Cauchy Sequences
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- čas přidán 12. 09. 2024
- 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.
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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.
Fantastic , mind-blowing explanation.....I am a big fan of you & maths ........I am from IIT Delhi....so, I can guarantee that your way of teaching is far better than our IIT professors......love from India ❤️
What's ur branch?
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.
Totally loved the concert analogy. Funny and informative. I will never forget the definition of a cauchy sequence ever. Thank you so much.
The way you explained was amazing, and with great examples! Thank you so much
You r grom Switzerland
8:23 Take epsilon = 6 feet.
I really like the explanation that the Cauchy sequence is bounded-- the picture was very helpful!
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.
that voulez vouz cauchy was spot on hahaha; on other note wonderful explanation. Thank you
Cauchy sequences are what connect mathematics to the real world. Nobody involved with physical sciences should have to worry about sequences which aren't at least Cauchy, or any space more complicated than a "complete metric space". I should never have had to learn about essential singularities. 3-||
The physicist does not use irrational numbers. I saw the math test to a linear function, where there was given only one point and the student should calculate the equation of the line. Teacher says , that student could use a ruler to find the second point. Students were given 4 or 5 from mathematic test. How absurd.
@@tgx3529 czcams.com/video/gATEJ3f3FBM/video.html
Really helped me in understanding the completeness of Hilbert Space. Thank you Sir.
Love the concert analogy.
Many reminders to the lectures during my studies in 1992.
Such a Detailed explanation.. great work sir!
Finally I've found a diagrammatic explanation that makes visual meaning. Much thanks
You're a fucking legend. Thanks a lot
this is actually the best explanation i could find. Thanks for posting.
4:29 good analogy. In this case N would be the concert hall entrance!
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 :).
YOU DESERVE A BIG THUMBSUP
you are a great man Dr. Peyam! thanks for making hard stuff look so easy.
much❤❤❤❤❤❤❤❤❤❤❤❤
Awww thank you!!!!
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.
15 mins with this video is more effective than the whole semester in my uni :))) thanks so much
Thank you!!!
Outstanding explanation. Keep up the good work!
That was a (real)ly neat trick to prove cauchy sequence is a bounded sequence.
thanks for posting these
@Dr Peyam
have you made that video about Cauchy sequences that do not go to a limit? I can't find it.
Great work, keep it up :D
Well those don’t “really” exist since every metric space can be completed. For a counterexample consider 3, 3.1, 3.14, ... in Q. It’s Cauchy in Q but doesn’t converge in Q. But it converges in R to pi, and this is really the most general example
This is really amazing 🙌🙌🙌
Great way to explain mathematics
Très très bonne explication comme d'habitude (that coucher joke made me want to speak français haha)
@dr peyam U may also use the signs of for all, there exists , such that...that would look good...n I want to say something all Cauchy sequence are convergent and all convergent sequences are Cauchy.cauchyness is a technique to show the convergency of a seq. Without the convergency point.... isn't it? Will this be proved in ur next vdo?
Thank u so much.💜️
Thank you
Absolutely excellent. Really fun to listen to. :)))
Why is Xn-X < epsilon/2? I understand that we need two of those terms but can we just get to pick epsilon/2 there? 5:30 Thanks for the vid!
Yes since epsilon is arbitrary
@@drpeyam does that mean it could be like (2*epsilon) /3 (which is going to be greater than epsilon when adding another (2*epsilon)/3) too?
Also how do you define what the threshold is?
Ok. Thank you very much.
Thank you sir
Nicely done. Monsieur. Merci beaucoup!
السلام عليكم D peyam
Sir, have u uploaded the video about convergence of Cauchy sequences ?
Yes, completeness
What is bounded sir?
Are small m and n real numbers or natural numbers?
Natural, always
for some reason I am sure that I can find the Cauchy sequence, which is not bounded
@RickScience Dr Peyam says it is not always convergent. It can be divergent. Watch the video 1 more time
3:30
@RickScience all convergent sequences are Cauchy sequences , but converse is not true .
Great videos, but you threw me off when you said Cauchy sequences do not converge (currently teaching analysis myself). I think it might be helpful for your viewers to mention "However, if X is a compact metric space, then all Cauchy sequences converge to a point in X. In particular, this implies all Cauchy sequences in R^k converges"
Well in general Cauchy sequences do not converge
Please help , I don't understand how ε + |Sₙ+₁ | is a fixed value ?
N is a constant, that’s why it’s fixed
I have a question. A 2-D Graph has no spot four a square.. at zero zero.
And in highschool when learning. About the x,y,z access. That 0,0,0 couldn't hold a square...
Now mine craft.. made a 3-D graph game...
That has a spot open. For 0,0,0.. most people cannot past. 0,0,3or 2. But 0,0,0 is Hypothetically there.
When we think of a graph 0,0 has no importance on an out come. 0,1 can be 1ft 2ft,1kilometer. It would all add up and formulate out correctly.
But with a 0,0,0. It chanhes things significantly what size cube needs to fit in that spot in a way that no matter what sized cube you put there.. all the corispondling math after words. Equals the same thing no matter what. What size cube from all increments of measure can fit a 0,0,0. That after words. All the math from that point on is the same?
Is there any other videos about metric space?
Yes check out the playlist
Dr. Peyam! When you get a chance, could you please please solve "show (Sn)^2 =S^2 ???? BTW Thank you for great videos!!
Already done
Really wish these videos were around when I took 104.
DJ Peyam!
Is it just me or does everyone experience some difficulty in learning these kinds of maths? And by these kinds of maths I mean the maths that include notations from set theory. Typically I can follow math somewhat easily but it took me a long time (with several rewatches) to understand almost all of it.
Dude I wish you were my college roommate. I went to Cal too.
Go bears!!!
@@drpeyam GO BEARS!
We need to crowdsource you a much larger whiteboard.
The concert hall is full IF & ONLY IF DJ Peyam is playing.
the crowd converges IF & ONLY IF its Dr Peyam playing the music. If the duet BPRP is playing the crowd will disperse because his fans are not Cauchy. Ok I get it!
😄유 유 유유🎸 ..... 🖋🖍☹ 유 유 유 유
Hahaha
KUSHY séquences?!? :-O
How ironic, to be spreading Cauchiness during a Peyamdemic.
"For health and safety reasons, we've decided not to offer Real Analysis this term, and instead offer Diophantine Equations. We require that, for all answers a, b you give this term, unless a = b, |a - b| >= 1."
Peyamdemic hahaha
I can't find the next video
Look at the playlist (description)
@@drpeyam Thank you
LEFT HAND GANG
"voulez vous coucher avec moi?"
"Voulez vous cauchy avec moi?"
@@ricardo7240 "For all n, m > N, |s_n - s_m| < epsilon" is quite a commitment. Maybe just "For all x, y in {x: |x - c| < delta}, |f(x) - f(y)| < epsilon."
Non parce que nous sommes dans une pandémie.
@@iabervon That formula is so ill formed it's meaningless
Dj 🥧 m