This is a question on a practice midterm. It seems intuitively true (otherwise $S$ would seem to have a finite upper bound), but I'm unsure of how to rigorously prove it. Any pointers would be appreciated!
2026-03-25 11:54:11.1774439651
if $\sup(S) = \infty$, then there is a sequence $s_n \in S$ such that its limit is $\infty$?
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Since $\sup S=+\infty$, there is an element of $S$ greater than $1$. Call it $x_1$. And since $\sup S=+\infty$, there is an element of $S$ greater than $2$. Call it $x_2$. And so on. Can you take it from here?