\begin{definition}[Definition:Orbit (Group Theory)/Definition 2]
Let $G$ be a group acting on a set $X$.
Let $\RR$ be the relation on $X$ defined as:
:$\forall x, y \in X: x \mathrel \RR y \iff \exists g \in G: y = g * x$
where $*$ denotes the group action.
From Group Action Induces Equivalence Relation, $\RR$ is an equivalence relation.
The '''orbit''' of $x$, denoted $\Orb x$, is the equivalence class of $x$ under $\RR$.
\end{definition}