Triangle Inequality

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  • Опубліковано 22 гру 2024

КОМЕНТАРІ • 60

  • @MrCigarro50
    @MrCigarro50 4 роки тому +63

    I remember my Math Professor saying..." Learn as much as you can about inequalities, you will need them very very often"

    • @lordandprotector
      @lordandprotector 4 роки тому +3

      More often than not. :P

    • @myoung1445
      @myoung1445 4 роки тому +11

      If you're in first year of university or last year of school then take this advice seriously . From a panic cramming 2nd year maths student

  • @tubalnavarro8962
    @tubalnavarro8962 4 роки тому +17

    That triforce in the thumbnail made me click as fast as I could

  • @LegendOfMurray
    @LegendOfMurray 4 роки тому +13

    I wasn't expecting a dab in a math video. Excellent!

  • @Jim-be8sj
    @Jim-be8sj 4 роки тому +6

    Good one. If I remember correctly, once you get up to working in function spaces it's time for the Minkowski inequality for many of the same applications that the triangle inequality enables.

  • @joudy5767
    @joudy5767 4 роки тому +2

    what a coincidence that i have to prove this for my teacher and you posted this 1 day ago🤩🤩 thank uu

  • @cerwe8861
    @cerwe8861 4 роки тому +12

    The "dab" you have to train... xD

  • @AbdallahAttiaA
    @AbdallahAttiaA Місяць тому

    8:30 i did not understand a word here , please if some one could reexplain it to me

  • @Apollorion
    @Apollorion 4 роки тому +4

    Is this triangle inequality also true for triangles in non euclidean spaces?

    • @EpicMathTime
      @EpicMathTime 4 роки тому +2

      Yes, it is. Non-Euclidean geometries take place in metric spaces, and the triangle inequality is required of a metric.
      The triangle inequality is foundational for the notion of "distance" or "length" to make sense. Its essence is that the distance from a to b reports the length of the shortest possible route from a to b. That's what we want distance to mean. We don't want a to be 15 miles away from b, but somehow if I go from a, to c, and then to b, I ended up traveling only 12 miles in total.

  • @sirjackio_zw
    @sirjackio_zw 2 роки тому +1

    Did he just do the dab 9:10😂😂

  • @weimeuret7689
    @weimeuret7689 4 роки тому +1

    I was hoping you could prove the Reverse Triangle Inequality. I'm also wondering why we need to establish |a-b| is greater than the difference of their absolute values...

    • @drpeyam
      @drpeyam  4 роки тому +3

      There’s a video on that

  • @MrQwefty
    @MrQwefty 4 роки тому +3

    The Cauchy Schwarz inequality is driving me mad! Will you do a video on that too?

    • @drpeyam
      @drpeyam  4 роки тому +2

      Already done ✅

    • @MrQwefty
      @MrQwefty 4 роки тому +1

      @@drpeyam Whoops! Thank you Peyam :D

    • @putin_navsegda6487
      @putin_navsegda6487 2 роки тому

      but actually it's Cauchy-Buniakovsky inequality

  • @jimmykornelijegunnarsson4265
    @jimmykornelijegunnarsson4265 4 роки тому +1

    I'm wondering why you don't consider the proof by using the dot product (a+bIa+b), seeing as the proof comes out of it naturally.

    • @drpeyam
      @drpeyam  4 роки тому +1

      That’s the way I would have done it as well, but in that class they don’t really mention dot products or R^n

    • @jimmykornelijegunnarsson4265
      @jimmykornelijegunnarsson4265 4 роки тому +1

      @@drpeyam Oh cool.

  • @minimurali9700
    @minimurali9700 4 роки тому +1

    Sir , but is there any example or case where one side will be equal to to sum of other side in a triangle ? The inequality says lesser or equal to

    • @xibbit6322
      @xibbit6322 Рік тому

      when the triangle is degenerate(smushed down into a line) this is true

  • @ragokyo
    @ragokyo 4 роки тому +5

    11:34 *"the legthgh"*

  • @LarryRiedel
    @LarryRiedel 4 роки тому +4

    I'm looking forward to Jensen's Inequality. :-)

    • @drpeyam
      @drpeyam  4 роки тому +1

      That’s a good one 😄

  • @foreachepsilon
    @foreachepsilon 4 роки тому +1

    My linear algebra professor used to call it the donkey inequality because it’s so simple, even a donkey gets it! (The donkey of course will walk a straight line to get to water, not go in a jagged path.)

