Definition:Sum of Cardinals
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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 $A \cup B$.
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
- 1975: T.S. Blyth: Set Theory and Abstract Algebra ... (previous) ... (next): $\S 8$