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.

[@kagayakuangel5828]

@@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]

@@kagayakuangel5828 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

[@michalnarbutt2057]

Cheers man. You've made more sense in this video than my professor did in a 3h lecture.

[@abublahinocuckbloho4539]

if someone needs 3 hrs to explain a cauchy sequence then they shouldnt be a professor

[@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

[@graceg.6040]

thank you for existing

[@mikeh2405]

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

[@markl7792]

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

[@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!

[@aniketmazumder7025]

Y can't everybody explain it like u?

[@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!

[@abigailsims4168]

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

[@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.

[@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...

[@lucasm4299]

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

[@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.

[@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!!

[@simpsonmokoena4395]

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

[@macmos1]

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

[@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❤️

[@sulgunrejepova3867]

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

[@mehmettemizsoy3231]

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

[@necosupr]

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

[@elirhm6331]

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

[@sthembisomgenge9711]

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

[@kendytan91]

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

[@sotirigeorgiou3205]

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

[@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.

[@SIMS6]

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

[@tekaaable]

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

[@xmax700]

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

[@real.xplo1t]

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

[@elysesully6679]

This was immensely helpful. Thank you!!

[@codingwithmat]

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

[@pipololaoluwaalao778]

Best explanation I have seen🤯

[@albertlylian1614]

Well done. You have taught me well.

[@ft790]

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

[@shankarkantharaj8697]

Very great explanation. very intuitive

[@gavinridley5727]

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

[@thembanovela4273]

Thanks a million times...

[@mrsecify]

God damn, that pen is gorgeous.

[@imruljacky3768]

Great discussion, many thanks :)

[@rakotondrazakatojoherilant6403]

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

[@ana-mariaana-maria5190]

Wonderfull explenation. Thank you

[@topiado2073]

Waoo sir

[@VilniusTV]

At least someone explained it well. Thanks a lot!

[@vikashpoonia8923]

wow great experience keep it up

[@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?

[@joshbroughton8346]

an absolutely brilliant video, thanks heaps :)

[@petertangel]

Great video my friend. Thank you!

[@jennylee1062]

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

[@y-3084]

Thank you for the explanation. Well explained.

[@Official-UR-Ronaldo-cristiano]

Nice one sir.

[@marcoss2ful]

What a spetacular lecture

[@debasishpradhan154]

Really very good explanation,thank you sir

[@NewJayqwe2]

What an absolute legend :D

[@mc.ivanov]

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

[@addaada321]

Thank you very much it was really helpful

[@gagadosuhubert3756]

So, I can now understand these concepts

[@gojo9597]

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

[@SzechSauce]

Thank you!

[@Ferdinaand]

great job mate

[@akashtripathi5967]

Big thanks 👍

[@diegoflores1468]

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

[@gsridevi4495]

Thank you heartfully

[@elliotnicholson5117]

G Sridevi You’re welcome.

[@nainamat6861]

THANK YOU VERY MUCH SIR 🙏☺

[@ozzy1873]

Thanks for the video very well explained

[@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!!

[@sebrilarengh4583]

What does epsilon stand for?

[@muratcan__22]

very nice

[@angelacui5358]

so good

[@AmitKumar-lm1uy]

love ur explanation

[@andrejaerjavec8197]

great explanation!! thanks

[@xoppa09]

what is the playlist for this video

[@rishabhsingh5488]

Brilliant!

[@silviapetrova8562]

thaaaank you

[@larissaveloso8562]

thank you, helped me a lot

[@MileeWilson]

He sounds like Harry Potter.

[@elliotnicholson5117]

Only on camera.

[@sofieooms8990]

Damn this was well explained

[@somerandomer654]

U have saved me

[@arushi63]

Woah I finally understand this

[@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.

[@lemyul]

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

[@ivanguillermolopezpedreane7904]

Tyvm

[@soumithnalli5169]

tq bro

[@nshah94]

You are god

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did he say yes

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[@ricardoparra7550]

what a boss, gimme more daddy

[@rahiabrar8400]

why cant our professors explain it like this? :(

[@5180073a]

Thank you!