You are better than my lecturer who has a PhD. I wish you all the best in doing these videos.And it would be great if you could do a series on complex analysis and Integration in real analysis.
I failed two times in Metric spaces B.Sc Mathematics, but got 82% marks after watching your videos. The concepts are very clearly explained and east to understand
I finished my first course in algebra in algebra with excellent grade thanks to this guy :) Im doing real analysis next semester. I think I just wanna start noe since all I need is here on this channel
I am really satisfied to receive such nicely presentation movie clips & animation to review my early life accumulated knowledge. I update my lost idea & renovate again my confused ideas. Thank to all gentle people who created such entertain knowledge world.
The detailing of minute concepts in your teaching is amazing....Very few people explain things with such detail...I am thankful to u for these video lectures...keep teaching and keep learning...
You are so genius, i have gone thru so many websites and videos explaining metric space and topology but you are so good at explaining things wow thank you!
I remember when I first looked at this video it meant NOTHING to me , then I did a basic Real Analysis Module with a college, and after watching this again I understand everything, probably because through the analysis class I learned about epsilon and delta and all that stuff.
bit out of the context but i have been wondering the following: what would happen if the second axiom is changed such that an element in our universe could at two points at the same time and thus making the distance zero or some other value? Such a question probably could be posed by a physicist who wants to work on some vector space bit different than the ones that we keep using but I have the impression that it would be interesting in the context of physics
Let us try praising youtube tutors without demeaning our university lecturers / professors. University teachers and youtube tutors are subject to very very different constraints and environmental variables, and so it is really not fair to compare and benchmark their performances.
Why does the distance between two members of a metric space map to a real number? The set of real numbers is itself (along with the Euclidean distance function) a metric space. In that case, how can real numbers be used to describe a property of real numbers?
Sujan Kapadia it doesn’t make sense to have non positive real distances The distance function measures ‘how far’ two elements in a set are: it needs to be +ve real, otherwise we couldn’t have theorems about convergence wouldn’t make sense
1. Thank you for explaining but 2. I believe it would be even better if you instead of reading letters, read the actual meaning. Example: instead of "for all epsilon greater than zero... if little n greater than big N..." the actual meaning is " No matter how small I chose the positive value of epsilon I can always find the Number of the element after which the all the consecutive elements will be no further than epsilon distance from my limit value." It might seem little difference here but in more complicated concepts it helps to understand. 3. For some listeners might help to mention the life implication like: I am a sequence and I want to be that close in my relationships to, say, Ashley. So no matter how close I want to be to her (kissing or sleeping) there exists a certain number of dates I have to go out with her so after that we get as close as I wanted.
Hi, i was just wondering. Why is it that you have no way for your audience to support you? I mean financially :) Have you ever considered something like Patreon or different service? Also, thanks for excellent videos :)
Nope, because if you do that you would have the same point instead of a triangle, and as he said, the distance from a point yo the same point is í zero.
Ты можешь использовать лишь три аксиомы: 1) d(x, x) = 0 2) d(x,y) = d(y,x) 3) d(x,y) < d(x, z) + d(z,y). Используя их можешь получить d(x,y)>0. ru.wikibooks.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B8%D1%8F_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D0%B9_%D0%B4%D0%B5%D0%B9%D1%81%D1%82%D0%B2%D0%B8%D1%82%D0%B5%D0%BB%D1%8C%D0%BD%D0%BE%D0%B3%D0%BE_%D0%BF%D0%B5%D1%80%D0%B5%D0%BC%D0%B5%D0%BD%D0%BD%D0%BE%D0%B3%D0%BE/%D0%9C%D0%B5%D1%82%D1%80%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE%D0%B5_%D0%BF%D1%80%D0%BE%D1%81%D1%82%D1%80%D0%B0%D0%BD%D1%81%D1%82%D0%B2%D0%BE
You are better than my lecturer who has a PhD. I wish you all the best in doing these videos.And it would be great if you could do a series on complex analysis and Integration in real analysis.
ua-cam.com/video/cVEbr0dEaZI/v-deo.html after 3 years lol u must be graduated by now
Thank you.
I love how the motivations behind the concepts are explained, something even my lecturer fails to do clearly
I failed two times in Metric spaces B.Sc Mathematics, but got 82% marks after watching your videos. The concepts are very clearly explained and east to understand
I finished my first course in algebra in algebra with excellent grade thanks to this guy :) Im doing real analysis next semester. I think I just wanna start noe since all I need is here on this channel
I failed it the first time, this is my second time I hope the video is as good as u say cuz I haven’t watched it yet
Absolutely phenomenal explanations. Thank you so much for the time you put into all of your videos.
