Definition of the Limit of a Sequence | Real Analysis

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  • Опубликовано: 13 дек 2024

Комментарии • 201

  • @WrathofMath
    @WrathofMath  3 года назад +12

    Support the production of this course by joining Wrath of Math to access exclusive and early videos, original music, plus the real analysis lecture notes at the premium tier!
    ruclips.net/channel/UCyEKvaxi8mt9FMc62MHcliwjoin
    Real Analysis course: ruclips.net/p/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli
    Real Analysis exercises: ruclips.net/p/PLztBpqftvzxXAN05Gm3iNmpz9SkVfLNqC

  • @nihilisticboi3520
    @nihilisticboi3520 3 года назад +76

    The moment you finished explaining the 1/100 example, I felt I reached enlightenment. Beautifully explained!

    • @WrathofMath
      @WrathofMath  3 года назад +5

      That's the best I can hope for! Thanks for watching, I am glad it helped!

    • @SequinBrain
      @SequinBrain 3 года назад +8

      if only textbook authors knew the value of using numbers in math books...

  • @pxlbits6442
    @pxlbits6442 3 года назад +71

    I learned more in this video than my entire semester in analysis class lmao...

    • @WrathofMath
      @WrathofMath  3 года назад +3

      Well that's good and bad haha - I'm at least glad my video was helpful! If you're looking for more analysis, check out my analysis playlist: ruclips.net/p/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli
      Lots more analysis coming! And if you're in the mood for some tunes, check out my new math song that came out today! ruclips.net/video/0Oro28Xkzbg/видео.html

  • @hamadkhan2339
    @hamadkhan2339 4 года назад +79

    Sir, this is the best lecture of this topic on u tube. Thank u so so much for explaining everything. This was hard to me but u explained it in a very easy way. why so underrated? You are really good, I hope that soon you will have subs in millions🙏🙌

    • @WrathofMath
      @WrathofMath  4 года назад +5

      Thanks for watching, Hamad! I really appreciate your kind words! It's a very important topic so I'm very glad you found my explanation clear! The long road to a million awaits us!

  • @swastikadeb8605
    @swastikadeb8605 Год назад +2

    I was really struggling to understand the definition of limit clearly. I looked up everywhere on the internet until I found this video, such nicely explained with that amazing 1/100 example. It's totally clear now! Thank you sir. Hope this reaches to everyone out there.

  • @stephen3418
    @stephen3418 2 года назад +10

    These intro to analysis videos are incredibly valuable. You have clarified the ‘setting out’ stage of the proof that my textbook simply failed to describe. How to choose an N? Thanks to your teachings, I can understand analysis and apply its techniques! I had thought that perhaps I had truly arrived at a level of maths which I’d find incomprehensible (at least without some miraculous discovery), but your teachings elucidated the simple technique of how to algebraically decide what N ought to be. So thank you so much! This will certainly be the most valuable lesson in analysis of my life! Such is the nature of this incredible inflection point!

  • @manarmagdy2329
    @manarmagdy2329 11 месяцев назад +3

    I cryied because I couldn't understand that and my exam after 4 days but now it's more than clear. Really thanks from my heart

  • @bigollameo
    @bigollameo 2 года назад +5

    Now I finally understand what the "n>N" condition means. For the longest time I've been puzzled as to just what this relation requirement was trying to communicate. Should have been apparent years ago, but better late than never.
    Thank you!

    • @WrathofMath
      @WrathofMath  2 года назад +1

      So glad it helped, thanks for watching!

    • @toxicfreeze-brawlstars121
      @toxicfreeze-brawlstars121 Год назад

      bro i still dont understand this n>N can you explain

    • @toxicfreeze-brawlstars121
      @toxicfreeze-brawlstars121 Год назад

      i mean what is the big n here

    • @blazobanicevic
      @blazobanicevic Год назад

      @@toxicfreeze-brawlstars121 not sure if I got it myself but as for how I understand it, n is the index of an element of sequence (an) and N is a number so when you say n>N I think it is saying that every next element of a sequence after number N has to be between the limit and number N(so if I say 1/n and N=100 then every element after a100-after 100th element of a sequence-has to be between limit and 1/100 for every n>N) hopefully I helped but as I said I dont understand it completely however this is the way I currently understand it to be.

