Triangle Inequality

Triangle Inequality

In this video, I define the concept of an absolute value and use it to prove the triangle inequality in R, which is the most important inequality that we'll use in analysis. Enjoy!

[MrCigarro]

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

[tubalnavarro]

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

[LegendOfMurray]

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

[Jim-besj]

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.

[cerwe]

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

[joudy]

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

[weimeuret]

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...

[AbdallahAttiaA]

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

[MrQwefty]

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

[Apollorion]

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

[sanjeevkumardhiman]

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). :))))

[LarryRiedel]

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

[jimmykornelijegunnarsson]

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.

[foreachepsilon]

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.)

[minimurali]

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

[fromblonmenchaves]

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

[DidierDegonon]

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

[纃]

Wait what? 🤯🤯, I.. I'm new to this

[kamaljitkaurdhiman]

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

[visualgebra]

Professor ! Why It is called Triangle Inequality ?