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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Пікірлер: 27
8:59 A good place to stop right before showing an empty intersection for 9 minutes
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.
Thank you for these videos, they're so helpful for Real Analysis!
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.
One of the most amazing facts is that the Cantor set is compact!
17:56 run time. I predict its half blank.
Thank you so much !!! Finally ,now my concepts are cleared 🙏🏻
Wouldn’t a random picking of elements for a sequence require the axiom of choice? Or is it possible to construct an explicit sequence?
@martothelfriky
3 жыл бұрын
Closed and bounded sets in R contain their minima. Just make a sequence of them. No AC required.
@martothelfriky
3 жыл бұрын
If we're not in R, you will have to get the minima according to an injective function from your space onto R.
Open Cells nested has a number in common?
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.
@tomatrix7525
3 жыл бұрын
It is a limit point.
@carl3260
3 жыл бұрын
@@tomatrix7525 What if K_n={a} for all n?
Thank you for your helpful videos. Please excuse me while I scream into the void. I'M LOSING MY F*CKIN' MIND AHHHHHHHHHHHHHHHHHHH
What happens from 9:00 until the end? Just a black screen...
@noahtaul
3 жыл бұрын
It wasn’t a good place to stop
Maybe he was trying to add the picture of his t shirts or something and accidentally he added a black screen at the end 😔
I have to say I kind of dislike how he started to focus on sets so much instead of sequences and series
You don't explain the reasoning behind anything you do. Stereotypical maths teacher who assumes their audiences (students) know more than they should... 🥱😒
@loopingdope
3 жыл бұрын
?
@________6295
3 жыл бұрын
check out his previous videos before posting stupid comments
@JB-ym4up
3 жыл бұрын
Stereotypical student: doesnt do the previous work, then complains the current work is too hard and therefore the teacher is bad.
@killdm
3 жыл бұрын
I don't understand the meaning of this comment. I m not a pro in maths but still can follow(mostly) and see the beauty(i mean it) of this channel. Can assure completely outside of the "stereotypical maths teacher" u meant before.
@bigcheese6855
3 жыл бұрын
🥱
Open Cells nested has a number in common?