# Category:Cartesian Product

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This category contains results about **cartesian products**.

Definitions specific to this category can be found in Definitions/Cartesian Product.

Let $S$ and $T$ be sets.

The **cartesian product** $S \times T$ of $S$ and $T$ is the set of ordered pairs $\tuple {x, y}$ with $x \in S$ and $y \in T$:

- $S \times T = \set {\tuple {x, y}: x \in S \land y \in T}$

## Subcategories

This category has the following 20 subcategories, out of 20 total.

### B

### C

- Cartesian Product of Subsets (6 P)
- Cartesian Product of Unions (4 P)

### E

- Equality of Ordered Pairs (7 P)

### O

- Ordered Pairs (5 P)

### P

## Pages in category "Cartesian Product"

The following 67 pages are in this category, out of 67 total.

### B

### C

- Cardinality of Cartesian Product of Finite Sets
- Cartesian Product Distributes over Intersection
- Cartesian Product Distributes over Set Difference
- Cartesian Product Distributes over Union
- Cartesian Product Exists and is Unique
- Cartesian Product is Anticommutative
- Cartesian Product is Anticommutative/Corollary
- Cartesian Product is Empty iff Factor is Empty
- Cartesian Product is Empty iff Factor is Empty/Family of Sets
- Cartesian Product is not Associative
- Cartesian Product is Set Product
- Cartesian Product is Set Product/Family of Sets
- Cartesian Product is Unique
- Cartesian Product of Bijections is Bijection
- Cartesian Product of Bijections is Bijection/General Result
- Cartesian Product of Countable Sets is Countable
- Cartesian Product of Equivalence Relations
- Cartesian Product of Family is Empty iff Factor is Empty
- Cartesian Product of Family of Subsets
- Cartesian Product of Group Actions
- Cartesian Product of Homeomorphisms is Homeomorphism
- Cartesian Product of Infinite Set Equivalent to Itself implies Axiom of Choice
- Cartesian Product of Intersections
- Cartesian Product of Mappings is Continuous iff Factor Mappings are Continuous
- Cartesian Product of Natural Numbers with Itself is Countable
- Cartesian Product of Semirings of Sets
- Cartesian Product of Sets is Set
- Cartesian Product of Subsets
- Cartesian Product of Unions
- Cartesian Product Preserves Cardinality
- Cartesian Product with Complement
- Composition of Cartesian Products of Mappings
- Composition of Relations Preserves Subsets
- Composition of Symmetric Relation with Itself is Union of Products of Images
- Construction of Inverse Completion
- Correspondence between Set and Ordinate of Cartesian Product is Mapping
- Cross-Relation Equivalence Classes on Natural Numbers are Cancellable for Addition