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:
- $\mathbf a \mathbf b := \map \Card {A \times B}$
where:
- $A \times B$ denotes the Cartesian product of $A$ and $B$
- $\map \Card {A \times B}$ denotes the cardinal associated with $A \times B$.
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): $\S 8$