    • @drpeyam
      @drpeyam  4 роки тому +2

      LOL, I love this 😂

    • @foreachepsilon
      @foreachepsilon 4 роки тому +1

      Dr Peyam he still teaches at CSUF, though I guess you’re leaving UCI in the fall.

  • @punditgi
    @punditgi 4 роки тому +2

    Awesome explanation!

  • @fromblonmenchaves6161
    @fromblonmenchaves6161 2 роки тому +1

    Why in proof 1. case 1 when x ≥ 0 then x = |x| ≤ -|x| ; and not
    x = |x| ≥ -|x| ?

  • @ImNostalgic
    @ImNostalgic 2 роки тому +1

    was that the triforce??

  • @sanjeevkumardhiman6783
    @sanjeevkumardhiman6783 4 роки тому +1

    It is true coz if both a and b are positive then abs(a+b)=abs(a)+abs(b) but if one of then is negative; let’s say b is negative and let’s say that a=32 and b is equal to -31, then abs(a+b)=abs(32-31)=1; but it is not equal to abs(32)+abs(-31)=32+31=63;in fact the abs(a)+abs(b) is greater than or equal to abs(a+b). :))))

  • @tymothylim6550
    @tymothylim6550 3 роки тому +1

    Great video! Thanks a lot for this :)

  • @thomasjefferson6225
    @thomasjefferson6225 2 роки тому

    Lmao I love the dab!!!! 🤣🤣🤣

  • @rabehajaved
    @rabehajaved Рік тому

    You make it more harder for me😢🙆🏽‍♀️

  • @纃
    @纃 3 роки тому

    Wait what? 🤯🤯, I.. I'm new to this

  • @DidierDegonon
    @DidierDegonon 4 роки тому +1

    you could define abs(x) = Max (x,-x), then your lemma is evident

    • @DidierDegonon
      @DidierDegonon 4 роки тому

      dam you're fast answerer, hello from France!

  • @Sahanie
    @Sahanie 4 роки тому +1

    I trust my Toyota Corollary.

  • @lesprivatrizal
    @lesprivatrizal 4 роки тому

    Nice, thanks

  • @computerguy678
    @computerguy678 Рік тому

    the triforce :skull zelda refrence

  • @yoannroch6477
    @yoannroch6477 4 роки тому

    good video!

  • @JM-st1le
    @JM-st1le 24 дні тому

    subscribed just after the dab ; )

  • @dm_saj1119
    @dm_saj1119 4 роки тому

    Hi dr 💚

  • @kamaljitkaurdhiman7696
    @kamaljitkaurdhiman7696 4 роки тому

    Analysis is adult version of calculus. Isn't it??

    • @drpeyam
      @drpeyam  4 роки тому +4

      It really is!

  • @jamesbra4410
    @jamesbra4410 4 роки тому

    Next measure theory

  • @romaindec1717
    @romaindec1717 4 роки тому +1

    i prefer algebra.

  • @visualgebra
    @visualgebra 4 роки тому

    Professor ! Why It is called Triangle Inequality ?

    • @drpeyam
      @drpeyam  4 роки тому

      Look at the picture

  • @AditYa-sv1nz
    @AditYa-sv1nz 4 роки тому +1

    👍

  • @kelvinmasasire6737
    @kelvinmasasire6737 2 роки тому

    The explanation's a bit hard to grasp Doc. Its a bit too complex

    • @drpeyam
      @drpeyam  2 роки тому +1

      Good for you

    • @mohamedtrfnx6632
      @mohamedtrfnx6632 Рік тому +1

      @@drpeyam i dont think its good for him that he didn't grasp it :(