  • @nikeshlilani5215
    @nikeshlilani5215 4 года назад +3

    this is by far the best lecture on this topic on youtube..thanks a lot sir !

    • @WrathofMath
      @WrathofMath  4 года назад +1

      That means a lot, thanks so much! I am glad it helped and let me know if you ever have any questions!

  • @DoEvenly
    @DoEvenly 2 месяца назад

    this video is the best video about limit I have seen in this year 😮

  • @bactran7799
    @bactran7799 3 года назад +1

    amazing explanation of the limit of sequence definition that blows my mind. Thanks a lot Wrath. Please keep doing your great works

    • @WrathofMath
      @WrathofMath  3 года назад +2

      You're very welcome, thanks so much for watching! If you're looking for more analysis, check out my playlist! ruclips.net/p/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli

  • @ConstanceShayamano-ei7fc
    @ConstanceShayamano-ei7fc Год назад

    Yu the best online teacher I have ever encountered with

  • @nateman44ify
    @nateman44ify 4 года назад

    My professor just went over this topic and I just could not follow along or understand what he was trying to say. But this actually makes sense, because of you im actually completing my homework. Thank you!

    • @WrathofMath
      @WrathofMath  4 года назад

      So glad you found it helpful! Thanks for watching and let me know if you ever have any questions!

  • @Anonymous-rv3gz
    @Anonymous-rv3gz 3 года назад

    Man you saved my 48hrs of stress......
    May god bless you man.....

    • @WrathofMath
      @WrathofMath  3 года назад

      So glad it helped. Thank you very much for watching!

  • @IdoYos
    @IdoYos 3 года назад +4

    Best explanation I have found so far!! If you could make videos explaining linear algebra as well it would be phenomenal!! Thank you so much!!

    • @WrathofMath
      @WrathofMath  3 года назад

      So glad to hear it, thanks for watching! You can find more analysis lessons in my Real Analysis playlist: ruclips.net/p/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli
      As for linear algebra, I definitely plan on getting to it, but it will be some time. It was not one of my stronger subjects in college, so I have more than just brushing up to do!

    • @IdoYos
      @IdoYos 3 года назад

      @@WrathofMathHaha tell me about it 😉
      Thanks again for a great intuitive explanation!!

  • @zb5775
    @zb5775 Год назад

    Your videos and your teaching skills are outstanding. Thank you for all your work.

  • @le_great_escape
    @le_great_escape 2 месяца назад

    I finally understand where my professor for 1/epsilon. THANK YOU!

  • @victoriacorcimaru1731
    @victoriacorcimaru1731 Год назад

    Best, most intuitive explanation!!! A must watch )))

    • @WrathofMath
      @WrathofMath  Год назад

      Thank you! Lots more analysis lessons to come - thanks for watching!

  • @BlaqueT
    @BlaqueT 2 года назад

    This video was a good step to help my understanding, as this epsilon definition of a limit has confuded me so much in the beginning of my real analysis course. Thank you so much!

    • @WrathofMath
      @WrathofMath  2 года назад

      So glad it helped! Thanks for watching and check out my analysis playlist for more! Let me know if you have any questions! ruclips.net/p/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli

  • @aqsamaryam8580
    @aqsamaryam8580 4 года назад

    I think it is the best explanation for anyone to understand this concept.....

