A [[Binary Operation]] on [[Set|Sets]]. For any two [[Set|Sets]] $A,B$, the [[Cartesian Product]] of $A$ and $B$, denoted as $A \times B$, is defined as the [[Set]] of all ordered pairs $(a,b)$ $\huge A\times B = \set{(a,b) \mid a \in A \wedge b \in B } $ The [[Cartesian Product]] is [[Associative]] but not [[Commutative]]. $\huge \begin{align} A\times B &\neq B \times A\\ \end{align}$ $\huge A\times\pa{B\times C} = \pa{A\times B}\times C = A\times B \times C$ The [[Cardinality]] of the [[Cartesian Product]] of two [[Finite]] [[Set|Sets]] is equal to the product of the two sets [[Cardinality]]. $\huge |A|,|B| \in \N \iff |A\times B| = |A| |B| $