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.
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
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.
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.
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.
Haha
There we go.... Another good example of isolated and limit points!
2nd half of video is empty set.
no, there is still a logo in the bottom right corner
6:52 may that's a good place to stop and we come back and look at the notion of the closed set,.......
Michael penn I really like the way you attack the problem and the method of your explanation. Keep it up. With love from India
I really don't know about ISOLATED. POINTS then also I watched the video for having fun with MICHAEL PENN
0:57 That’s a pretty introverted way to describe limit points and isolated points lol
The Graphical Representation helped a lot. Thanks!
Thank you so much, Dr. Penn!
6:50 before entering the void for 11 minutes 🤔
nice one
finally something new
Maybe 6:50 was not a good place to stop?
Very well explained, Michael!
What a short video but nice and super clear; what happened after minute 7?
The quantity of useful content converged to zero😅
Ends around 6:55
I already thought that i can wake up to 1 7 m i n u t e s of this goodness
The Maths grind just doesn't stop here 😎💪🏻
3:25 it seems that the intersect of the set and the e-neighborhood would be the empty set. What am I missing?
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
Could you please send me the link of the previous video you talked about (0 the accumulation point)
A nice video to explain the isolated point and closed set!
But there are too many advertisements that distracting me from watching it.
Saludos. Debería haber una opción para subtitulos en español.
Tank you meter for this vidios can you explained graph theory
Look up Sarada Herke on UA-cam
@@________6295 tank you
Tank you
@@noumaneelgaou1624 tank？
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.
Hi,
Not enough time to eat my cake as usual, so... no, not really a good place to stop :)
🔥🔥🔥
Until 6:55
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.
Good video but PLEASE stop interjecting “maybe” every couple of sentences.