\begin{definition}[Definition:Orbit (Group Theory)/Definition 1]
Let $G$ be a group acting on a set $X$.
The '''orbit''' of an element $x \in X$ is defined as:
:$\Orb x := \set {y \in X: \exists g \in G: y = g * x}$
where $*$ denotes the group action.
That is, $\Orb x = G * x$.
Thus the '''orbit''' of an element is all its possible destinations under the group action.
\end{definition}