Interpreting Sequences and their set Notation

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I am using Ross: Elementary Analysis 2nd Edition.

I do not know how to interpret sets of this type:

" If $L=\limsup s_n \neq \infty$ then for every $\alpha >L$ the set $\{n: s_n > \alpha \}$ is finite."

Generally, how do you interpret sets like $\{n: s_n > \alpha \}$?

Does this set include as its the element every index, $n$, of every term in the sequence $(s_n)$ greater than $\alpha$? i.e. The elements of the set will just be natural numbers...?