Proof: The Limit of a Sequence is Unique | Real Analysis

[@sanelprtenjaca9147]

This proof seems more natural than standard proof which uses triangle inequality. If I got this question in exam, I'll prove it this way. Thank you.

[@tanaykashyap2459]

In my first calc class in uni and this helped sooo much

[@WrathofMath]

Glad to hear it, thanks for watching!

[@urty4395]

If I had this video about a month Ago it'd have changed my life....but still thanks it'll help alot... this is the only video thats legit on youtube

[@WrathofMath]

Thanks a lot for watching! I am glad it helped, even if a little late! You may be interested in my in-progress real analysis playlist: kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli

[@joshmckinney6034]

Love your teaching style.

[@benjaminkoskei4143]

That's great. Watching from Kenya

[@WrathofMath]

Thank you! If you're looking for more real analysis, be sure to check out my analysis playlist! kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli Let me know if you ever have any questions!

[@punditgi]

The limit may be unique but so are you, sir! 😆

[@WrathofMath]

I try to differentiate myself from the crowd and not be derivative 😆

[@sakshirajput199]

I'm finding the proof like u proved and I'm here with ur video which clear all my doubts u explained so well....

[@jv004k]

You’re the GOAT

[@oreoluwaoshodi]

This video was really helpful. Thank you so much

[@WrathofMath]

Glad it was helpful!

[@ntab5489]

would this proof still work if we say epsilon = (b-a)/3 because thats what I did and I am kinda stuck..

[@henrywoo1668]

Very well explained .Thanks a lot for the great video !

[@kamalzee7503]

Can this be used to show that a(n) can have at most one limit ?

[@WrathofMath]

Thanks for watching and this proof has demonstrated that. Certainly a sequence either has a limit or it doesn't. This proof has shown it can't have more than one, thus any sequence has either 0 or 1 limit. If you're looking for more analysis, check out my playlist, and let me know if you have any questions! kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli

[@urshitaray633]

Hi! Could you please explain why you assumed E=b-a/2 Thanks in advance!

[@tranmymy9411]

E=b-a, b>a, b different a, (A=an) • lA-al < b-a a-b < A-a < b-a 2a-b < A < b • |A-b| < b-a a-b < A-b < b-a a < A < 2b-a Such that we have: 2b-a > b > A > a > 2a-b 2b > a+b > A > a+b > 2a From: a+b > A > a+b => contradiction (These are what I think. If there are any mistake, please correct me)

[@mahmoudalbahar1641]

Many thanks for your good videos.

[@WrathofMath]

My pleasure, thank you for your support!

[@grantusmercy371]

Thank you soo much 💞

[@WrathofMath]

Thanks for watching!

[@sakshirajput199]

Want to study maths from you via online classes r u giving classes also or only on youtube

[@benedekmorvai7264]

nice proof

[@WrathofMath]

Thank you!

[@leocrino5144]

Love you

[@ioannaathineos5269]

amazing!

[@WrathofMath]

Thanks!

[@photoguy-yz3vz]

how do we know that a and b are positive, if they aren't, then this choice of epilon is invalid

[@WrathofMath]

The choice of epsilon is valid regardless. We've still assumed (without loss of generality) that b>a, so whether or not they are negative, we have b-a > 0.

[@akihayakawa788]

ur amazing thank u sm!!!!

[@WrathofMath]

Glad I could help!

[@cozumel5608]

thanks I love you

[@WrathofMath]

thanks love you too

[@samyakjain8147]

my goat

[@armanrasouli2779]

I have a suggestion what is the answer to this system of differential equations: y'y''=1and yy'=1 ? I came up with C1e^x+C2e^(-x) as an answer for y but when I checked it, It was totally wrong and I don't know why :(

[@gurjara_pratiharas]

👍

[@WrathofMath]

Thanks for watching!