Introduction to Cauchy Sequences

We introduce Cauchy sequences in an abstract metric space.

[@anthonys5542]

I wanna thank you for this extremely helpful video, but I'd rather compliment you. This material is extremely difficult to just understand. To teach it and have thousands of viewers understand shows how intelligent you really are. Good for you dude, I hope I can reach your level one day.

[@steliostoulis1875]

Anthony S I've learned it alone with an introduction to analysis book.

[@mc.ivanov]

@@steliostoulis1875 you are very smart

[@NathanCookCapn]

@@andrewlones8251 It takes time/effort to translate from the symbols to a concept, and even more time to translate to plain English. It's not that difficult to comprehend *IFF* the symbol -> concept map is already in place. Your statement is like saying "I can read Cyrillic, and I understood this poem written in Cyrillic that I found online. It's really not that difficult to comprehend." Not everyone can read math symbology fluently.

[@dangerousangel777]

@@NathanCookCapn Ikr, little assholes lol I'm 25 years old and going in my 4th year of college and just learning this for the first time, and it's complicated lol For me and my classmates lol Idk what books they give these children...lol but they need to give me these books because we have hard ones.

[@jebaebenezer2742]

@@dangerousangel777 I am also in fourth year of college and understood this concept only after watching this video eventhough I have listened to 3 hrs lecture on this same concept of my Professor before.I bet they are just showing off

[@player6769]

I know there’s a million comments saying this already, but it really is the best explanation I’ve come across. Thanks for making this

[@nunyabizz3357]

of all the videos of fancy math teachers using fancy effects, your 360p single cam over paper is consistently the best explained. i went over 5 much higher quality videos of (i would assume) much more experienced teachers before yours, and not a single one of them bothered to show a visual representation of the definition. which you've done not once but in several different examples. good on you man, thanks!

[@simpsonmokoena4395]

You're a KZbin Treasure. Thank you man. Truly!

[@markl7792]

I appreciate the explanation! This video gives a great introductory conceptual understanding of Cauchy sequences and is a fantastic spot to start learning!

[@mikeh2405]

Sorry to becoming here so late! Wonderful video, thank you for your contribution to my education.

[@manueljenkin95]

Thank you so much. This is the first video I’m seeing after a lot of search that clearly describes what a sequence really is in the first place.

[@graceg.6040]

thank you for existing

[@mohammedmukaram8841]

U make it so easy... U are the teacher we always wanted. May God bless you I wonder y our so called qualifies lecturers cant explain like this...

[@abigailsims4168]

I've listened to 3 lectures and read/reread my textbook chapter about this. Finally I understand!! THANK YOU!!!!

[@sonampriya3012]

It's my third year n today I got to know what type of sequence is cauchy sequence n this is because of you. Thanks❤️

[@devashish890]

i don't know GOD exists or not but after watching your lectures i can definnately say that GOD exists and you are GOD for me.Your explanation and efforts are speechless.And you are doing it free of cost.

[@calledmoe]

Best explanation ever. It was far more trivial than I thought it would be

[@elliotnicholson5117]

It is a very intuitive concept underneath all the greek.

[@aniketmazumder7025]

Y can't everybody explain it like u?

[@SacredScout]

I cannot thank you enough. Preparing myself for a huge exam which is 12CP worth. This helped me A LOT! I really cannot thank you enough!!

[@macmos1]

I don't think I have subscribed to any channel faster after first hearing this.

[@sthembisomgenge9711]

This is brilliant, I was so lost in my class for this entire week due to this Cauchy sequences thing

[@lucasm4299]

You’re literally a god. Feeling lost in class and out of class is such a horrible feeling. This video makes sense

[@SIMS6]

Good afternoon, I wanna thank you for such an awesome video!!!! The video was really helpful in understanding this subject! a million thanks!

[@sulgunrejepova3867]

Finallyyyyyyyy I understood this topic. I'm soo appreciate. Thank u soo much for this video. Your explanation is very clear.

[@kendytan91]

Thank you very much for the video! Really appreciate it! So much! From the bottom of my heart! Sincerely!

[@mehmettemizsoy3231]

Beautiful demonstration:) Keep on teaching real analysis!!!!

[@prod.theozim730]

bless your heart. i'm having a big brain moment rn

[@elliotnicholson5117]

Excellent. :)

[@george527]

@@elliotnicholson5117 this video was uploaded 6y ago. I'm impressed you're still replying!

[@elirhm6331]

the best explanation of cauchy sequence ever!! thank you :)

[@xmax700]

you are the best i love the way how you explain the idea. you are even better than my professor

[@necosupr]

Dude thank you so much, this makes it all so perfectly clear

[@sotirigeorgiou3205]

Take a Bow son.. What a video. Got it first time round!

