Group_Examples_x_y_over_1_xy

Let $G = \set {x \in \R: -1 < x < 1}$ be the set of all real numbers whose absolute value is less than $1$. Let $\circ: G \times G \to \R$ be the binary operation defined as $\forall x, y \in G: x \circ y = \dfrac {x + y} {1 + x y}$ The algebraic structure $\struct {G, \circ}$ is a group.