Proof: Triangle Inequality Theorem | Real Analysis

[@WrathofMath]

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[@thedeathofbirth0763]

This is how a person who truly understands logic, can beautifully and precisely communicate it . Thank you.

[@WrathofMath]

Thank you!

[@punditgi]

Very clear proof. Well done!

[@WrathofMath]

Thank you, glad it was clear!

[@androidandroid9591]

An excellent AND simple way to grasp a crucial theorem for the understanding of analysis. Txs.

[@WrathofMath]

Glad to help!

[@red3987]

Beautiful and concise!! thank you for helping me understand this proof better!

[@WrathofMath]

Thanks so much, glad it helped! Thanks for watching and let me know if you ever have any questions!

[@red3987]

@@WrathofMath WIll do!!!

[@johnsally8320]

My man, you're awesome! Much love from Toronto, Canada.

[@WrathofMath]

Thanks so much!

[@ryantrynda3029]

why is it called triangle inequality thou

[@edisonnogalesantezana4761]

The triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.

[@theboss078]

@@edisonnogalesantezana4761How could the sum of two sides of the triangle be equal to the third side? Even if it does then it won't be a triangle anymore!

[@typo691]

​@@theboss078these shapes are usually called degenerate or trivial. Although we dont think of them as triangles visually, it's interesting to note the theorem still works regardless if the triangle flattens down to a single line (generalisation is always fun)

[@clementecarbonaro619]

Thank you sir ❤. Your videos are helping me study for my Principles of Mathematics for Economics exam. Your lessons are fast and intuitive

[@punditgi]

Can you do an entire video on absolute value identities as building blocks for other theorems? I would also illustrate these both on a 1D number line and on a 2D plane as vectors.

[@davaariantara3704]

like |xy|=|x|*|y|? i think you will find it obvious if you proof it by case-by-case like above in the above video or you can even proof it by |x|=squareroot(x^2) ^ just trying to give you an idea that its not hard

[@Alan-sv6ym]

We really love you here in south Africa 🇿🇦😭💜💜💜

[@WrathofMath]

Thank you so much! Love back from the USA's east coast!

[@gerardsagliocca6292]

I am glad you didn't go 100 mph to discuss this inequality , absolute algebraic proof . Is the proof for the inequality without the absolute part , involving similar sort of steps ? .

[@benjtheo414]

if 2:44 wasn't directly obvious to you as it was for me you can use this in the proof: a1

[@mahmoudalbahar1641]

Many thanks for this good video.

[@Bhaskar3D]

It's very good sir. I am from Assam, Indian.

[@harjassingh7758]

thank you bro / sir appreciated !!

[@H3XED_OwO]

beautiful and simple proof!

[@WrathofMath]

Thanks for watching!

[@shhaque9448]

This guy really did a 2 hour lecture in 5 minutes

[@TahaCodes]

Very nice and neat. Thank you. Got yourself a new sub!!!

[@EgonuPatrick]

Am passing maths analysis because of you much love

[@WrathofMath]

Glad to help - thanks for watching!

[@husseinsslehi4428]

Very clear explanation thank you

[@WrathofMath]

Thanks for watching! If you're looking for more analysis, check out my playlist: kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli

[@valeriereid2337]

Thanks for explaining this clearly. If you are able to, please do some work from Abbott's "Understanding Analysis." It would be awesome.

[@jamesjones6359]

Great explanation. Thank you.

[@WrathofMath]

My pleasure, thanks for watching and check out my Real Analysis playlist if you're looking for more! kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli Many new real analysis lessons are coming this year, let me know if you ever have any requests!

[@putin_navsegda6487]

great proof, very understandable! Thank you!

[@WrathofMath]

Thank you, glad it helped! Check out my analysis playlist for more! kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli

[@Divine_wsk21]

Can you please do the same proof with a,b and c

[@jeswintitusjv5927]

Sir , could I know why this is called as "triangular inequality" ? Is this related to triangle when viewed geometrically ?

[@WrathofMath]

Thanks for watching and the question! Yes, particularly with vectors involved. Suppose we have points A, B, and C, and then three vectors AB, CB, and AC, that make a triangle. The vector AB is the same as AC + CB if you know vector addition. And this side of the triangle, AB = AC + CB has length |AB| = |AC + CB|, and this length must be no greater than the sum of the other two sides, that is |AC| + |CB|.

[@samuelbassey6806]

Thanks for sharing

[@ralw7635]

Great, thank you

[@silvo9460]

wow thank you so much sir!!!!!

[@yibanathimnyanda725]

Thank this really helped.

[@WrathofMath]

So glad to hear it, check out my Real Analysis playlist if you're looking for more, many more analysis lessons still to come! kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli

[@TVSuchty]

Can you show that over R^n and all possible dot products, where ||a||^2 = a dot a ?

[@qedmath1729]

let a = . By definition of dot product we have a dot a = x^2+y^2. Similarly for a = , ||a|| = sqrt(x^2 + y^2) or ||a||^2 = x^2 + y^2. Hence we see that the 2 are equal.

[@TVSuchty]

@@qedmath1729 I mean that u show that the theorem holds over all dot products, where by definition ||a||^2 = a dot a

[@ProgressiveVoice]

Thanks!

[@bekhaddaderrar2111]

Thank you so much for this video

[@WrathofMath]

My pleasure, thanks for watching! If you're looking for more real analysis, check out my playlist! kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli

[@Umar-lj5jx]

Thanks a bunch

[@anasshuaibu2530]

Very good ' but plz prove it again when â and b are real numbers.

[@ali-hg103]

That outro thooo🔥

[@WrathofMath]

Artist goes by Crayon Angel now - love his stuff!

[@augustus2834]

great! the only thing that bothered me a little bit is that we didnt take into account when a number is negative and the other is positive. but that case is trivial so i guess doesnt matter that much ahahaha

[@rosepierce9382]

I think it doesn't really matter because he is only taking the sum of a + b to be negative or positive.

[@muhammadasghar7153]

I Asked question but you didn't answer me

[@pakistaninstituteofmedical7185]

Yes I also ask question but didn't reply

[@ahh61]

I asked a question and he answered me so be happy. Maybe next time ask a better question.

[@muhammadasghar7153]

Shut up loser baby hahhahah🤑🤑

[@ahh61]

@@muhammadasghar7153 At least I'm not dumb like you. Your question was probably what's 2+2. You stupid. My questions are always answered. He even answered a bunch of my questions on the last live episode.

[@WrathofMath]

I'm working on it folks, I get a lot of comments and don't have much time. If you ever come by a live stream, that is time I set aside specifically to answer your questions so you can be sure I'll respond if you come by one of those! Thanks for watching and I'm trying to catch up on the comments!

[@navjyotsinghvishen3287]

Group theory from basic 🙏

[@gianlucalepiscopia3123]

Beautiful

[@WrathofMath]

Thanks for watching!

[@이머현]

super good

[@WrathofMath]

Thank you! If you're looking for more analysis, check out my playlist! kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli

[@bonniem1865]

Thank you thank you thank you

[@WrathofMath]

You are very welcome!

[@existentialrap521]

Wrath, once i get this mfing masters degree ima invite you to a carne asada thx G

[@samborn3515]

Please I stil find this difficult

[@monaalhassanquran2160]

Wow ❤

[@keithplays1184]

1st 😊

[@WrathofMath]

Thanks for watching, Keith!

[@samuelbassey6806]

Thanks for sharing