Monoid/Examples

Examples of Monoids

Operation Defined as $x + y + x y$ on Real Numbers

Let $\circ: \R \times \R$ be the operation defined on the real numbers $\R$ as:

$\forall x, y \in \R: x \circ y := x + y + x y$

Then $\struct {\R, \circ}$ is a monoid whose identity is $0$.