Okay. The problem I have is:(adsbygoogle = window.adsbygoogle || []).push({});

Let {x_n} be bdd and let E be the set of subsequential limits of {x_n}. Prove that E is bdd and E contains both its lowest upper bound and its greatest lower bound.

So far, I have:

{x_n} is bdd => no subseq of {x_n} can converge outside of {x_n}'s bounds=>E is bounded.

Now, sse that y=sup(E) is not in E=> there is a z in E s.t. y-e < z < y for some e > 0.

Now, how would one proceed from here?

**Physics Forums - The Fusion of Science and Community**

# Prove that a sequence of subsequential limits contains inf and sup

Have something to add?

- Similar discussions for: Prove that a sequence of subsequential limits contains inf and sup

Loading...

**Physics Forums - The Fusion of Science and Community**