Stopping time, event, simple description

Question

Let us suppose that we have two stopping times $T$ and $S$, where $T \leq S$.

Can someone explain on a practical example why is event ${(T \leq n)} \subseteq {(S \leq n)}$?

Answer 1

I think you have it backwards: $T \leq S$ means that if $S \leq n$ then $T \leq n$. In other words $\{ \omega : S \leq n \} \subseteq \{ \omega : T \leq n \}$.