User:Jshflynn/Sandbox1

Definition
Let $S$ and $T$ be sets.

Let $S \times T$ denote the cartesian product of $S$ with $T$.

Define a binary operation $\circ$ on $S \times T$ as follows:


 * $\forall \left({a, b}\right), \left({c, d}\right) \in S \times T: \left({a, b}\right) \circ \left({c, d}\right) = \left({a, d}\right)$

Then the algebraic structure $\left({S \times T, \circ}\right)$ is referred to as the rectangular band on $S \times T$.