I am really satisfied to receive such nicely presentation movie clips & animation to review my early life accumulated knowledge. I update my lost idea & renovate again my confused ideas. Thank to all gentle people who created such entertain knowledge world.
The detailing of minute concepts in your teaching is amazing....Very few people explain things with such detail...I am thankful to u for these video lectures...keep teaching and keep learning...
This dude is a genious, have no better words for describing him.
I cannot express how excited I am that I found these videos, i have hopes for passing my course on real analysis now
I hope you continue to like them so much and don’t get fed up of me. :)
You are so genius, i have gone thru so many websites and videos explaining metric space and topology but you are so good at explaining things wow thank you!
Whenever I have problems regarding concepts, I go for you tube and I find my solution always in Ben1994
Thank you Ben1994
The best teaching.after learning this my concepts are very cleared.....you make seem so easy with easy language.. THANK YOU SO SO MUCH
Thank you for the video. It really helps clear the concepts that I have been struggling for a long time.
Really appreciate what you are doing here ! Keep making such videos. This one made me understand the subject better. Thanks. :)
Your video's are saving me. I am a grad student in the dep. of Math and this video is my main reference.
just finished the whole series, Awesome and really helpful videos!
How long did it take you boy genius?
Very well explained. Great job! Thank you!!!
You got my knickers in a knot the way you defined the distance function in relation to the Cartesian product of the set with itself.
You make me to understand more the concept of metric, may God bless you...
I remember when I first looked at this video it meant NOTHING to me , then I did a basic Real Analysis Module with a college, and after watching this again I understand everything, probably because through the analysis class I learned about epsilon and delta and all that stuff.
Sir you are teaching superb
Your videos are really helpful and concept clearing
Thank you for uploading the video! The graphic example of limit on the real line and the example of Cartesian product are very helpful.
bit out of the context but i have been wondering the following: what would happen if the second axiom is changed such that an element in our universe could at two points at the same time and thus making the distance zero or some other value? Such a question probably could be posed by a physicist who wants to work on some vector space bit different than the ones that we keep using but I have the impression that it would be interesting in the context of physics
you are one of the best teachers
I love this guy's enthusiasm towards mathematics hahaha
jesus christ this guy's channel is awesome, very recommended
Thank you for your nice words.
I got your video today and it was too late cuz i got an exam tomorrow so am gonna watch all of your videos after, thanks dude
Cool video, a bit long but definitely worth to watch as concepts are explained clearly. Big thanks ))
GREAT videos..concepts are made crystal clear. Thank you so much for uploading them.
Fantastic job explaining. Kudos!
people like this are awesome. you, 3blue1brown, and math is beautiful. How to make sense in engineering classes. ahah
you are a fantastic teacher
The 3 rules for a distance function are axioms which define the theory of metric spaces
Let us try praising youtube tutors without demeaning our university lecturers / professors. University teachers and youtube tutors are subject to very very different constraints and environmental variables, and so it is really not fair to compare and benchmark their performances.
Or we all live our lives the way we see fit and criticize whomever warrants criticism? How about that?
@@danielsanchez8565I had, luckily UA-cam was around though.
Some people just deserve it.
It is getting very hard to justify the university system itself and the fees it charges, with free very well explained videos like this available.
Why does the distance between two members of a metric space map to a real number? The set of real numbers is itself (along with the Euclidean distance function) a metric space. In that case, how can real numbers be used to describe a property of real numbers?
Sujan Kapadia it doesn’t make sense to have non positive real distances
The distance function measures ‘how far’ two elements in a set are: it needs to be +ve real, otherwise we couldn’t have theorems about convergence wouldn’t make sense
Yes, that is a circular argument. I guess you have to start somewhere with an assumption.
Easily explained. Thank you .
You make it seem so easy. Can you post more videos on d3:R^2*R^2---->R when d3(x,y)=min{1,d(x,y)}
Mashallah baht khub sir g
Do you reccommend any specific books to follow this series of your videos ? :) Best Regards. :)
AMAZING THANK YOU . wouldve been better if you sequenced your all topology videos in an order .
You should do Calculus of Variations.
Thank you for the great work, it helped me a lot!!
you gotta work on closing curly bracecs
There's a good way to do that.
