Nested Interval Property and Proof | Real Analysis

[@WrathofMath]

The real analysis playlist has a long ways to go, but I'm working on it! kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli

[@Joshs8707]

bro deserves much much more views, pls keep making more videos on analysis, love from Colorado❤

[@thunayyanhussam713]

I never get disappointed watching your videos! Always very informative and well delivered. Please keep on you are the best math tutor on YT!

[@suhanisoni735]

Very very informative video, literally saved my life. Thank you so much

[@WrathofMath]

Glad to hear it, thanks for watching!

[@jscotch2879]

Still helping people even now! Thanks so much it was sooo much easier to understand!

[@mfonpeter124]

I love the way you explained the concept, making use of genius and simple examples. Keep up the good work 👍.

[@WrathofMath]

Thanks so much!

[@punditgi]

A very important and informative video!

[@WrathofMath]

Absolutely! I pretty much skipped over a typical first chapter in analysis in my playlist, but I'll come back to it eventually to really set the stage for all the material. And NIP is a cool part of that!

[@MathPhysicsEngineering]

I think you may also like the Calculus playlist on my channel, specifically, I would recommend that you check the video from my channel called: "Visual Proof of The Heine-Borel Theorem and Compactness of [a,b]" I make very rigorous visual proof from calculus in this playlist. I also made a video about this theorem called : Cantor's Lemma Proof and Visualization

[@chelekakaumba1262]

My exam is one week away, I find your videos very helpful. ♥️

[@WrathofMath]

Glad to hear it, good luck on the test!

[@apratick]

You are a legend. Wish you all the success in life. Will definitely support you after I start earning.

[@WrathofMath]

Thanks so much - let me know if you ever have any questions!

[@divyamverma2606]

Thanks! Explained with great clarity

[@WrathofMath]

Glad it was helpful!

[@APh_]

Great video as always ☺️

[@WrathofMath]

Thank you!

[@himsuexplains]

Your videos are coolest , Helped me in exams

[@WrathofMath]

Thank you, glad to help!

[@TranquilSeaOfMath]

Good illustration of the theorem.

[@WrathofMath]

Thank you!

[@user-pd6vy7my2f]

Thank you❤

[@adityasethy]

Most lucid explanation of the Nested Interval Theorem

[@wtt274]

Thank you sir for this great video !

[@vinwithaw]

Question, how does this prove that the real no. Line has no holes? If x belongs to the closed interval [a_n,b_n], then that could imply that x CAN be equal to a_n or b_n, thereby producing a hole between a_n and b_n?

[@brendanmccann5695]

I like it. Clear!

[@Mathematics-with-MohsinRaja]

Really explained nicely....❤ ❤

[@WrathofMath]

Thank you!

[@gonzajuarez4918]

Hey. Thanks for the video. I've been stuck at this for a couple of hours. One question though. Why doesn't this proof consider the case where one of the nested intervals is the empty set. My best guess is that this has to do with it being about an *infinite* sequence of closed nested sets. But again, the empty set is included in itself so it could go on and on and on and... on. If the empty set is considered in the sequence, then such x wouldn't exist. As per my understanding.

[@Nikkikkikkiz]

a_n\leq x\leq b_n means that it has to be at least the single point x

[@gonzajuarez4918]

@@Nikkikkikkiz how can I prove that implication?

[@tommasoc.2207]

did you solve this? I was asking myself the same thing

[@siriuss_]

We are dealing with real numbera here, consider a set [-1,1], then it contains [-1/2,1/2] and so on. Whats up with the empty one? here subsets of Reals are infinite, if it gets finite you get that that finite as your answer. Say, if empty set is contained here, the answer is empty, but it should be NESTED

[@kirtiyadav967]

Thank you so much 😊😊

[@ericoduroboateng5269]

please, it is always given in a closed interval?

[@siriuss_]

Hey WoM,any case where that x can be a set (finite), I cant find such Example and my stupid brain is getting more inclined towards a singleton set

[@mathmaniaa6497]

nice video, thx for upload this... may I ask...how to create the nested set so the intersection is (-2,1]

[@okikiolaotitoloju2208]

Could we have used an infimum instead of a supremum for x?

[@mark-hs4bo]

Thanks m8

[@WrathofMath]

Glad to help!

[@realperson3341]

I love you

[@WrathofMath]

love you too

[@naidely4768]

i love you

[@arthurlbn]

(an , bn) nested has common element?

[@siriuss_]

uh, thats my question too, and if that element is singleton only

[@Lakkshay]

I am block head

[@WrathofMath]

How'd you get a block for a head?

[@Lakkshay]

@@WrathofMath i am stupid for this proof not understand 😑 but thanks for video