Intro to Cauchy Sequences and Cauchy Criterion | Real Analysis

[@lightnightsky]

Just wanted to let you know you're a life saver, I was at the brink of thinking I might have to quit math until I discovered your videos and started understanding so much that went over my head from my lectures

[@gvnbrn]

Having looked at various resources to get Cauchy sequences clear in my head, this is the first one I've truly understood. Thank you so much! Your explanation is super-clear.

[@WrathofMath]

Thanks a lot, I'm so glad it helped! Check out my analysis playlist for more! kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxl

[@jbhagawati9536]

Absolutely

[@Rsingh1]

I agree

[@jinglepinglepie611]

Dude, you are seriously a gifted teacher. Thank you for your hard work.

[@hansgans7066]

Seriously this is next level, I just listened without pause the video to think about what you said. THANK YOU VERY MUCH. Keep going on with this, you are talented!!!!!!!!!!!!!!!!!!!

[@saheedadisa8077]

First time to understand this definition for the past 5 years I have been coming across it in my academic journey. Thank you!

[@santi044]

Your videos are just brilliant every time. Honestly gives me so much hope every time I feel like I wanna quit Math, because it proves to myself that I actually can understand these theorems. Thank you man.

[@WrathofMath]

Thanks so much for the kind words! I’m continuing to work on my real analysis playlist, I hope you’ll find many more of the videos helpful!

[@santi044]

@@WrathofMath I'm glad to hear that. Keep up the good work!

[@WrathofMath]

Thanks for watching! Learn more in my Real Analysis playlist: kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli Support on Patreon to help me continue producing lessons and for early access to select videos! www.patreon.com/join/wrathofmathlessons

[@EvrYRAp]

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[@anthonytaylor6297]

Wow, I was just taken for a ride.. a wild ride. But thank heavens I did, that was amazing. I'm taking mathematical analysis and it's been tough for me to understand, kinda feeling like I shouldn't be there. We aren't onto this topic at the moment but on uniform continuity. You broke that down so well, that I now feel empowered because I understood all your steps. It was clear, well-structured and beautiful. Thank you so much for this wonderful piece. Take care.

[@mcalkis5771]

Brilliant. Absolutely brilliant. The best explanation of Cauchy sequences I've come across

[@WrathofMath]

Thanks so much! Check out my real analysis playlist for more, and let me know if you have any requests! kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli

[@aris.konstantinidis]

Finally, some motivation and context regarding this topic.. much appreciated! :)

[@WrathofMath]

My pleasure, thanks for watching! If you're looking for more analysis, check out my playlist! kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli

[@schenzur]

Thanks for creating this video and creating the whole real analysis playlist!

[@elrichardo1337]

getting ready to take real analysis this fall, these videos look like they're gonna be a great help - thanks in advance!

[@WrathofMath]

I hope they will be! Good luck and let me know if you ever have any questions! I don't know what text you'll be using, but my playlist mostly follows Real Analysis by Jay Cummings and Understanding Analysis by Abbott, though the playlist is still far from complete.

[@victorvelasco9446]

if ur studying before you even start to take it, you're already set

[@delzeltyna]

i swear unis make everything complicated when it doesn't have to be! thank you so much!

[@WrathofMath]

Glad to help! Check out my analysis playlist for more and let me know if you have any questions! kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli

[@abcdefghijklnopqrstuvwxyz5259]

I cannot thank you enough for this...had almost given up in trying finding a video on this topic 💕💕

[@WrathofMath]

So glad to help! I have lots more real analysis videos in my analysis playlist, and many more in the works!

[@pantelisvasileiadis2858]

thank you very much man. Amazing explanation. I finally get a good understanding of this

[@sinabirkeland1026]

Thank you so much this was an amazing video:D Finally I could understand the Cauchy-criteria fully. Love from Norway (Sina and Natnael Tesema)

[@yogitajindal3149]

Excellent explanation. Really very helpful Thank you so much

[@yogitajindal3149]

Very easily understandable explanation Thank you so much It helped too much

[@WrathofMath]

Awesome! Thanks for watching!

