As an extension to the title question:
If a sequence is bounded below (by say 0) but not above (infinity), does the Bolzano-Weierstrass theorem apply? (i.e. does it have a convergent subsequence?).
I think the answer is yes, since the subsequence can consist of those elements that tend towards zero but I'm not sure since I'm just getting familiar with the Bolzano-Weierstrass theorem.
Would like to kindly check my understanding. Thank you!