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 $A^B$.

Also see

• Cardinality of Set of All Mappings

Sources

• 1972: A.G. Howson: A Handbook of Terms used in Algebra and Analysis ... (previous) ... (next): $\S 4$: Number systems $\text{I}$: A set-theoretic approach