Real Analysis 12 | Examples for Limit Superior and Limit Inferior

[@mattetor6726]

I am getting hungry hearing all this talk about lim soup!

[@brightsideofmaths]

Most tasty soup ever :)

[@qiaohuizhou6960]

1:30 property of lim sup and lim inf 3:30 summation of two sequence 3:45 product of two sequence

[@waynelau3256]

Thank you for saving my exams!

[@brightsideofmaths]

Happy to help!

[@eamunozzzzzz]

I wish all the best to you, will make sure my students stop by

[@luiginotcool]

real analysis exam in 2 days... yeah i got time!

[@brightsideofmaths]

You can do it!

[@xoppa09]

In general I believe this property holds , inf { (a_n ) }

[@mathsandsciencechannel]

Nice sir. Keep it up. I love solving challenging calculus, algebra, trigonometry and geometry maths problems on my.....

[@videogamemusicguy4208]

at around 2:30, with property (b), why is the liminf necessarily equal to infinity? what if the sequence diverges to infinity but has limit points at 1 and 2?

[@videogamemusicguy4208]

i feel as if potentially it is an issue with the iff? because we could have a divergent sequence with finite lim inf, so IF lim inf is infinity THEN the sequence is divergent to infinity, but the sequence being divergent to infinity does not imply that lim inf is infinity?

[@brightsideofmaths]

@@videogamemusicguy4208 We have liminf = limsup :)

[@brightsideofmaths]

@@videogamemusicguy4208 "divergent to infinity" is a notion you could also define with the property in (b),

[@videogamemusicguy4208]

@@brightsideofmaths so if we did define divergence to infinity with (b), would the sequence (for example) given by 'n if n is odd, 1 if n is even' diverge to infinity? because here the limsup = infinity but liminf = 1?

[@brightsideofmaths]

@@videogamemusicguy4208 Your sequence is not one that is divergent to infinity. It's a divergent sequence with an accumulation value 1 and an improper accumulation value +infinity.

[@pedrogoncalves8634]

Could you enable videos with subtitles for automatic translation?

[@brightsideofmaths]

Good question. I can try but I do not know how good the result is. It would be better if someone would write translations for the videos. I would be happy to include them then.

[@Deltax0428]

are u nadeking ?

[@brightsideofmaths]

No :D

[@Deltax0428]

@@brightsideofmaths haha joking but you have similar voice to him