I see that you have over fifty postings.
By now you should understand that this is not a homework service
So you need to either post some of your work on a problem or you need to explain what you do not understand about the question.
Let S be a non-empty set of real numbers and suppose that L is the least upper bound for S. Prove that there is a sequence of points in S such that --> L as n --> .
Prove or disprove:
For non-empty bounded sets S and T: lub(SUT) = max{lub(S), lub(T)}.
I think the question stated that we need to PROVE that there is a sequence of points such that as .
I've done some work on this thanks to other sources, but I'm sure it either has some errors or is completely wrong.
For some such that where as .
Can anyone tell me if I'm missing anything or if I did something wrong?
I'm not exactly sure how that is meant to work into the first half of the question, or I'm mistaking it for being related to the first half when it's meant for the second.
I came up with my current answer from this link: http://www.mathisfunforum.com/viewtopic.php?id=1645, but I'm sure there's something in it that's missing.
The proof in the link is wrong. Use the same counterexample I gave.
The usual problem that goes with a similar proof is:
If then there is a sequence of distinct points from that converges to .
But the example where may not work except for almost constant sequence.