Cauchy Sequences

Cauchy Sequence

In this video, I define one of the most important concepts in analysis: Cauchy sequences. Those are sequences which "crowd" together, without necessarily going to a limit. Later, we'll see what implications they have in analysis.

[mithilaabraham]

Totally loved the concert analogy. Funny and informative. I will never forget the definition of a cauchy sequence ever. Thank you so much.

[Yaya_]

One day this channel would have a million subscribers, and I wouldn't be quick enough to make the second comment. Thanks for this Dr Peyam.

[ggmb]

You are one of the best in breaking down analysis. This explanation of Cauchy is terrific and mind blowing .Continue the good works and God bless you. I'm a big fun.

[VulcanXX]

The way you explained was amazing, and with great examples! Thank you so much

[FT]

8:23 Take epsilon = 6 feet.
I really like the explanation that the Cauchy sequence is bounded-- the picture was very helpful!

[sirstanegyir]

Finally I've found a diagrammatic explanation that makes visual meaning. Much thanks

[kalles]

Many reminders to the lectures during my studies in 1992.

[prasantakumarmondal]

Fantastic, mind-blowing am a big fan of you & maths am from IIT Delhi....so, I can guarantee that your way of teaching is far better than our IIT from India ❤️

[richardd]

this is actually the best explanation i could find. Thanks for posting.

[aitijhyasaha]

Really helped me in understanding the completeness of Hilbert Space. Thank you Sir.

[shreyabinwal]

Such a Detailed explanation.. great work sir!

[PuzzleQodec]

Imagine trying to tempt a date into a sparkling session of math ("Voulez-vous Cauchy avec moi?") and getting something entirely different instead! Such a disappointment.

[_PranavDesai]

It finally makes sense. I couldn't understand my teacher and whenever I tried to read it on my own, I doubted my own understanding because I had nothing solid to compare it to.

[thequiickbrownfox]

that voulez vouz cauchy was spot on hahaha; on other note wonderful explanation. Thank you

[tuanhuynguyen]

15 mins with this video is more effective than the whole semester in my uni :))) thanks so much

[frozenmoon]

Hmm, this could be (just a motivation) inspiring the audience - us - to deeper topics of Pure Math, such as the Twin Prime Conjecture. Whatever, I just came to say that I love your video :).

[Bertilbif]

You're a fucking legend. Thanks a lot <3

[jshook]

4:29 good analogy. In this case N would be the concert hall entrance!

[mohammedal-haddad]

That was a (real)ly neat trick to prove cauchy sequence is a bounded sequence.

[berrymarodza]

you are a great man Dr. Peyam! thanks for making hard stuff look so easy.
much❤❤❤❤❤❤❤❤❤❤❤❤