Real Analysis | Nested compact sets.

We prove a generalization of the nested interval theorem. In particular, we prove that a nested sequence of compact sets has a non-empty intersection.

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[goodplacetostop]

8:59 A good place to stop right before showing an empty intersection for 9 minutes

[phnml]

I really like the videos. I'm not a student at college right now because I'm still at high school but I'm still very interested in pure maths and these videos help me with working myself through my textbook which can be quite dry sometimes.

[사기꾼진우야내가죽여]

The most interesting part of mathematics is when we discover that some properties that seem to be applied to certain objects can be generalized to more various objects.

[JesseReed-no]

Thank you for these videos, they're so helpful for Real Analysis!

[JB-ymup]

17:56 run time. I predict its half blank.

[abhijitharakali]

One of the most amazing facts is that the Cantor set is compact!

[kindykomal]

Thank you so much !!! Finally, now my concepts are cleared 🙏🏻

[carl]

Think maybe a small step missing since a is not known to be a limit point (it’s a subsequence limit, but may equal one of the subsequence elements, so not a limit point). But for each K_n, a is either in the subsequence from then on and so directly in K_n, or not and so is a limit point of K_n and in it by closedness.

[Pieter]

What happens from 9:00 until the end? Just a black screen...

[arthurlbn]

Open Cells nested has a number in common?

[IbrAhMath]

Wouldn’t a random picking of elements for a sequence require the axiom of choice? Or is it possible to construct an explicit sequence?

[shylaatchison]

Thank you for your helpful videos. Please excuse me while I scream into the void.

I'M LOSING MY F*CKIN' MIND

[donaldbiden]

Maybe he was trying to add the picture of his t shirts or something and accidentally he added a black screen at the end 😔

[backyard]

I have to say I kind of dislike how he started to focus on sets so much instead of sequences and series

[bigcheese]

You don't explain the reasoning behind anything you do. Stereotypical maths teacher who assumes their audiences (students) know more than they should... 🥱😒

[arthurlbn]

Open Cells nested has a number in common?