Triangle Inequality

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Күн бұрын

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!
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Пікірлер: 58

@MrCigarro50 4 жыл бұрын

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

@lordandprotector 4 жыл бұрын

More often than not. :P

@myoung1445 4 жыл бұрын

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

@LegendOfMurray 4 жыл бұрын

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

@tubalnavarro8962 4 жыл бұрын

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

@Jim-be8sj 4 жыл бұрын

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.

@cerwe8861 4 жыл бұрын

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

@joudy5767 4 жыл бұрын

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

@MrQwefty 4 жыл бұрын

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

@drpeyam 4 жыл бұрын

Already done ✅

@MrQwefty 4 жыл бұрын

@@drpeyam Whoops! Thank you Peyam :D

@putin_navsegda6487 2 жыл бұрын

but actually it's Cauchy-Buniakovsky inequality

@ragokyo 4 жыл бұрын

11:34 *"the legthgh"*

@LarryRiedel 4 жыл бұрын

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

@drpeyam 4 жыл бұрын

That’s a good one 😄

@Apollorion 4 жыл бұрын

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

@EpicMathTime 4 жыл бұрын

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.

@punditgi 3 жыл бұрын

Awesome explanation!

@weimeuret7689 3 жыл бұрын

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 3 жыл бұрын

There’s a video on that

@fromblonmenchaves6161 2 жыл бұрын

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

@drpeyam 2 жыл бұрын

It’s a typo I think

@fromblonmenchaves6161 2 жыл бұрын

@@drpeyam I see. Thankss

@jimmykornelijegunnarsson4265 4 жыл бұрын

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 4 жыл бұрын

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 4 жыл бұрын

@@drpeyam Oh cool.

@minimurali9700 4 жыл бұрын

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 Жыл бұрын

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

@foreachepsilon 4 жыл бұрын

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 4 жыл бұрын

LOL, I love this 😂

@foreachepsilon 4 жыл бұрын

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

@tymothylim6550 2 жыл бұрын

Great video! Thanks a lot for this :)

@sirjackio_zw 2 жыл бұрын

Did he just do the dab 9:10😂😂

@ImNostalgic 2 жыл бұрын

was that the triforce??

@drpeyam 2 жыл бұрын

Yeah

@ImNostalgic 2 жыл бұрын

@@drpeyam pogggggg

@sanjeevkumardhiman6783 4 жыл бұрын

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). :))))