Please please keep making these! The number of creators who make quality undergrad maths content is VERY VERY small. Your videos have been so helpful for my first year :)
Taking Analysis for the first time and I am not understanding it too well. I also work a full-time job and 2 part time jobs, so I don't have too much time to study. Your video has helped me grasp it in such a way I feel more comfortable working on some proofs! Thank you!
Replace '1 full time job and 2 part time jobs' with 'one full time job and 2 young childre'n and this sounds like my story. Not too many of us taking online Real Analysis - which school do you go to ?
Isn't it crazy that you can create content complaining about one boogey man or another and become a multi-millionaire on you tube and yet most of the creators of more serious intellectual content can't make a living doing it.
Hey, I have a question At 10:20 You said wasn't (-2,1) compact because every one of its open covers did not have a finite subcover, So what is "every open cover" in that example and how do they not contain finite subcovers?
In that example we looked at one open cover which happened to have a finite subcover. We did not establish anything about "all open covers" of (-2,1) which would be necessary to establish compactness. I don't explicitly show you an open cover without a finite subcover because the previous example showed how an an open cover of an open interval could be constructed so that it has no finite subcovers, showing open intervals are not compact.
@@matsobanemarksmokhudu2584 It's not compact because it didnt satisfy the definition. The definition states an "if and only if" and so he used the first example to prove it's not compact
At 8:48 are you saying that the first example (0,2) : {(1/k, 2-1/k)} will not have a finite subcover because if we restrict the indexing set of k from 1 to infinity then it will always be impossible for that set to be able to cover (0,2). If other words k must go from 0 to infinity for {(1/k, 2-1/k)} to cover (0,2)? Is that line of thinking correct? Many thanks for all the Real Analysis videos, you have been a great help with my degree 😄
So glad they've been helpful - thanks for watching! My playlist is mostly based on Jay's book and the Stephen Abbott text - at least so far, so it's definitely a good match! I intend on making many more this summer. Also, Jay Cummings appeared in my TI-108 documentary, if you're curious and have an hour+ to spare: th-cam.com/video/xrmqoKchspo/w-d-xo.html&pp=ygUFdGkxMDg%3D
Hello, thank you very much for making the video, it helped me a lot. And please excuse my not good english. And i have a question on the third example that is about open cover of [0,2]. You wrote union between two sets and i think then it would make it (-0.1, 2.4) which is not family of sets, then i think it can't be the cover. But if you write it differently like {"the family of sets", (-0.1, 0.1), (1.8, 2.4)} then i think it can be a cover of [0,2]. (but i am not that sure of it and if i am wrong please correct me, thank you)
You say "any index set" but it seems only countable sets are used. What would happen if we specified a, say subset of the reals as the index set. Take the unit interval of R as the index for example. What then? (No this is not any homework problem.)
I try to make the volume loud and clear so anyone on a phone can hear easily. I notice on my phone sometimes the videos are a little hard to hear even on max volume. But I know I’ve gone overboard a couple of times haha, I hope the video was helpful otherwise.
@@WrathofMaththat is the case for me as well, there are times where i can barely hear anything despite the volume being on max, thanks for being that considerate
Please please keep making these! The number of creators who make quality undergrad maths content is VERY VERY small. Your videos have been so helpful for my first year :)
Taking Analysis for the first time and I am not understanding it too well. I also work a full-time job and 2 part time jobs, so I don't have too much time to study. Your video has helped me grasp it in such a way I feel more comfortable working on some proofs! Thank you!
Glad to help! Good luck with your busy schedule and the class, let me know if you ever have any questions!
Replace '1 full time job and 2 part time jobs' with 'one full time job and 2 young childre'n and this sounds like my story. Not too many of us taking online Real Analysis - which school do you go to ?
This is a great video, sucks that higher level math doesn't do well on youtube. Thank you
Isn't it crazy that you can create content complaining about one boogey man or another and become a multi-millionaire on you tube and yet most of the creators of more serious intellectual content can't make a living doing it.
Taking my first real analysis class and this video really helped with understanding covers! Thank you so much.
Glad it helped - best of luck!
Your videos really help me understand a compact set and open cover.
Thank you
Glad to help, thanks for watching!
You really explain very well. Thanks a lot.
Thank you!
Thank you for the quality content! Im loving these Real Analysis videos.❤
Thank you for watching! More real analysis videos to come this summer, I find they take the longest to make!
so clear and helpful!!
