Cartesian Product

Definition#

Let \(S\) and \(T\) be any sets. Then the Cartesian product \(S \times T\) is the set of all ordered pairs \((s,t)\), with \(s \in S\) and \(t \in T\).

Informally: The Cartesian product is the permutation of element in \(S\) and \(T\).

Example#

Let \(S = \{1,2,3\}\) and \(T = \{2,3\}\). Then:

\[ S \times T = \{(1,2), (1,3), (2,2), (2,3), (3,2), (3,3)\} \]

Source#

Gregory T. Lee. Abstract Algebra. 1st ed. Springer Cham, 2018. pp. 4.