Lecture 23(A): Compact Sets and Metric Spaces; Bolzano-Weierstrass Theorem

[@adwait9806]

Thank you , this video is beautifully compact

[@ArizonaMathCamp]

Thanks! It's bounded! It's closed! Glad it was helpful.

[@hemnkhdr5658]

Thank you for your excellent explanations.

[@eppson9778]

Thank you very much! This is a very clear and well thought out explanation!

[@ArizonaMathCamp]

Glad you enjoyed it. Thanks for the good feedback on it.

[@vishwpatel8992]

Bit mistake at 4:52 Xn=1/n not in (0,1) for n=1 Btw it won't matter bcz still seq converges at 0

[@ArizonaMathCamp]

Yes, I should have used the interval (0,1] for this example.

[@zaidgharaybeh8422]

Thanks a lot!! learning this as background for multi armed bandit problem

[@emanhasheim3654]

Thank you very much 🥰🥰 I watching you from iraq and it was very useful

[@ArizonaMathCamp]

Great! I'm glad it was helpful.

[@ameliali9489]

I am curious about why there is no video about fixed point theorem? Or is it just me not finding it. Hope that you are all well, Mark!

[@ArizonaMathCamp]

A timely question. Fixed point theorems coming soon (after a second video on Maximum Theorem).

[@zhiqipeng7826]

Thank you so much， THIS REALLY HELPS！

[@ArizonaMathCamp]

Great! I'm glad it was helpful.

[@김명자-g8z]

thank u very much the clear explanation helped me a lot. by the way r u over the glassboard ?

[@ArizonaMathCamp]

I'm glad it was helpful. Not sure what you mean by "over the glassboard"? Do you mean "am I not doing it anymore"? I hope to do more soon.

[@ArizonaMathCamp]

Here's the answer: kzbin.info/www/bejne/d5XQY6WXpMiEkJY

[@SO-dl2pv]

Thank you it is a great lecture. I have a question how to find an explicit formula for x(n+1) = 2*sqrt[x(n)]/(1 + x(n) )?

[@ArizonaMathCamp]

I think what you mean is that you want an explicit solution of this difference equation. I don't see the solution right off, and this seems unrelated to the lecture, so you'll have to do this one on your own.