Mathematical logic and foundations Definition

Cartesian product

Definition

Let $A$ and $B$ be sets. The Cartesian product of $A$ and $B$ is the set $A \times B = \{(a, b) \mid a \in A \text{ and } b \in B\}$ of all ordered pairs $(a, b)$ with $a \in A$ and $b \in B$ .

Remarks

Example: $\{1, 2\} \times \{x, y\} = \{(1, x), (1, y), (2, x), (2, y)\}$ . For finite sets with $m$ and $n$ elements, $A \times B$ has $mn$ elements. The plane $\mathbb{R}^2$ is $\mathbb{R} \times \mathbb{R}$ . A binary relation from $A$ to $B$ is a subset of $A \times B$ .

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Element definition
Set definition
Ordered pair definition
Cartesian product definition

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Tag	`0C81YBVTWH`
URI	`m2://0C81YBVTWH`
Kind	definition
Writing	W1 stated
MSC	03E20
Defines	Cartesian product
Uses	Ordered pair

Cartesian product

Definition

Remarks

Reading path

Where this leads

Further reading

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