ThmDex – An index of mathematical definitions, results, and conjectures.
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Definition D326
Cartesian product

Let $X_j$ be a D11: Set for each $j \in J$ such that
 (i) $\bigcup_{j \in J} X_j$ is the D77: Set union of $X = \{ X_j \}_{j \in J}$
The cartesian product of $X = \{ X_j \}_{j \in J}$ is the D11: Set $$\prod_{j \in J} X_j : = \left\{ x : J \to \bigcup_{j \in J} X_j \mid \forall \, j \in J : x_j \in X_j \right\}$$
Children
 ▶ D327: Canonical set projection ▶ D5639: Complex cartesian product ▶ D2758: Cylinder set ▶ D68: Set of maps
Results
 ▶ R4630: Bijection between parenthesis-sliced cartesian triple products ▶ R4315: Cardinality of a finite set raised to a finite power ▶ R4632: Cardinality of cartesian triple products is invariant under insertion of parentheses ▶ R4631: Cardinality of finite cartesian products is invariant under insertion of parentheses ▶ R221: Cartesian product is not associative ▶ R4263: Countable cartesian product with empty set is empty ▶ R4262: Finite cartesian product with empty set is empty