Real Analysis Ep 12: Subsequences & Bolzano Weierstrauss

Episode 12 of my videos for my undergraduate Real Analysis course at Fairfield University. This is a recording of a live class.

This episode is about subsequences and the Bolzano-Weierstrauss theorem.

[citizencj]

This is hilariously edited. Nice star wars text haha.

[valeriereid]

Professor I needed that laugh, thank for directing your viewers to your rapping colleague. I am laughing soo hard I forgot everything you said earlier in the video.

[pulkitmohta]

At 27:33, the point marked π should actually be 2π, and the one that is marked 1.5 should be π.

[evenaicantfigurethisout]

EDIT: oh wait nvm just saw it in part (d)

for c ii, if i had chose the sequence say $\(\sin\(\frac{n\pi}{6}\)\)$, then i could make a convergent subsequence out of that correct?

[MichaelKelly-ll]

This was my frustration as a math major in college. The professor not going through the whole proof because it’s too rigorous or it’s too trivial. Like I actually want to see the whole thing. Only way I can learn is knowing the full context. Math textbooks are also this vague. I love math, but it’s frankly not assessable. Don’t get me wrong, these lectures are great. But as a 21 year old undergraduate, I would have been spinning my wheels with no idea how he can conclude anx converges.

[ashishrajyaguru]

Dear Chris: Does all sub-sequence need to be monotone or not to satisfy Bol-Wei theorem? Is is possible to obtain lectures notes for these lectures? :)


Kind Regards,
Ashish

[lonemaven]

What's the point of question d at the end? Does it want to show that the inverse of the Bolzano-Weierstrass theorem is not true - i.e., if a sequence has a convergent subsequence, then that sequence is bounded?