\begin{definition}[Definition:Ordering Induced by Injection]
Let $\left({T, \le}\right)$ be an ordered set, and let $S$ be a set.
Let $f: S \to T$ be an injection.
Define $\le_f$ as the '''ordering induced by $f$ on $S$''' by:
:$\forall s_1, s_2 \in S: s_1 \le_f s_2 \iff f \left({s_1}\right) \le f \left({s_2}\right)$
That $\le_f$ is in fact an ordering is shown on Ordering Induced by Injection is Ordering.
\end{definition}