Limits Question: Proving Sn <= b for Finite n

[phygiks]

Hello,
I'm having trouble with this question.
Let Sn be a sequence that converges. Show that if Sn <= b for all but finitely many n, then lim sn <= b.
This is what I'm trying to do, assume s = lim Sn and s > b. (Proof by contradiction) abs(Sn-s) < E, E > 0. Don't know what to do from there, but maybe set E = s -b. E is epsilon by the way. Probably to start using latex...

If anyone could help, that would be awesome.

 

[Mandark]

Your idea is fine so far. Now what does $$|s_n - s| < \epsilon = s-b$$ for all n > N imply?

 

[phygiks]

s is a upper bound, so the Sn-s is negative. So abs(Sn-s) < s -b doesn't hold true all n. I'm not sure though