    • @WrathofMath
      @WrathofMath  4 года назад

      Thanks a lot, I'm very glad to hear that! 😊

  • @fatimaintekhab7357
    @fatimaintekhab7357 Год назад

    Thank you for explaining the definition with a graph! I was really struggling with this❤

  • @marcusnzioka6624
    @marcusnzioka6624 3 года назад

    thanks for this explanation, I have struggled looking for good content like this

    • @WrathofMath
      @WrathofMath  3 года назад

      Thanks for watching, Marcus! If you're looking for more analysis, check out my Real Analysis playlist: ruclips.net/p/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli
      And let me know if you ever have any video requests, lots more analysis lessons coming!

  • @samaritan2899
    @samaritan2899 3 месяца назад

    Math 101 in Uni and you make it sound so simple. I like the style

    • @WrathofMath
      @WrathofMath  3 месяца назад

      So glad to help - thanks for watching! I hope you'll continue to find my analysis playlist helpful, good luck!

  • @VocalBeast
    @VocalBeast Год назад +1

    Man thank you so much. Was pretty stumped understanding this but you explained it so clearly, thank you:)))

    • @WrathofMath
      @WrathofMath  Год назад +1

      Glad to help! Check out my analysis playlist for more and let me know if you have any questions! ruclips.net/p/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli

  • @chad2336
    @chad2336 Год назад

    best explanation so far, great video man!

  • @AmeenaMuddasir
    @AmeenaMuddasir 3 месяца назад

    Ahh great sir ! I was focusing on what is actually written in the book but got really upset because I was wasting my own time ! Then it clicked in my mind Ka I should watch a video and luckily I got you and your video ! Very good job sir thank you ❤

    • @WrathofMath
      @WrathofMath  3 месяца назад

      Thank you - glad it helped!

  • @hanskywalker1246
    @hanskywalker1246 Год назад

    Finally somebody explained why we have to use N instead of just always n, thanks!

    • @WrathofMath
      @WrathofMath  Год назад +1

      Glad to help, thanks for watching and let me know if you ever have any questions!

    • @hanskywalker1246
      @hanskywalker1246 7 месяцев назад

      ​@@WrathofMathI have a question: 9:31 can't we also say that |an-L| is greater zero because like the limit will actually never reach the final value?

  • @existentialrap521
    @existentialrap521 Год назад

    We makin it outta the trenches with this one.
    That visual helped a ton. Made the absolute value of an-L make sense.

  • @liss35
    @liss35 3 года назад +2

    perfectly explained, well defined that makes things clearer than on the mere printed definition from the book.. Thanks for this tutorial video it really helps a lot.. 👏👏👏

    • @WrathofMath
      @WrathofMath  3 года назад

      So glad to hear that, thanks for watching! If you're looking for more analysis, check out my playlist! ruclips.net/p/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli

  • @dark.violin
    @dark.violin Год назад

    You are really good at explaining. Thank you so much :)

  • @arabmohcin-13
    @arabmohcin-13 15 дней назад

    wow ! is just you make eveything obvious ! love you bro

  • @alfieplant6927
    @alfieplant6927 2 года назад

    Perfect explanation. I understand completely now

    • @WrathofMath
      @WrathofMath  2 года назад

      Glad to hear it! Thanks for watching, and check out my real analysis playlist if you're looking for more!

  • @braverodger
    @braverodger 3 года назад +1

    you explain very goodly. thank you!

    • @WrathofMath
      @WrathofMath  3 года назад +1

      Glad it was clear, thanks for watching!

  • @aniketgupta1340
    @aniketgupta1340 2 года назад

    at 10:40 , i guess there is a mistake cuz for some a>b and a>c, we cant establish the fact that b>c or c>b

  • @evgenirusev818
    @evgenirusev818 4 года назад

    Super clear and intuitive. Thanks!

    • @WrathofMath
      @WrathofMath  4 года назад

      So glad it was clear! Thanks for watching!

  • @pamodpeiris154
    @pamodpeiris154 2 года назад

    Best explanation of limit..

