Proof: Reverse Triangle Inequality Theorem | Real Analysis

[@WrathofMath]

Support the production of this course by joining Wrath of Math to access exclusive and early videos, original music, plus the real analysis lecture notes at the premium tier! kzbin.info/door/yEKvaxi8mt9FMc62MHcliwjoin Real Analysis course: kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli Real Analysis exercises: kzbin.info/aero/PLztBpqftvzxXAN05Gm3iNmpz9SkVfLNqC

[@axtonpayton1852]

Sorry to be so offtopic but does someone know a way to get back into an Instagram account..? I was dumb lost the login password. I appreciate any tricks you can offer me.

[@rohansilas396]

@Axton Payton instablaster :)

[@axtonpayton1852]

@Rohan Silas Thanks so much for your reply. I found the site on google and I'm waiting for the hacking stuff atm. Takes a while so I will reply here later with my results.

[@axtonpayton1852]

@Rohan Silas it worked and I now got access to my account again. I'm so happy! Thank you so much you saved my ass :D

[@rohansilas396]

@Axton Payton Happy to help xD

[@Churchill-r]

Usually I find people commenting, "Wow this video teaches better than my professor" and comments like, "You saved my life", to be really lame and I cringe at them, however this video is the real deal. I thought I got this inequality down already but my solution had some problems which I ignored. This video helped clarify that. I'm now subbed and will plan on finishing the entire Analysis playlist before Analysis finishes me.

[@WrathofMath]

Thanks so much! I'm trying hard to build this channel so I can afford to spend the time necessary to finish the playlist. I hope you'll enjoy what I have created for it so far!

[@caseystrong1498]

This just helped me finish the last step of a huge proof in a Masters engineering class that I have been working on for about 5 hours. Thank you so much for this amazing video

[@everettharry8789]

I don't like abstract math. But you make it so easy that I can't help but love it. I can follow your proofs: Everything seems so logical! On my own I wouldn't know where to start. That's why I don't like abstract math. Applied math? That I can deal with at any time ( I am a Mechanical Engineer by the way). I am always amazed by your elegant proofs and I wonder if I will ever be able to follow your footsteps. Those are giant footsteps by the way. I decided to take Real Analysis (pure math) as a hobby and it gives me so much joy to follow you. Thank you from the bottom of my heart.

[@WrathofMath]

Thank you so much, Everett! I'm very happy to hear you've found my videos clear and enjoyable! And that's really cool that you're studying Real Analysis, I hope it goes well and you enjoy it - I'll be uploading lots more real analysis lessons this year! Practice won't make perfect, but it will certainly make better! Read the material closely, do lots of exercises, and you will understand the material. To actually get better at proofs, and being able to figure out where to start, I think reading proofs from many different fields of math helps a lot. Flipping through a number theory text, graph theory, real analysis, combinatorics, and so on, and doing some exercises from these fields, I think the varied exposure helps make your mind far more flexible when it comes to thinking of ideas that might work! My number one rule, when trying to prove something, is write it down! By that I mean, don't think "Oh I could try this...ehh that wouldn't work". Whatever your idea is, whatever you know about the objects involved, whether you think it's important or not, write it down. Start to play with the objects involved, and figuring out whatever you can with the given information. While this may begin as blindly wandering through a dark forest, the ideas you come up with may very well come together at a beautiful clearing, where the path to the end of the proof becomes totally apparent. It can also be very useful to address subcases of a proof to make headway. You may not know how to proceed in your proof, but you may think "if I add this additional restriction, I think I'd be able to prove that". That can be a great place to start. I first learned proofs from "Book of Proof" by Richard Hammack. If you look it up, you can get it for free in a PDF! Its physical edition is fantastic also - very big print that is easy to read. Thanks for your support!

[@everettharry8789]

@@WrathofMath Really appreciate you taking the time to address my shortcoming and how to overcome it. I think you are the ideal Math Professor that one would wish they could have: You are gifted at transmitting knowledge and I am certainly glad that I found your channel. I am getting the physical copy of "Book of Proof". Thanks for everything you do. You are helping a lot of people appreciating a difficult subject. Keep up the good work and God bless.

