Proof: Reverse Triangle Inequality Theorem | Real Analysis

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  • Опубликовано: 22 авг 2024

Комментарии • 49

  • @WrathofMath
    @WrathofMath  3 года назад +5

    Check out my Real Analysis playlist for more! ruclips.net/p/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli
    Let me know if you have any requests!

    • @axtonpayton1852
      @axtonpayton1852 3 года назад

      Sorry to be so offtopic but does someone know a way to get back into an Instagram account..?
      I was dumb lost the login password. I appreciate any tricks you can offer me.

    • @rohansilas396
      @rohansilas396 3 года назад

      @Axton Payton instablaster :)

    • @axtonpayton1852
      @axtonpayton1852 3 года назад

      @Rohan Silas Thanks so much for your reply. I found the site on google and I'm waiting for the hacking stuff atm.
      Takes a while so I will reply here later with my results.

    • @axtonpayton1852
      @axtonpayton1852 3 года назад

      @Rohan Silas it worked and I now got access to my account again. I'm so happy!
      Thank you so much you saved my ass :D

    • @rohansilas396
      @rohansilas396 3 года назад

      @Axton Payton Happy to help xD

  • @Churchill-r
    @Churchill-r 9 месяцев назад +5

    Usually I find people commenting, "Wow this video teaches better than my professor" and comments like, "You saved my life", to be really lame and I cringe at them, however this video is the real deal. I thought I got this inequality down already but my solution had some problems which I ignored. This video helped clarify that. I'm now subbed and will plan on finishing the entire Analysis playlist before Analysis finishes me.

    • @WrathofMath
      @WrathofMath  9 месяцев назад +2

      Thanks so much! I'm trying hard to build this channel so I can afford to spend the time necessary to finish the playlist. I hope you'll enjoy what I have created for it so far!

  • @caseystrong1498
    @caseystrong1498 Год назад +8

    This just helped me finish the last step of a huge proof in a Masters engineering class that I have been working on for about 5 hours. Thank you so much for this amazing video

  • @everettharry8789
    @everettharry8789 3 года назад +12

    I don't like abstract math. But you make it so easy that I can't help but love it. I can follow your proofs: Everything seems so logical! On my own I wouldn't know where to start. That's why I don't like abstract math. Applied math? That I can deal with at any time ( I am a Mechanical Engineer by the way). I am always amazed by your elegant proofs and I wonder if I will ever be able to follow your footsteps. Those are giant footsteps by the way. I decided to take Real Analysis (pure math) as a hobby and it gives me so much joy to follow you. Thank you from the bottom of my heart.

    • @WrathofMath
      @WrathofMath  3 года назад +7

      Thank you so much, Everett! I'm very happy to hear you've found my videos clear and enjoyable! And that's really cool that you're studying Real Analysis, I hope it goes well and you enjoy it - I'll be uploading lots more real analysis lessons this year! Practice won't make perfect, but it will certainly make better! Read the material closely, do lots of exercises, and you will understand the material. To actually get better at proofs, and being able to figure out where to start, I think reading proofs from many different fields of math helps a lot. Flipping through a number theory text, graph theory, real analysis, combinatorics, and so on, and doing some exercises from these fields, I think the varied exposure helps make your mind far more flexible when it comes to thinking of ideas that might work!
      My number one rule, when trying to prove something, is write it down! By that I mean, don't think "Oh I could try this...ehh that wouldn't work". Whatever your idea is, whatever you know about the objects involved, whether you think it's important or not, write it down. Start to play with the objects involved, and figuring out whatever you can with the given information. While this may begin as blindly wandering through a dark forest, the ideas you come up with may very well come together at a beautiful clearing, where the path to the end of the proof becomes totally apparent. It can also be very useful to address subcases of a proof to make headway. You may not know how to proceed in your proof, but you may think "if I add this additional restriction, I think I'd be able to prove that". That can be a great place to start. I first learned proofs from "Book of Proof" by Richard Hammack. If you look it up, you can get it for free in a PDF! Its physical edition is fantastic also - very big print that is easy to read. Thanks for your support!

    • @everettharry8789
      @everettharry8789 3 года назад +4

      @@WrathofMath Really appreciate you taking the time to address my shortcoming and how to overcome it. I think you are the ideal Math Professor that one would wish they could have: You are gifted at transmitting knowledge and I am certainly glad that I found your channel. I am getting the physical copy of "Book of Proof". Thanks for everything you do. You are helping a lot of people appreciating a difficult subject. Keep up the good work and God bless.