    • @WrathofMath
      @WrathofMath  2 года назад +1

      Thank you, glad it was clear! And if you're looking for more analysis, check out my playlist! ruclips.net/p/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli

  • @michelleyuangu7462
    @michelleyuangu7462 Год назад

    So well explained. Thank you so much

  • @snclassical8263
    @snclassical8263 3 года назад

    I hated Real Analysis and THANK YOU! for giving me new hope!!

  • @mathechne
    @mathechne Год назад

    just the classical, very good, thanks

  • @Teja-tm4zi
    @Teja-tm4zi 11 месяцев назад

    excellent vid! thank you so much for the effort you put into these videos!

    • @WrathofMath
      @WrathofMath  11 месяцев назад

      Thank you for watching!

  • @citizenofreality2751
    @citizenofreality2751 2 года назад

    WOW! Thanks for all the work!

  • @Carol.26
    @Carol.26 Год назад

    Thank you so much Sir! Your explanation was really helpful!

  • @arthurbouchardet6932
    @arthurbouchardet6932 3 месяца назад

    This is such a good video. Thank you, for real. Liked and Subscribed.

    • @WrathofMath
      @WrathofMath  3 месяца назад

      Appreciate it, thanks for watching!

  • @rishabhsharma1982
    @rishabhsharma1982 3 года назад

    Great video, incredibly helpful!

  • @mohamedbenjbara8663
    @mohamedbenjbara8663 Год назад

    thank you for the approach 😍😍

    • @WrathofMath
      @WrathofMath  Год назад

      Glad to help, let me know if you have any questions!

  • @J078_
    @J078_ 4 года назад

    Gud work sir....keep updating with sch wondrfl classes from real analysis....

    • @WrathofMath
      @WrathofMath  4 года назад

      Thank you! Will do, I have many more analysis lessons planned. Let me know if you have a specific request you'd like to see soon!

  • @karlathebarla
    @karlathebarla 3 года назад

    Excellent explanation!!

    • @WrathofMath
      @WrathofMath  3 года назад +1

      Thanks Karla! If you're looking for more analysis, check out my playlist and let me know if you ever have any questions! ruclips.net/p/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli

  • @OGMarkuss
    @OGMarkuss 2 года назад +3

    Hello Wrath of Math. I'm preparing for a test righ now. The explanation in masterly presented, although I don't understand there part where you wrote N > 1/e . Could you, please, briefly explain why is that so?

  • @mahmoudalbahar1641
    @mahmoudalbahar1641 4 года назад +1

    Many thanks for this good video.

  • @danielcamacho5434
    @danielcamacho5434 3 года назад +1

    amazing work dude! thank you so much!

    • @WrathofMath
      @WrathofMath  3 года назад

      Thank you, it's my pleasure! Be sure to check out my Real Analysis playlist if you haven't, many more analysis lesson to come! ruclips.net/p/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli

  • @sukhofruktt
    @sukhofruktt Год назад

    you are a life saver!!! thank you so much

  • @sahelaria993
    @sahelaria993 Год назад

    Thanks that was very helpful

    • @WrathofMath
      @WrathofMath  Год назад

      Awesome, thanks for watching! Lots more analysis videos on the way, let me know if you ever have any questions!

  • @IODell
    @IODell 3 года назад

    Great explanation. Thanks.

    • @WrathofMath
      @WrathofMath  3 года назад

      My pleasure, thanks a lot for watching! If you're looking for more real analysis, check out my playlist! ruclips.net/p/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli

  • @zyshri
    @zyshri Год назад

    Thankyou so much sir 🌸✨❤️

    • @WrathofMath
      @WrathofMath  Год назад

      Glad to help - thank you for watching!

  • @deisooja2961
    @deisooja2961 2 года назад

    this was an excellent video about limit of sequences. I was on a lecture and didnt understand shit about it. Really thanks man !!!