[@shankarkantharaj8697]

Very great explanation. very intuitive

[@codingwithmat]

Thanks man helped me a lot :) You explained it much better than my lecturer.

[@vikashpoonia8923]

wow great experience keep it up

[@albertlylian1614]

Well done. You have taught me well.

[@pipololaoluwaalao778]

Best explanation I have seen🤯

[@ft790]

Thank you for doing a concrete example. So many videos don't do this!

[@RachelDance]

This is a brill explanantion... but then using your numbers as in video; I put in the (1/500) - (1/550) = 1.818E-04, which is still less than 0.001562... I was expecting this to be greater than epsilon ...?? Does this work? I've seen on other pages that it must be N > (2/epsilon)? But following that gives N=1281, and then that didnt work for me either ... am I losing the plot?

[@gavinridley5727]

a great explanation! I like how points were drawn on a plane.

[@elysesully6679]

This was immensely helpful. Thank you!!

[@rakotondrazakatojoherilant6403]

Thank you so much , very helpful, God bless you my friend 🙏🏽

[@debasishpradhan154]

Really very good explanation,thank you sir

[@jennylee1062]

ur explanations are very clear. thank u !!!!!!

[@tekaaable]

8:33 Jungian moment: "oh thats my shadow" :)

[@TOP3VERSE]

Nice one sir.

[@real.xplo1t]

You are a....a...a ray of hope

[@y-3084]

Thank you for the explanation. Well explained.

[@ana-mariaana-maria5190]

Wonderfull explenation. Thank you

[@imruljacky3768]

Great discussion, many thanks :)

[@petertangel]

Great video my friend. Thank you!

[@thembanovela4273]

Thanks a million times...

[@mrsecify]

God damn, that pen is gorgeous.

[@richeardparker4647]

im a bit confused, in the defn. we said m and n must be bigger than N and these are reel numbers right? But in the example we take the distance between 0 and 1/N but in that case (for the 0 case) m or n, one of them must infinity since there is no reel number that makes the sequence 1/n 0 right?? can anyone explain? Thanks!!

[@joshbroughton8346]

an absolutely brilliant video, thanks heaps :)

[@Ferdinaand]

great job mate

[@VilniusTV]

At least someone explained it well. Thanks a lot!

[@addaada321]

Thank you very much it was really helpful

[@mc.ivanov]

I love you man! Thank you so much for this great explanation!

[@diegoflores1468]

Really helpful. Tomorrow i have to explain this in front of all my classmates ... damm it's a little hard

[@marcoss2ful]

What a spetacular lecture

[@xoppa09]

what is the playlist for this video

[@AmitKumar-lm1uy]

love ur explanation

[@ozzy1873]

Thanks for the video very well explained

[@nainamat6861]

THANK YOU VERY MUCH SIR 🙏☺

[@gsridevi4495]

Thank you heartfully

[@elliotnicholson5117]

G Sridevi You’re welcome.

[@gojo9597]

thanks man i've been looking for this explanation only......

[@akashtripathi5967]

Big thanks 👍

[@gagadosuhubert3756]

So, I can now understand these concepts

[@sebrilarengh4583]

What does epsilon stand for?

[@topiado2073]

Waoo sir

[@NewJayqwe2]

What an absolute legend :D

[@andrejaerjavec8197]

great explanation!! thanks

[@mcab2222]

very nice

[@rishabhsingh5488]

Brilliant!

[@humblehmathgeo]

Thank you!

[@angelacui5358]

so good

[@larissaveloso8562]

thank you, helped me a lot

[@ivanguillermolopezpedreane7904]

Tyvm

[@somerandomer654]

U have saved me

[@RayKellyChristoffel]

what is epsilon?

[@jmochogi]

Any positive number chosen arbitrarily.

[@RazorM97]

Pick any number (noted, the greek letter epsilon), the bigger it gets, the smaller it's distance between points is going to be. compare it to the initial point and you would notice exactly what i said earlier.

[@sofieooms8990]

Damn this was well explained

[@soumithnalli5169]

tq bro

[@arushi63]

Woah I finally understand this

[@lemyul]

its sso similiar to convergence i don't know the difference

[@MileeWilson]

He sounds like Harry Potter.

[@elliotnicholson5117]

Only on camera.

[@silviapetrova8562]

thaaaank you

[@TacoSt8]

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did he say yes

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[@ricardoparra7550]

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[@rahiabrar8400]

why cant our professors explain it like this? :(

[@SzechSauce]

Thank you!