Real Analysis | Isolated points

[@sinecurve9999]

The end of this video is an isolated point from the set of useful content in this video. The good place to stop is a limit point in the set of useful content in this video.

[@clonebin0]

Haha

[@anirudhranjan7002]

There we go.... Another good example of isolated and limit points!

[@JB-ym4up]

2nd half of video is empty set.

[@nikitakipriyanov7260]

no, there is still a logo in the bottom right corner

[@parameshwarhazra2725]

6:52 may that's a good place to stop and we come back and look at the notion of the closed set,.......

[@parameshwarhazra2725]

Michael penn I really like the way you attack the problem and the method of your explanation. Keep it up. With love from India

[@Reliquancy]

0:57 That’s a pretty introverted way to describe limit points and isolated points lol

[@datsmydab-minecraft-and-mo5666]

The Graphical Representation helped a lot. Thanks!

[@goodplacetostop2973]

6:50 before entering the void for 11 minutes 🤔

[@________6295]

nice one

[@________6295]

finally something new

[@vaxjoaberg9452]

Maybe 6:50 was not a good place to stop?

[@shivansh668]

I really don't know about ISOLATED. POINTS then also I watched the video for having fun with MICHAEL PENN

[@elgourmetdotcom]

What a short video but nice and super clear; what happened after minute 7?

[@jonaskoelker]

The quantity of useful content converged to zero😅

[@loopingdope]

I already thought that i can wake up to 1 7 m i n u t e s of this goodness

[@sitienlieng]

Thank you so much, Dr. Penn!

[@claudefazio]

Very well explained, Michael!

[@Cmummy]

The Maths grind just doesn't stop here 😎💪🏻

[@caladbolg8666]

Ends around 6:55

[@supermacc5]

Saludos. Debería haber una opción para subtitulos en español.

[@peacecitizen1]

3:25 it seems that the intersect of the set and the e-neighborhood would be the empty set. What am I missing?

[@pierreemad2220]

The answer here lies in understanding the difference between a set and an interval. An interval Is a region of the real number line bounded by an upper and lower bound (the bounds may or may not be included in the interval depending on whether it is a closed interval or an open interval respectively). A set is any collection of values. That's it. There doesn't have to be a rule for the elements of a set, just like how not every function has an equation. The set in 3:25 happens to be composed of an interval and some element *a* outside of that interval for no particular reason other than it is possible. That's why *a* is still considered an intersection. Because it is an element. An isolated element but an element none the less

[@weilam]

A nice video to explain the isolated point and closed set! But there are too many advertisements that distracting me from watching it.

[@CM63_France]

Hi, Not enough time to eat my cake as usual, so... no, not really a good place to stop :)

[@noumaneelgaou1624]

Tank you meter for this vidios can you explained graph theory

[@________6295]

Look up Sarada Herke on KZbin

[@noumaneelgaou1624]

@@________6295 tank you

[@noumaneelgaou1624]

Tank you

[@________6295]

@@noumaneelgaou1624 tank？

[@6cef]

½ way through following more closely than normal, wonder how much longer? 13 minutes. No way I'm going to understand what's at minute 15 of this video. 11 minutes of silence ftw.

[@arvindsrinivasan424]

🔥🔥🔥

[@arvindsrinivasan424]

Until 6:55

[@debendragurung3033]

Context : While trying to prove in the sequence {an} =1/n , that all the 1/n are isolated points. Isn't it sort of cheating when we are using ε>0. where ε is a real number. Anyways as bizzare as it is I get the jist of how we are trying to understand numbers.

[@paologat]

Good video but PLEASE stop interjecting “maybe” every couple of sentences.