  • @ioannaathineos5269
    @ioannaathineos5269 Год назад

    Master ! Thank you

  • @khalilmohammed2297
    @khalilmohammed2297 3 года назад

    Thank you so much, you are brilliant

  • @MuhammadAhmed-hu6dk
    @MuhammadAhmed-hu6dk Месяц назад

    Holy why tf the book makes it so hard on us I mean it such a simple concept thanks you

  • @hanskywalker1246
    @hanskywalker1246 7 месяцев назад

    I have a question: 9:31 can't we also say that |an-L| is greater zero because like the limit will actually never reach the final value?

  • @EduardoAdameSalles
    @EduardoAdameSalles 3 года назад +1

    Thank you! BTW, what is this board software you use with the drawing tablet?

    • @WrathofMath
      @WrathofMath  3 года назад +1

      You're very welcome, thanks for watching! I use Notability on iPad Pro! It works great! If you're looking for more real analysis, check out my Real Analysis playlist and let me know if you have any video requests! ruclips.net/p/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli

    • @EduardoAdameSalles
      @EduardoAdameSalles 3 года назад

      @@WrathofMath Thanks for answering. I'm actually having calc 1, but my professor have decided to start by Real Analysis. In fact, calculus isn't that hard, but I'm not sure about my skills in RA. I'll certainly be watching your videos

  • @mauryaneha589
    @mauryaneha589 4 года назад

    This vedio very helpful for me. Thank u so much sir

    • @WrathofMath
      @WrathofMath  4 года назад +1

      You're very welcome, thanks for watching!

    • @mauryaneha589
      @mauryaneha589 4 года назад

      @@WrathofMath sir plz upload some examples of limit of a sequence

  • @kehalitadesse5165
    @kehalitadesse5165 3 года назад

    Thanks man that helped a lot

    • @WrathofMath
      @WrathofMath  3 года назад

      So glad to hear it! Thanks for watching and if you're looking for more analysis, check out my real analysis playlist: ruclips.net/p/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli
      Many more on the way!

  • @hilmakara4907
    @hilmakara4907 Год назад

    May you please do another video with examples involving accumulation points

  • @bernatbosch
    @bernatbosch Год назад

    From 10:32 to 11:52 the reasoning is unnecessary because at 10:32 it was demonstrated that any n greater than 1/epsilon would match to the inequality.

    • @WrathofMath
      @WrathofMath  Год назад +1

      True, but the introduction of a definition like this is not the time for proceeding quickly in an explanation. I am deliberately redundant at times for important definitions.

  • @bernatbosch
    @bernatbosch Год назад

    2:16 "then, as like in this example, our sequence approaches zero, I can guarantee that..." and for me that is the problem of this type of definition of what a limit is: that just works if you already know in advance what the value of the limit is. Because otherwise, how could you calculate the absolute value of the difference between a number and L when you don't know yet what is the limit of the function as it approaches to...etc. A good definition of a limit L should be developed without having to know in advance the value of L. Otherwise, why the hell you need the definition if you are already sure that a certain number is indeed the limit you are searching for. Another idea that bothers me is that this particular way to prove seems just adapted for the case that we are wanting to know the limit of the sequence when it grows to infinity, but does not seem to be a good way to prove the limit of a sequence when it approaches a certain index n (lets say n=0 or n=1).

