# Extreme Value Theorem

• Mar 25th 2010, 09:33 AM
Extreme Value Theorem
Write a proof of the extreme value theorem that is based on the Bolzano-Weierstrass theorem. Thank you!
• Mar 25th 2010, 09:45 AM
Plato
Quote:

Write a proof of the extreme value theorem that is based on the Bolzano-Weierstrass theorem. Thank you!

So if this is not a demand, where is your work on this problem?
• Mar 25th 2010, 10:24 AM
Note: I wrote the question I'm being asked exactly. The "thank you" signifies my appreciation for any help with the proof. How that can be taken as a demand is bewildering to me. Help is no longer needed.
• Mar 26th 2010, 11:29 PM
Drexel28
Quote:

Write a proof of the extreme value theorem that is based on the Bolzano-Weierstrass theorem. Thank you!

Just out of curiosity, how did you do this? I am assuming the full question is something of the sort "If $X$ is a metric space with the B.W.P. and $\varphi:X\to\mathbb{R}$ is continuous that $\varphi$ assumes a max and min on $X$"?
• Mar 27th 2010, 09:33 AM
Quote:

Note: I wrote the question I'm being asked exactly. The "thank you" signifies my appreciation for any help with the proof. How that can be taken as a demand is bewildering to me. Help is no longer needed.

Quoting myself. Again, I wrote the question EXACTLY. I still don't know any kind of TeX and I'm not sure how you guys get all the math symbols, which is why I haven't shown any of my work. If I need help again I'll be sure to put in as much of an effort in asking the question as I could expect someone to give in answering it for me.
• Mar 27th 2010, 01:30 PM
Drexel28
Quote:

Quoting myself. Again, I wrote the question EXACTLY. I still don't know any kind of TeX and I'm not sure how you guys get all the math symbols, which is why I haven't shown any of my work. If I need help again I'll be sure to put in as much of an effort in asking the question as I could expect someone to give in answering it for me.

I'm not prompting you to show more work. I am just curious how you solved it. I don't see an easy method right off the bat.
• Mar 27th 2010, 05:33 PM
xxp9
See here: Extreme value theorem - Wikipedia, the free encyclopedia
Exactly using of B.W. theorem to prove that.

Quote:

Originally Posted by Drexel28
I'm not prompting you to show more work. I am just curious how you solved it. I don't see an easy method right off the bat.

• Mar 27th 2010, 07:04 PM
Drexel28
Quote:

Originally Posted by xxp9
See here: Extreme value theorem - Wikipedia, the free encyclopedia
Exactly using of B.W. theorem to prove that.

That seems like leaps and bounds to avoid just using the concept of open covers.