Glad it was helpful!
Thanks for this ❤️
can you also go over the Heine-Borel Theorem? love how you explain things
I certainly will! Which equivalence are you looking for, the open cover definition of compact sets and closed/boundedness?
yeah and also, K is closed/bounded and every open cover for K has a finite subcover
@@WrathofMath please make it before my exam in may plz, open covering!!!!!
Thank you so much , you make everything easy.
Glad to help, thanks for watching!
Thank you! You saved my life
It is my duty! Thanks for watching!
Really helpful ❤️
Glad it was helpful!
Hey, I have a question
At 10:20 You said wasn't (-2,1) compact because every one of its open covers did not have a finite subcover, So what is "every open cover" in that example and how do they not contain finite subcovers?
In that example we looked at one open cover which happened to have a finite subcover. We did not establish anything about "all open covers" of (-2,1) which would be necessary to establish compactness. I don't explicitly show you an open cover without a finite subcover because the previous example showed how an an open cover of an open interval could be constructed so that it has no finite subcovers, showing open intervals are not compact.
@@WrathofMath just explain why it makes that cover not compact because i still dont get why its not compact
@@matsobanemarksmokhudu2584 It's not compact because it didnt satisfy the definition. The definition states an "if and only if" and so he used the first example to prove it's not compact
Amazing video
It is really helpful! Thank you!
Wrath of Math hits the nitty-gritty. Awesome! 😃
Can't wait for 1000 videos from now when my Real Analysis playlist is done!
Do you have something on heine boral theorem ?
Thank you so much,Sir!
Glad to help!
At 8:48 are you saying that the first example (0,2) : {(1/k, 2-1/k)} will not have a finite subcover because if we restrict the indexing set of k from 1 to infinity then it will always be impossible for that set to be able to cover (0,2). If other words k must go from 0 to infinity for {(1/k, 2-1/k)} to cover (0,2)? Is that line of thinking correct? Many thanks for all the Real Analysis videos, you have been a great help with my degree 😄
So helpful thank you!!
Glad to help - thanks for watching!
Thanku for this genius explanation
I do my best, thanks for watching!
Thank you for your great video ❤
My pleasure, thanks for watching!
continue de playlist plssss i wanna know more about compact sets
THANKS THIS HELPED ME
Glad to hear it, thanks for watching!
hey unrelated to the video but which note taking app do you use? it looks really cool
Notability for iPad Pro! It's a great app, though the developers insist on regularly updating it to make it worse.
I really appreciate your videos. This real analysis series with the book I'm reading by Jay Cummings is of a great match!please up load more!!!!
So glad they've been helpful - thanks for watching! My playlist is mostly based on Jay's book and the Stephen Abbott text - at least so far, so it's definitely a good match! I intend on making many more this summer. Also, Jay Cummings appeared in my TI-108 documentary, if you're curious and have an hour+ to spare: th-cam.com/video/xrmqoKchspo/w-d-xo.html&pp=ygUFdGkxMDg%3D
Brooooooooo.u justttnailedddd ittt
Hello, thank you very much for making the video, it helped me a lot. And please excuse my not good english. And i have a question on the third example that is about open cover of [0,2]. You wrote union between two sets and i think then it would make it (-0.1, 2.4) which is not family of sets, then i think it can't be the cover. But if you write it differently like {"the family of sets", (-0.1, 0.1), (1.8, 2.4)} then i think it can be a cover of [0,2]. (but i am not that sure of it and if i am wrong please correct me, thank you)
In R
interesting video. not monotonous. I understand hurray!!
Awesome - thanks for watching!
legend
What literature would you recommend as an alternative for this video? [I learn better from reading than watching videos.]
why [ (-infinity,0) , (-1,0.5) , (0.1,9) ], is not compact ?
it has -2 and 1 in the subsets.
You say "any index set" but it seems only countable sets are used. What would happen if we specified a, say subset of the reals as the index set. Take the unit interval of R as the index for example. What then? (No this is not any homework problem.)
Painful to listen to without turning the volume down lol
I try to make the volume loud and clear so anyone on a phone can hear easily. I notice on my phone sometimes the videos are a little hard to hear even on max volume. But I know I’ve gone overboard a couple of times haha, I hope the video was helpful otherwise.
@@WrathofMath I already passed analysis qual it’s fine lol
@@WrathofMaththat is the case for me as well, there are times where i can barely hear anything despite the volume being on max, thanks for being that considerate