    • @WrathofMath
      @WrathofMath  Год назад

      It should be unsurprising that to prove a limit converges to L, we need a candidate for L. There are various other ways this might take form, but regardless it is not like we have to KNOW what a limit is for sure before we can attempt this sort of proof, we need only a candidate, a number we think the limit is. With specific sequences, computation and/or intuition can produce a reliable candidate. In other situations of analysis that are less particular, a candidate may be rather abstract, and thus a proof of the convergence is very important. In our proofs of all the sequence limit laws, we don't KNOW the limit of a_n + b_n is a + b, but we suspect it is and so proceed with the proof to settle the matter.
      All that said, it is no doubt a significant and necessary weakness in this definition that you point out. The fact we must have some idea what the limit could be to use the definition is an obstacle. Later in my analysis playlist are several videos about Cauchy Sequences, in which we develop an equivalent definition of a convergent sequence that does not depend on the limit at all.
      Regarding the n to infinity point - there is no way, as we have defined sequences, to take a limit anywhere other than infinity. For any sequence a_n, if we consider the "limit as n approaches 4" for example, this doesn't really mean anything. The closest n gets to 4 is a_3 and a_5. In each case, either a_3 = a_4 and/or a_4 = a_5. Or, there is some distance between these terms. This is to say, a_4 either does not get approached by its neighboring terms, or it equals its neighboring terms. In a functional limit this is different because we could take a limit as x approaches 3 since x actually CAN approach 3. x = 2.9, 2.99, 2.999, etc. But for sequences, n is discrete, and can approach nothing other than infinity. Hope that's helpful!

  • @ΔημήτρηςΖυγάς
    @ΔημήτρηςΖυγάς 4 года назад

    Thank you for making this clear!
    Could you maybe tell me how this example would work if we could guess the limit L of the sequence?
    How would we take out the absolute value, etc?

  • @sukrandinc5836
    @sukrandinc5836 2 года назад

    Perfect, thank you

    • @WrathofMath
      @WrathofMath  2 года назад

      Glad it was helpful! Let me know if you have any questions and check out my analysis playlist for more! ruclips.net/p/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli

  • @azizahsaswandila6708
    @azizahsaswandila6708 2 года назад

    Thank you Sir

    • @WrathofMath
      @WrathofMath  2 года назад

      Glad to help! Thanks for watching and check out my analysis playlist if you're looking for more! ruclips.net/p/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli

  • @MathematicsApplications56
    @MathematicsApplications56 14 дней назад

    Thanks alot

  • @successorof68
    @successorof68 Год назад

    I know the video is 3 years old but if you see this can you show an example where the definition for convergence of a sequence breaks. Maybe something like this:
    Prove 1/n limit is 1 when n goes to infinity. We know 1/n approaches 0 as n goes to infinity but would like to see how the proof breaks

  • @cyrillamphosa3285
    @cyrillamphosa3285 3 года назад

    Great stuff

  • @EvrYRAp
    @EvrYRAp 2 года назад

    holy. you are so good

  • @mohamedaliekoroma5040
    @mohamedaliekoroma5040 3 года назад

    I enjoyed the lesson and I learned a lot.
    You don’t mind me sir; I have a question that I want you to help me solve.

  • @aubreydebruyn84
    @aubreydebruyn84 8 месяцев назад

    I consulted YT vids and RA books, did not get the N part. As so as you put on a graph, the lights turn on. Thank you so much.

    • @WrathofMath
      @WrathofMath  8 месяцев назад

      Glad to help - thanks for watching!

  • @si_monster7365
    @si_monster7365 3 года назад

    10:39 Why does the big N have to be bigger than 1/epsilon?

    • @WrathofMath
      @WrathofMath  3 года назад +1

      Thanks for watching and for the question! In the scratch work we did, we saw that n being greater than 1/epsilon will give us the result we want. However, by convention/definition, we don't take n to be greater than whatever we please, we only have that n is greater than N. I think of N as some point in the sequence, after which we get what we want. So since we want n to be greater than 1/epsilon, and we will have n > N, and we can pick what N is greater than, we need N to be greater than 1/epsilon so that n is as well. Then we're saying as long as we pick N to be greater than 1/epsilon, all terms of the sequence after the Nth term will satisfy our desired inequality. So for all n > N, |1/n - 0| < epsilon. Does that help?

    • @si_monster7365
      @si_monster7365 3 года назад

      @@WrathofMath Very clear, thanks!

