Real Analysis 9 | Subsequences and Accumulation Values

[@oskaradolfson7450]

I actually had difficulty understanding "limit point" for a long time but this video made it so much clearer! Danke für deine tollen Videos! :-)

[@sajidhaniff01]

Similarly thanks!!

[@qiaohuizhou6960]

0:28 the subsequence is just omitting some members but still have infinitely many members 1:05 index with additional index 1:46 example 3:30 any subsequence is convergence if the original sequence convergent 3:50 why do we need subsequence : to study divergent sequence 5:50 accumulation value is a generalization of limite 6:50 definition of accumulation value/point / cluster point/ limit points

[@ruanramon1]

7:36 the correct pronunciation of the name “Weierstrass”

[@RuizhanGu]

thanks bro:)

[@david_doret]

Thanks

[@brightsideofmaths]

Thank you :)

[@punditgi]

Yes, accumulation points, cluster points, etc. need a good explanation and thankfully we have one here! 🙂

[@brightsideofmaths]

Thank you very much :)

[@MrOvipare]

Okay okay, you have a new supporter on Steady :) Content like this has not always been available on youtube, I'm grateful to have it now :) I hope to see some group theory, differential geometry or fractal geometry on your channel one day hehe... Cheers!

[@brightsideofmaths]

Thank you very much :)

[@michaelmatusek777]

For a very long time I had trouble understanding what exactly a cluster point is, but this really cleared up the entire idea for me. As always, thank you for your insight!

[@brightsideofmaths]

You're very welcome!

[@punditgi]

On second viewing I really like the example of subsequences with their own accumulation points. Very illustrative of the concept. 😃

[@TranquilSeaOfMath]

Great explanation, visuals, and details.

[@brightsideofmaths]

Thanks a lot :)

[@RuizhanGu]

In Chinese Accumulation Values often called:“子数列的极限” it means the limit of the subsequence.

[@brightsideofmaths]

Very good name!

[@just4simplegg428]

Great video

[@ldrtch]

Great series ! How many parts will be in this series ?

[@brightsideofmaths]

I don't know yet but I guess it will have many parts :)

[@AvivNoah-h4w]

Superb video! Thank you

[@brightsideofmaths]

Thank you very much! And thanks for the support!

[@tlli5066]

Hallo! Eine kurze Frage, was wäre der deutsche Korrespondenz zu Real Analysis? Bin selbst mathematisch sehr interessierter Physik Student, ich habe einige Mathe Vorlesung für Mathematiker besucht und finde der Stoff ist alles unter den Namen Analysis versteckt...

[@brightsideofmaths]

Ja, alles Analysis am Ende des Tages :)

[@tlli5066]

@@brightsideofmaths danke für die Rückmeldung!

[@AbulAlArabi07]

Thanks a lot for the video.

[@brightsideofmaths]

You are very welcome :)

[@arturo3511]

I do not understand how the last definition applies to (-1)^n as there are not infinitely many points around 1 or -1 as there are only 2 points in the set. But we said previously that 1 and -1 are accumulation points by previous definition

[@brightsideofmaths]

Infinitely many sequence members is the key here.

[@davidescobar7726]

I hope I can understand topics like these one day ... some advice maybe?

[@brightsideofmaths]

This is a very good question. What is knowledge so far? Maybe my introduction here can help you: kzbin.info/aero/PLBh2i93oe2qtbygdXz4u6Mkh7c_hMLBA8

[@evionlast]

I would say that this series is remarkably accesible for anyone with some curiosity on math, but of course math needs practice the more exercises you do the better you understand the subtleties involved in computation, logic and concepts I encourage to try give it a chance, and if you find it hard, seek help or give it some time, and use your imagination try changing stuff

[@videogamemusicguy4208]

Is there not a mistake in either the definition or example of a subsequence here? You state 'strictly monotonically increasing' in the definition, and then use a sequence which is strictly monotonically decreasing in the example... btw I am loving this course it's making my notes really clear so thank you!!

[@brightsideofmaths]

n_k is increasing :) (not a_n)

[@videogamemusicguy4208]

@@brightsideofmaths Ah! This makes sense, completely overlooked that. Thank you very much!

[@gauravnainwal5026]

Do you mind my asking as to which book you follow for your videos?

[@brightsideofmaths]

No, particular book. I follow my own lecture notes.

[@PunmasterSTP]

Subsequences? More like "Super video series!" Thanks again so much for making and sharing all of these really high-quality videos.

[@vijaysinghchauhan7079]

Why this video has only 2 quality options?

[@brightsideofmaths]

That is strange. I have a quality options available. Maybe check another browser?

[@desrucca]

Potato device