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 | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

**Physics Forums | Science Articles, Homework Help, Discussion**