Orbit of Trivial Group Action is Singleton

Theorem
Let $\left({G, \circ}\right)$ be a group whose identity is $e$.

Let $S$ be a set.

Let $*: G \times S \to S$ be the trivial group action:
 * $\forall \left({g, s}\right) \in G \times S: g * s = s$

Let $s \in S$.

Then the orbit of $s$ under $*$ is $\left\{{s}\right\}$.

Proof
By definition:
 * $\operatorname{Orb} \left({s}\right) = \left\{{t \in S: \exists g \in G: g * s = t}\right\}$

By definition of the trivial group action:
 * $\forall g \in G: g * s = s$

Hence the result.