Proof of Bolzano-Weierstrass theorem using Axiom of Completeness.

kindlychung
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This is an analysis exercise, I don't get the definition of S. Could anyone explain, please?
See the attached pic.
 

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It might help you to look at an example. Let an = (-1)n/n. Plot a few of these: -1, 1/2, -1/3, 1/4, ...

Now what x would be in your set S? Can you see any x ≤ 0 is in S but any x > 0 isn't?
 

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