*1. Start here* `
`
'
'
` *2. Lift pen; go to v. bottom*
; *4. Done*
;
:
; *3. i.e. here*
i stopped in mid to like this comment!!
Very useful
1. Thank you for explaining but
2. I believe it would be even better if you instead of reading letters, read the actual meaning. Example: instead of "for all epsilon greater than zero... if little n greater than big N..." the actual meaning is " No matter how small I chose the positive value of epsilon I can always find the Number of the element after which the all the consecutive elements will be no further than epsilon distance from my limit value." It might seem little difference here but in more complicated concepts it helps to understand.
3. For some listeners might help to mention the life implication like: I am a sequence and I want to be that close in my relationships to, say, Ashley. So no matter how close I want to be to her (kissing or sleeping) there exists a certain number of dates I have to go out with her so after that we get as close as I wanted.
Thank you.
Thank you random stranger on the internet
Is there a way to generalize even further and eliminate the necessity for numbers both in topology and in metric space to deal with sets of any kind ?
Is it not very similar to Cauchy sequence? I am confused now.. kindly somebody state the difference.
Great video and thanks alot 😄
very nicely explained! Thank you!
I don't understand how the axioms relate to the limit notion at the end. If anyone could explain, that would be really wonderful.
Why is it called the Symmetric Property and not the Commutative Property? If
Very eloquent video. Thanks for uploading!
the video quality is very poor but the way you teach is great. love it
Thank you.
@@elliotnicholson5117 it is only 360p so can we get better quality in this video?
I don’t think so I’m afraid. The way I make videos now is very different though.
good explanation
Tnx aLot Sir. 4m Sri Lanka.
❤️
i know this will save me. TYSM
I like your videos !
hats off to you sir👍👍👍
How are you? Sir please share with me the best book of metric space which is one of the best concept able book. Please send me.
sir, can you please put a video explaining the proof of urysohn's lemma.
Hello Sir !
could you please tell me that what are the abstract distance spaces other than metric and normed spaces ?
Sir, Please tell me.. How to Determine whether the permutation is even or odd. Please reply me.. I am Waiting
thank you a good reminder
good video
Thank you so much!
Very welcome.
you are fantestic job
Hi, i was just wondering. Why is it that you have no way for your audience to support you? I mean financially :) Have you ever considered something like Patreon or different service? Also, thanks for excellent videos :)
Why do we define thé number epsilon ?
A set with a distance function.
can anyone advice whats prequisite to understand this series or the motivation. Do we need some real analysis?
A rigorous basis for geometry.
Hi, What kind of book do you advise for functional analysis
Can i contact you ? I have a question about metric space
Hi , are x y z three distinct points ? or we can have x=y=z or x=y or y=z or x=z in triangle inequalty ?
Nope, because if you do that you would have the same point instead of a triangle, and as he said, the distance from a point yo the same point is í zero.
nice
what kind of book have you read for functional analysis
The triangle inequality has several useful consequences. Show that
|d(w x) - d(x y)| =< d(w z) + d(z y)
wish u are my lecture
vry helpful
Awesome
what is that BIG N?
thanks sir
Ты можешь использовать лишь три аксиомы: 1) d(x, x) = 0 2) d(x,y) = d(y,x) 3) d(x,y) < d(x, z) + d(z,y).
Используя их можешь получить d(x,y)>0. ru.wikibooks.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B8%D1%8F_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D0%B9_%D0%B4%D0%B5%D0%B9%D1%81%D1%82%D0%B2%D0%B8%D1%82%D0%B5%D0%BB%D1%8C%D0%BD%D0%BE%D0%B3%D0%BE_%D0%BF%D0%B5%D1%80%D0%B5%D0%BC%D0%B5%D0%BD%D0%BD%D0%BE%D0%B3%D0%BE/%D0%9C%D0%B5%D1%82%D1%80%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE%D0%B5_%D0%BF%D1%80%D0%BE%D1%81%D1%82%D1%80%D0%B0%D0%BD%D1%81%D1%82%D0%B2%D0%BE
completed
Greetings from Ukraine.
No one:
Guy in UA-cam video: “ZEAD”
*"Zed"
Which is also the 'proper' way to pronounce the english letter z for pretty much anywhere other than America.
What can't you explain?
5:35 I see what's going on, her initials must be B L
RIP headphones users
has anyone ever told you that you sometimes sound like a cyberman
I hope you work as a teacher...