Definition:Sum of Cardinals

Definition

Let $A$ and $B$ be sets.

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

Then the sum of $\mathbf a$ and $\mathbf b$ is defined as:

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

where:

$A \sqcup B$ denotes the disjoint union of $A$ and $B$

$\operatorname{Card} \left({A \sqcup B}\right)$ denotes the cardinal associated with $A \cup B$.