponentiation of $\mathbf a$ to $\mathbf b$ is defined as:

$\mathbf a^{\mathbf b} := \operatorname{Card} \left({A^B}\right)$

where:

$A^B$ denotes the set of all mappings from $B$ to $A$
$\operatorname{Card} \left({A^B}\right)$ denotes the cardinal associated with $A^B$.