[@drewjackson7949]

Very informative video with excellent examples.

[@egegulce5577]

i love you, im at one of the best universities in the world studying comp sci and no prof explains this like you lmao

[@WrathofMath]

Thank you! Good luck in your studies, I'm happy to be able to help!

[@MrHolmes7]

You are amazing. Please keep doing what you do. You make the language of math as easy as the ABC song. Is there any reason you used 2/ep.... or can one just choose any epsilon? I see now...Thanks again

[@augusthuangmx]

Thank you so much for the video!!! Really helps me a lot.

[@Rluo42069]

hi there, thanks for the video. I'm just still a bit confused on why we need to use the Archemedian property and how to know when to use this property in proofs. Thanks again

[@siavashazimi3633]

04:35 the information is not true. " In every metric space, each convergent sequence is a Cauchy sequence. The converse is not true in general."

[@dabeeramir1407]

Oh my god, thank you so much for this you really saved me 🙏

[@WrathofMath]

Glad to help!

[@poissontutor8524]

This is super duper great!❤

[@STG642]

Great explanation 👍👍

[@WrathofMath]

Thanks, Shadab! Let me know if you have any questions, and check out my analysis playlist for more! kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli

[@davieskayombo9106]

You are just the best

[@max_codez]

such an amazing video

[@WrathofMath]

Thank you!

[@SELIMofficial64]

Outstanding

[@chrisdowdy5212]

your videos are amazing

[@WrathofMath]

Thank you so much 😀

[@ThenSaidHeUntoThem]

Thank you for this video.

[@WrathofMath]

Thanks for watching!

[@mohamedbenjbara8663]

thank youuu for the approach

[@WrathofMath]

My pleasure. thanks for watching!

[@ScottyLane_]

Thank you so much! New subscriber

[@MUSHIN_888]

at 6:20, why is m,n > 21 not m,n => 21?

[@kvitka_lily]

Thank you!!!!!💓💓💓

[@WrathofMath]

You are so welcome!

[@KurdaHussein]

every converge is cauchy but not conversely. ex: 1/n on R-{0}

[@SephirothVG]

@14:21 You say that replacing m and n with big N which is smaller would make the sum BIGGER...Dont you mean smaller? @Wrath of Math

[@kelvinndereba5423]

Thanks for the video

[@WrathofMath]

You're very welcome, thanks for watching! If you're looking for more real analysis, check out my playlist! kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli

[@siavashazimi3633]

By the way the video was great. Thanks a lot

[@jbhagawati9536]

Thank you so much

[@WrathofMath]

Glad to help! Thanks for watching and check out my analysis playlist if you're looking for more! kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli

[@lippy21]

thank you so much !! :)

[@kadagaladileep1862]

Thanks😁

[@WrathofMath]

You're welcome, thanks for watching! If you're looking for more analysis, check out my playlist, and let me know if you have any requests! kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli

[@kadagaladileep1862]

help ful🌼🦋

[@krishnabahetra4641]

12:32, this is not correct to say that after applying the triangle inequality, it is not necessary for it to be less than epsilon.

[@WrathofMath]

I do not understand your comment, could you rephrase?

[@ochenambrose2121]

Thank u 🙏🏾🙏🏾

[@WrathofMath]

My pleasure, thanks for watching! If you're looking for more real analysis, check out my real analysis playlist! kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli Many more lessons to come, let me know if you ever have any requests!

[@diliniuthpala1802]

How getN>2/£

[@Yamiku]

It is explained at 12:06

[@Cuzimbluebadaboodeedaboodie]

Bro sounds like Sheldon…

[@winstonrodney9929]

Thank you for the video but you didn't explain how you got your 1/10

[@drewjackson7949]

It was just chosen arbitrarily to show that the Cauchy inequality holds.

[@JacklineNabawanuka-ii1en]

👍👍👍

[@egegulce5577]

fucking legend

[@hammadmhadi8135]

♥️

[@WrathofMath]

Thanks for watching!