Limsup vs Limits

Limsup vs Limits

In the next 2 videos, I explain the difference between the limsup and the classical notion of a limit. Here I show that IF the limit of a sequence exists, then the limsup has to be equal to that limit. It's a beautiful analysis exercise for you and the whole family, enjoy!

[frozenmoon]

Ah, the good old limits vs lime soup. This is what analysis is all about and we can enjoy it thanks to you, Dr. Peyam!

[RR_theproahole]

Hands down the best lectures on limsup and liminf. I was struggling so much with this particular topic in real analysis until I found your videos, thanks a lot sir.

[mathkaveli]

I remember some analysis in grad school, I don't think I fully comprehended these ideas then...and now I feel like I'm on my way. Thank you.

[Test-zdmp]

Nice proof! Thank you for your commitment to this channel, it helps greatly!

[MrGaugeBoson]

Thank you so so much. You explained exactly the point I didn’t quite understand.

[wtt]

Very nice proof .Thank you sir for your great video !

[punditgi]

Many thanks for explaining these concepts!

[johnniewalkerjohnniewalker]

very good explanation sir.Thank you for the help!!!

[justincallan]

at 7:52 why can we just drop epsilon? I'm confused at that part, since it was arbitrary we can drop it?

[tomatrix]

The recipe in this video for the soup has a little bit too much lime. I think if you didn’t let N blow to inf then it would taste better

[Bran]

Why exactly would the student with a high score of 98% dropout? It'd make more sense for the limit inferior.

[anthonysawyer]

Why would you assume that the person that scored at 98 would drop out? 5:36

[jidrit]

can you make video on sieve of euresthenes in number theory book by underwood dudley

[deepikask]

Can you give proof of lim sup sn< lim sup tn when sn< tn