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 $\displaystyle X$ 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 $\displaystyle X$"?
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.
See here: Extreme value theorem - Wikipedia, the free encyclopedia
Exactly using of B.W. theorem to prove that.