[@displaylens]

Thank you so much, your videos are amazing! I am now studying Mathematics in University after years of being scared of the subject. As a child, I was told that I don't get it and never will -- to the point where doing a simple two-digit sum out loud became intimidating for me. I've had to teach myself everything from scratch as an adult, and now that I'm taking analysis, everything seems so dense and I keep finding myself wondering how I can even begin to work out proofs on my own without seeing examples first (despite the fact that I did a full course on proofs, and gone through the Book of Proof cover-to-cover). Watching your videos gives me hope though, because often, after I finish one, I also manage to finish the proof I was working on. Thanks so much for being a great educator :)

[@ahmedabdihakim1250]

legends watch short time before exam......its so helpful thank you.

[@RealEverythingComputers]

Thanks so much, helped me for a math proofs prep course thats meant as a precursor to an analysis course! Really good tutorial

[@michellwmc5868]

Thank you sooooo so much for this video. I am so happy I found your channel!

[@cheatyhotbeef2636]

That was well explained! Had to rewatch it a couple times though since I suck at paying attention late at night. :3

[@WrathofMath]

Thank you, and you and me both! I'm studying at the pace of about a page per hour by 10 pm. Though admittedly one page per hour is pretty good depending on the text haha!

[@henlofrens]

For those looking for more elaborate steps in the second part, I did it like this (one step at the time): From the triangle inequality: |y - x + x | = -|y-x| |x| - |y| >= -|x-y| Let me know if I did anything wrong!

[@LD-qb3ht]

Thank you for clearly justifying each step of this proof.

[@WrathofMath]

Glad to help, thanks for watching and check out my analysis playlist if you're looking for more! kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli

[@valeriereid2337]

Thanks for this excellent explanation. It most certainly helped.

[@mariafrenchieperez9721]

Amazing work!❤

[@WrathofMath]

Thank you! 😄

[@NesmaTAG]

Thank youuuuuuu I was dying trying to find this for my school assignment

[@WrathofMath]

No problem, glad it helped and thanks for watching!

[@MarkDMetzger]

Using m and n was a very clever!

[@klaramuchnova2623]

Hi, may I ask how do we choose the values of "m" and "n"?

[@muliemihretu4936]

Thanks for your activity 👍 continue for the next

[@Kingdomlove_Acc]

pls i want to know the reason why you represent the m to y-x and n as x but not the other way round

[@artherladett442]

Peace, thanks for the vid brother

[@WrathofMath]

My pleasure - thanks for watching!

[@valeriereid2337]

Just wondering if you have a video for series and sequences of complex numbers

[@Heatblast-u9r]

great video

[@WrathofMath]

Thank you!

[@mahmoudalbahar1641]

Many thanks for this good video.

[@ellenimamo9243]

Thanks

[@WrathofMath]

Glad to help, thanks for watching!

[@thedeathofbirth0763]

You are awesome!

[@WrathofMath]

Thank you!

[@shubhamkumar-le3vi]

Nyc explanation bro 👍

[@WrathofMath]

Thank you! Glad it was clear! If you're looking for more real analysis, check out my analysis playlist: kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli Many more lessons to come! Let me know if you ever have any video requests.

[@existentialrap521]

You little goober, you. That little m,n trick was NASTY. I WAS LIKE DAAAANG MLG PLAAAY. Legit tho good stuff. We makin it out the hood with this one, dawg

[@leticiabarbaneramenezes2751]

Hi! new subscriber here, hope you can help me, please! i understood what you did, i just don't get why this works. i mean, if you add/subtract something from both sides (by naming m=x-y and n=x instead of solely x and y), how does this "change" the equation so you can get to the result? Shouldn't it be unaffected (and so, shoulnd't we come back to the beginning ?)

[@anonymousvevo8697]

hey , can you do please equivalence ordre ? and relation thanks so much

[@WrathofMath]

Thanks for watching and I am not sure what you mean, are you asking about partial orders or total orders on a set or something else?

[@anonymousvevo8697]

@@WrathofMath yeah , that's what i wanted to say , i translated it just like this from french to english , sorry can you to that please ? i haven't seen it in your videos so far thanks

[@lilmaxez]

Please how do you prove this? | |||x||| − |||y||| | ≤ |||x − y|||

[@WrathofMath]

Thanks for watching! Unless all those extra abs val bars mean anything different, that just looks like the result this video is proving.

[@lilmaxez]

@@WrathofMath thanks for your help

[@MilnerMarunda]

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