    • @muhtedbaig7011
      @muhtedbaig7011 Год назад

      @@WrathofMath thanks for the explanation I really appreciate it. I just had one query. Since n>N, we can also consider N to be *greater than or equal to* 1/epsilon right? Adding that *or equal to* shouldnt affect it as n>N. I would be glad ify help me clear this confusion :)

  • @syedalauddinbukhari9801
    @syedalauddinbukhari9801 4 года назад

    help a lot man thankx

    • @WrathofMath
      @WrathofMath  3 года назад

      My pleasure, thanks for watching!

  • @guranahemanthkumar8976
    @guranahemanthkumar8976 3 года назад

    Thank you
    So much :)

    • @WrathofMath
      @WrathofMath  3 года назад

      My pleasure, thanks for watching! Be sure to check out the whole Real Analysis playlist if you haven't, many more new lessons to come! ruclips.net/p/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli

  • @Godfather-ps6zv
    @Godfather-ps6zv 2 года назад

    Man love from India

  • @AryanSingh-tt4kt
    @AryanSingh-tt4kt 2 месяца назад

    could u please attach a word or pdf file for the format of the answer to be written like "Let E>0.................Hence, proved"

  • @noahniklaus5070
    @noahniklaus5070 4 года назад

    Thank you

    • @WrathofMath
      @WrathofMath  4 года назад

      No problem, thanks for watching! Looking forward to making some more real analysis lessons.

  • @WiskundeTraining
    @WiskundeTraining 3 года назад

    what is the difference between the N-epsilon definition and the epsilon-delta definition? why we need to use the N-epsilon definition for a sequence and not the epsilon-delta one?

    • @WrathofMath
      @WrathofMath  3 года назад +1

      Thanks for watching and good question! The N-epsilon definition is for limits of sequences as n goes to infinity. The epsilon-delta definition is for limits of functions at their accumulation points.

  • @navyatayi6956
    @navyatayi6956 4 года назад

    Here how is the value of epsilon considered? Is it a value related to the series or is it any number?

    • @WrathofMath
      @WrathofMath  4 года назад

      Thanks for watching and epsilon is an arbitrary positive number. For any positive epsilon, a convergent sequence will eventually get within epsilon of its limit. Does that help?

  • @user-xg8zi9tm7u
    @user-xg8zi9tm7u Год назад

    You are best

  • @mohamedaliekoroma5040
    @mohamedaliekoroma5040 3 года назад

    This is my question; Sum the following series “the sum of n where r = 1 ~ r(r-1)

  • @athethird4945
    @athethird4945 3 года назад

    Aahhhhh thank you, When am Amat major attempts pmat

  • @ekemm
    @ekemm 4 года назад

    Thanku, and i subscribed 😁😁

    • @WrathofMath
      @WrathofMath  4 года назад

      My pleasure and thank you for watching and subscribing! Let me know if you ever have any requests!

  • @Groove_Lyrics
    @Groove_Lyrics 2 месяца назад

    Someone please explain why he changed < sign to n>1/epsilon

    • @WrathofMath
      @WrathofMath  2 месяца назад

      Not 100% sure what you're talking about (timestamp would be helpful) but if you're talking about going from (1/n) < epsilon, then we can invert both sides as long as we change the direction of inequality, thus getting n > (1/epsilon), telling us how big n needs to be for our argument to work.

  • @dehey4310
    @dehey4310 5 дней назад

    That is Archimedean property right, sir?

  • @mo8046
    @mo8046 3 года назад

    What could go wrong if I tried to prove that the sequence converges to any other number? What could go wrong if I tried to prove that, for example, (n+1)/n converges to 3 rather than 1?

    • @WrathofMath
      @WrathofMath  3 года назад +1

      Thanks for watching and that's a really great question! You should give it a go! Try proving (n+1)/n converges to 3 the same way you normally would. As you work with the expression | (n+1)/n - 3 |, you'll eventually see an expression clearly greater than or equal to 1 for all n, so you'll not be able to make it arbitrarily small.
      Then, you could say for epsilon = 1 and all n, we see what you just showed about | (n+1)/n - 3 | being at least 1, and so clearly there is no N that will make | (n+1)/n - 3 | less than epsilon for all n > N; proving the sequence does not converge to 3. I may make a video on this, it's a great thing to see when we begin working with the limit of a sequence definition!

