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

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- Mar 25th 2010, 08:33 AMpaulreadExtreme Value Theorem
Write a proof of the extreme value theorem that is based on the Bolzano-Weierstrass theorem. Thank you!

- Mar 25th 2010, 08:45 AMPlato
- Mar 25th 2010, 09:24 AMpaulread
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, 10:29 PMDrexel28
Just out of curiosity, how did you do this? I am assuming the full question is something of the sort "If $\displaystyle X$ is a metric space with the B.W.P. and $\displaystyle \varphi:X\to\mathbb{R}$ is continuous that $\displaystyle \varphi$ assumes a max and min on $\displaystyle X$"?

- Mar 27th 2010, 08:33 AMpaulread
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, 12:30 PMDrexel28
- Mar 27th 2010, 04:33 PMxxp9
See here: Extreme value theorem - Wikipedia, the free encyclopedia

Exactly using of B.W. theorem to prove that.

- Mar 27th 2010, 06:04 PMDrexel28