Please Subscribe here, thank you!!! goo.gl/JQ8Nys Reverse Triangle Inequality Proof. A very careful proof of the Reverse Triangle Inequality for real numbers.
couldnt you also say: that mod(b) is less than or equal to mod(a) for that mod(mod(b)-mod(a)) be greater or equal to 0. hence mod(b)-mod(a) is greater or equal to zero but mod(b)-(mod(a)) is greater or equal to mod(a+b) but if that holds then mod(a+b) is greter than zero and hence taking mod of both sides leaves the lhs equal to mod(a+b) since mod of a number always positive doesnt change the number? thats alteast my thought process i may be wrong
I "think" this version appears in the book by Fitzpatrick on Advanced Calculus. I don't have it with me here to check, but pretty sure it's there. Hope this helps:)
@@TheMathSorcerer I have the 2nd international edition of that book and I can't find the phrase 'reverse triangle'. My supervisor said I am not allowed to use this phrase for that inequality unless I can show him a source that uses this phrase. I am surprised to find out none of the books I have actually use this phrase...
Its cool how you could also prove this using the same exact technique done in *your* video for the regular triangle inequality (for real numbers): ua-cam.com/video/lj765RaxreE/v-deo.htmlsi=QhhZV4GR7snVQceN
You're close to the only "math help" channel I've found for introductory real analysis. Thank you so much for existing.
Is the Reverse triangle Inequality not ||x|-|y||
Yeah I thought of that too. Kek
Thank you! This was very helpful, and well explained, thank you for sharing!
lolXDrofl I am glad it helped!!
it was really the obvious part that wasn't obvious to me. I didn't think of using the definition of absolute value to justify the final result.
thank you so muchhhhhh, you helped me understand this inequality and I able to finished my homework 🔥 (subscribed!)
Awesome and welcome to the channel !!
What about complex numbers or vectors?
couldnt you also say: that mod(b) is less than or equal to mod(a) for that mod(mod(b)-mod(a)) be greater or equal to 0. hence mod(b)-mod(a) is greater or equal to zero but mod(b)-(mod(a)) is greater or equal to mod(a+b) but if that holds then mod(a+b) is greter than zero and hence taking mod of both sides leaves the lhs equal to mod(a+b) since mod of a number always positive doesnt change the number? thats alteast my thought process i may be wrong
This would be more helpful if it was the actual Reverse Triangle Inequality. (| |x| - |y| |
Yeah, the guy loses credibility when he sets off the prove the wrong thing.
||x-y|| =? ||y-x|| this should be stated to complete the proof
Just insert - b then the right hand side is |a+-b| = |a-b| as you wanted
You're my hero m8, this was miles better than my lecturers.
happy it helped:)
Many thanks for this good video.
Sir I wanna asked u one question plzz
i would buy you a beer.. You are a true hero!
new sub here!
Thank you!
Thank u... excellent video
Excellent video of a fundamental property
Thank you!
The Math Soucerer Once again saving my life bro your the GOAT of math
Can you please refer me to an official source that uses the phrase 'reverse triangle inequality'?
The term Reverse Triangle Inequality often means similar things written different ways.
Another way is:
||x| - |y||
I "think" this version appears in the book by Fitzpatrick on Advanced Calculus. I don't have it with me here to check, but pretty sure it's there. Hope this helps:)
@@TheMathSorcerer I have the 2nd international edition of that book and I can't find the phrase 'reverse triangle'. My supervisor said I am not allowed to use this phrase for that inequality unless I can show him a source that uses this phrase. I am surprised to find out none of the books I have actually use this phrase...
Your voice is so relaxing and, this video is the best between triangle inequality proofs. You literally saved my life
Thank you 😃
I searched more than half hour in internet to get this problem,now finally here I get
👍
Thanks a lot...why couldn't i think of this...
It’s hard to do on your own the first time👍
Thanks!
You really saved my life👌🏻going
very happy it helped!!
If |x|< a and |y|< b then |x| + |y| < a + b.
Sir! Can you make a video on it's proof? Is this true generally?
Of course a,b>=0
Absolute savior thanks bro
np man
What a calm voice. Thanks !
thanks!!
You are welcome! I hope you could make a video about proofs on subsequences (Advanved Calculus).
It really helped👍👌
Awesome
thank you man you are my hero
👍
+The Math Sorcerer
I thought |a - b| ≥ | |a| - |b| | is the reverse inequality.
Its cool how you could also prove this using the same exact technique done in *your* video for the regular triangle inequality (for real numbers): ua-cam.com/video/lj765RaxreE/v-deo.htmlsi=QhhZV4GR7snVQceN
life saver
glad it helped!
| |x|-|y| |
save my life