    • @mo8046
      @mo8046 3 года назад

      @@WrathofMath Thanks for the great explanation!

  • @RamyChenafi
    @RamyChenafi Год назад

    what do you think about n=1+[1/e]

  • @noorjahanjaleel8116
    @noorjahanjaleel8116 4 года назад

    can you make vdios on properties of infinite series of real analysis

    • @WrathofMath
      @WrathofMath  4 года назад

      Thanks for watching and I have more real analysis lessons in the works. If you have a request for a specific property of infinite series I can try to hurry that one along!

  • @realworld2716
    @realworld2716 Год назад

    What is N?

  • @Itsjustj82
    @Itsjustj82 2 года назад

    Why do we say that the bigger N is greater than 1/epsilon? (N>1/E)? please someone answer, i'm confused..

  • @uniquename2386
    @uniquename2386 2 месяца назад

    Can someone explain to me why he wrote that big n is greater than 1/epsilon

  • @sumeyye7014
    @sumeyye7014 2 года назад

    How can we assume that N is bigger than 1/Epsilon ?

    • @WrathofMath
      @WrathofMath  2 года назад +1

      N is a thing that we can choose, it effectively represents how far in the sequence we need to go in order to make the rest of the math work. When we do an epsilon proof, we're proving that no matter how small epsilon is, we CAN go far enough in the sequence so that all terms are within epsilon of the limit. N will generally depend on epsilon, because the smaller epsilon is, the further in the sequence we need to go in order to be sufficiently close to the limit.

  • @navyatayi6956
    @navyatayi6956 4 года назад +1

    And why is epsilon any positive number close to 0? Why not a negative number?

    • @WrathofMath
      @WrathofMath  4 года назад +1

      Let An represent an arbitrary term from a sequence which converges to L. Epsilon is positive because it is used to describe how the distance between a convergent sequence and its limit gets arbitrarily small. The distance between An and L is |An - L| which is always at least 0 by definition. Thus, it is arbitrarily small positive numbers which the distance between An and L must get less than, since by definition it will always be greater than any negative number. For a convergent sequence, |An - L| will eventually be smaller than any given positive number epsilon. Does that help?

    • @navyatayi6956
      @navyatayi6956 4 года назад +1

      @@WrathofMath yes it does. Thank you very much. I understand now. Amazing video btw :)

  • @brainsofmathematics
    @brainsofmathematics 2 года назад

    I can't explain how much u help me

  • @tashfeenamahmud4391
    @tashfeenamahmud4391 4 года назад

    but what if a_n

    • @WrathofMath
      @WrathofMath  4 года назад

      Thanks for watching and good question! Yes, the definition works just the same. Remember we use the absolute value, we require that | a_n - L | is less than epsilon. This is the distance between a_n and L, and it does not matter whether a_n or L is negative. Their distance, given by | a_n - L |, will always be nonnegative.

  • @SerielxSylv
    @SerielxSylv 3 года назад

    can N equals epsilon?

    • @sayakray4740
      @sayakray4740 3 года назад +1

      epsilon is a very small number close to zero. Whereas in the definition you need a number n such that n>N and the distance between f(n) and the limit should be less than epsilon. Now for us to get this value of limit we must increase this value N as much as possible so that we can go more closer to the value of the actual limit of the sequence. That is why N can't be equal to epsilon. You can always put them to be equal but then you won't be reaching any close to the limit.

    • @SerielxSylv
      @SerielxSylv 3 года назад +1

      @@sayakray4740 thanks for replying, im confused because i found some youtbe videos that put them = instead of > ... but u cleared my doubts thanks a lot👍

  • @rodrigodeboni4108
    @rodrigodeboni4108 Год назад

    YOU A G