  • @displaylens
    @displaylens Год назад +3

    Thank you so much, your videos are amazing!
    I am now studying Mathematics in University after years of being scared of the subject. As a child, I was told that I don't get it and never will -- to the point where doing a simple two-digit sum out loud became intimidating for me. I've had to teach myself everything from scratch as an adult, and now that I'm taking analysis, everything seems so dense and I keep finding myself wondering how I can even begin to work out proofs on my own without seeing examples first (despite the fact that I did a full course on proofs, and gone through the Book of Proof cover-to-cover).
    Watching your videos gives me hope though, because often, after I finish one, I also manage to finish the proof I was working on. Thanks so much for being a great educator :)

  • @RealEverythingComputers
    @RealEverythingComputers День назад

    Thanks so much, helped me for a math proofs prep course thats meant as a precursor to an analysis course! Really good tutorial

  • @cheatyhotbeef2636
    @cheatyhotbeef2636 3 года назад +6

    That was well explained! Had to rewatch it a couple times though since I suck at paying attention late at night. :3

    • @WrathofMath
      @WrathofMath  3 года назад +1

      Thank you, and you and me both! I'm studying at the pace of about a page per hour by 10 pm. Though admittedly one page per hour is pretty good depending on the text haha!

  • @michellwmc5868
    @michellwmc5868 2 года назад +4

    Thank you sooooo so much for this video. I am so happy I found your channel!

  • @NesmaTAG
    @NesmaTAG 3 года назад +2

    Thank youuuuuuu
    I was dying trying to find this for my school assignment

    • @WrathofMath
      @WrathofMath  3 года назад

      No problem, glad it helped and thanks for watching!

  • @henlofrens
    @henlofrens 2 месяца назад

    For those looking for more elaborate steps in the second part, I did it like this (one step at the time):
    From the triangle inequality:
    |y - x + x | = -|y-x|
    |x| - |y| >= -|x-y|
    Let me know if I did anything wrong!

  • @LD-qb3ht
    @LD-qb3ht 2 года назад

    Thank you for clearly justifying each step of this proof.

    • @WrathofMath
      @WrathofMath  2 года назад +1

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

  • @klaramuchnova2623
    @klaramuchnova2623 Год назад +2

    Hi, may I ask how do we choose the values of "m" and "n"?

  • @valeriereid2337
    @valeriereid2337 11 месяцев назад

    Thanks for this excellent explanation. It most certainly helped.

  • @MarkDMetzger
    @MarkDMetzger Год назад

    Using m and n was a very clever!

  • @Kingdomlove_Acc
    @Kingdomlove_Acc 2 года назад +1

    pls i want to know the reason why you represent the m to y-x and n as x but not the other way round

  • @artherladett442
    @artherladett442 3 года назад +2

    Peace, thanks for the vid brother

    • @WrathofMath
      @WrathofMath  3 года назад

      My pleasure - thanks for watching!

  • @muliemihretu4936
    @muliemihretu4936 2 года назад

    Thanks for your activity 👍 continue for the next

  • @existentialrap521
    @existentialrap521 11 месяцев назад +1

    You little goober, you. That little m,n trick was NASTY. I WAS LIKE DAAAANG MLG PLAAAY. Legit tho good stuff. We makin it out the hood with this one, dawg

  • @valeriereid2337
    @valeriereid2337 Год назад

    Just wondering if you have a video for series and sequences of complex numbers

  • @mahmoudalbahar1641
    @mahmoudalbahar1641 3 года назад

    Many thanks for this good video.

  • @leticiabarbaneramenezes2751
    @leticiabarbaneramenezes2751 Год назад

    Hi! new subscriber here, hope you can help me, please! i understood what you did, i just don't get why this works. i mean, if you add/subtract something from both sides (by naming m=x-y and n=x instead of solely x and y), how does this "change" the equation so you can get to the result? Shouldn't it be unaffected (and so, shoulnd't we come back to the beginning ?)

  • @anonymousvevo8697
    @anonymousvevo8697 3 года назад +1

    hey , can you do please equivalence ordre ? and relation thanks so much

    • @WrathofMath
      @WrathofMath  3 года назад

      Thanks for watching and I am not sure what you mean, are you asking about partial orders or total orders on a set or something else?

    • @anonymousvevo8697
      @anonymousvevo8697 3 года назад

      @@WrathofMath yeah , that's what i wanted to say , i translated it just like this from french to english , sorry
      can you to that please ? i haven't seen it in your videos so far
      thanks

  • @shubhamkumar-le3vi
    @shubhamkumar-le3vi 3 года назад

    Nyc explanation bro 👍

    • @WrathofMath
      @WrathofMath  3 года назад +1

      Thank you! Glad it was clear! If you're looking for more real analysis, check out my analysis playlist: ruclips.net/p/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli
      Many more lessons to come! Let me know if you ever have any video requests.

  • @ellenimamo9243
    @ellenimamo9243 2 года назад

    Thanks

    • @WrathofMath
      @WrathofMath  2 года назад +1

      Glad to help, thanks for watching!

  • @thedeathofbirth0763
    @thedeathofbirth0763 Год назад

    You are awesome!

  • @MilnerMarunda
    @MilnerMarunda 10 месяцев назад

  • @lilmaxez
    @lilmaxez 2 года назад

    Please how do you prove this? | |||x||| − |||y||| | ≤ |||x − y|||

    • @WrathofMath
      @WrathofMath  2 года назад

      Thanks for watching! Unless all those extra abs val bars mean anything different, that just looks like the result this video is proving.

    • @lilmaxez
      @lilmaxez 2 года назад

      @@WrathofMath thanks for your help