Functional Analysis 2 | Examples for Metrics - Euclidean or Discrete Metric?

[@michaadamus5885]

Man, you are a lifesaver. I normally don't comment on KZbin, but wanted to let you know how much i appreciate your work, which you put in explaining maths to People here. Great job

[@brightsideofmaths]

Thank you very much! I am very glad that the videos help you :)

[@qiaohuizhou6960]

0:25 a metric space helps generalize notion in real analysis 0:59 example : complex plane 1:39 example : Euclidean metric in Rn 2:33 example: a maximum metric in Rn 4:10 example: X is any set, a discrete metric

[@Mango_9934]

thank you

[@himanshuhani]

The lecture is so nice that even an undergraduate like me in my second year can easily understand it.

[@brightsideofmaths]

Nice :)

[@tomaszhejna8446]

i study it in my first semester of my first year so its not that complicated

[@SATOUBLOGS]

Thank you. I was alway scared of metrics and things involving set theory notation, but it's not as scary as I thought.

[@stat5web]

Excellent presentation! One of the best math series on youtube.

[@brightsideofmaths]

Thank you :)

[@xwyl]

This is really the bright side.

[@shouryasmondal6199]

This is the best series about metric space ❤️ easiest explanation....great help man ✨

[@brightsideofmaths]

Glad you liked it

[@robertschlesinger1342]

Worthwhile video. Many thanks.

[@PunmasterSTP]

Examples for metrics? More like "Exemplary material for students!" Thanks for putting out so much very helpful information.

[@zazinjozaza6193]

Awesome, can't wait for more!

[@lucaug10]

Great video, looking forward to seeing more functional analysis!

[@suwandi178]

this explanation made me understand more about the functional analysis 👍👍

[@danielyuan9862]

Honestly, you can think of the discrete metric as the minimum number of teleports to get from one place to another, given that you can teleport anywhere in the metric space. In that case, unless you are already at your destination, which would just mean d(x,y)=0 for x=y, you would only need one teleport to get to a different spot, which means d(x,y)=1 for x≠y. And because the definition I stated is like a "minimum path length" definition, it should satisfy the triangle inequality.

[@gregoryfenn1462]

To visualise the discrete metric, use a complete graph. Eg if a set X has three elements, draw an equilateral triangle. Then the distance from any vertex to another is 1 but the distance from a vertex to itself is 0.

[@strai5150]

Really a helpful series as like Measure Theory😊

[@泽峰刘]

man what can i say，best video i ever seen

[@renfreedom8444]

Great video, thanks for sharing this.

[@adityamanimishra5053]

Excellent video as always.

[@sanyatiwari2294]

Ha beta

[@fabiangabel]

If you are looking for some counter-examples to complement this video, I have you covered: kzbin.info/www/bejne/lamZmZuDgLqcbtk

[@rabbit719]

I have a question on the visualisation of example 3. For y and z, does it imply they have the same values in the other dimensions except 1 and 2? Thanks

[@alexandralaw1476]

Thank you for this brilliant video! By the way, if you would introduce deeper on norm (sup norm, p norm etc.) I will be really grateful!

[@ahalyageorgeclinton486]

Hi, This video helps lot of me. I want to ask you a question if u have time , can you help me? Assume that d1 and d2 are two metrics on X. how to show d(x,y)=d1(x,y)+d2(x,y)

[@duchengp2422]

if it's possible, can you have a series about topology

[@fatimasani62]

Good day, sending you love from Nigeria 🇳🇬 thank you for the videos Am just coming across your functional analysis videos now which are really helpful to me, because I have not been understanding the course and am about to start writing my examinations, I don't know if you can help me with some of the exercises we're given for practice, if you can make a video of there solutions, it will really be helpful for me. Thank you and have a wonderful time

[@PunmasterSTP]

How did your exams go?

[@fatimasani62]

@@PunmasterSTP It went really good with the help of the videos honestly, i watched the whole collection. Thank you for asking *smile*

[@PunmasterSTP]

@@fatimasani62 Hey thank you for responding, and I'm glad everything went well! This channel and the videos on it are truly amazing. I've looked around and watched a bunch of other stuff, but the explanations and the examples here are truly outstanding.

[@lokenaththakur2007]

WHICH APPLICATION DID YOU USE FOR THIS NICE PRESENTATION

[@brightsideofmaths]

XOURNAL :)

[@gamefaq]

Do you plan on covering hilbert and banach space theory in this series?

[@brightsideofmaths]

Yes, I do :)

[@shouryasmondal6199]

You should make videos about multivariate calculus too 🥺it would be a great help ✨❤️

[@arghyachakraborty5181]

3:37 d(x,y)=d(x,z) why?

[@brightsideofmaths]

Because of the maximum definition in this case.

[@sanjivsentil3850]

Thank you sir but pls cover all the maths topics

[@mubarakmjungudo6677]

Thanks for your help sir

[@brightsideofmaths]

Always welcome

[@ujjalmajumdar618]

I just have a little point to add the triangle inequality in case of Euclidean metric is not trivial. It requires Minkowski's inequality to be proven true. That is if x, y are members of lp spaces then (summation from i=1 to ∞|xi+yi|^p)^1/p≤(summation from i=1 to ∞|xi|^p)^1/p+(summation from i=1 to ∞|yi|^p)^1/p

[@brightsideofmaths]

l^p spaces will be discussed in part 7 :)

[@ujjalmajumdar618]

Looking forward to more of this. I already completed upto Banach spaces. Thanks however for taking some time out to discuss these complicated topics.

[@brightsideofmaths]

@@ujjalmajumdar618 Yeah, you are welcome! I am not as quick with the uploads as I wanted to be because I have so much to do at the moment. However, don't worry, I try to upload at least one new video each week.

[@husseinshimal7567]

شكرا جزيلا

[@gerardtavares45]

Thanks for the video I like it😊

[@brightsideofmaths]

Thank you too

[@hafsarasheed4006]

When will you complete the whole course of functional analysis ?? Kindly let me know..

[@yuechengyin1213]

Hi, may I translate this series into Chinese and post them on Bilibili channel?

[@brightsideofmaths]

You can write Chinese subtitles that I can put in this video.

[@sebastiancosta55]

That's almost the Hamming Metric!

[@himashreekalita6787]

Thank you

[@brightsideofmaths]

You're welcome! And thanks for your support :)

[@اممودةليث]

Please translate into Arabic for all videos

[@brightsideofmaths]

I need someone who can do that.

[@mmanojkumar3950]

Helllllowwwww

[@brightsideofmaths]

Welcome :)

[@mmanojkumar3950]

@@brightsideofmaths You'll see me quite often here from now!

[@brightsideofmaths]

@@mmanojkumar3950 Enjoy the videos :)