Are stopping times ordered?

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Stopping times are random variables, so they are measurable functions. Let $S$ and $T$ be stopping times. Is it always possible to say $S<T$ or $T>S$ or $S=T$?

Possible answer: We can't compare two functions, because for some $\omega$'s $S<T$ or $T>S$ or $S=T$, right? But S and T gets values in index set which is ordered. Sounds confusing.

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Consider a sequence of coin flips. Let $S$ be the first head and let $T$ be the first tail.