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?
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 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?
@@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.
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.
1:30 property of lim sup and lim inf
3:30 summation of two sequence
3:45 product of two sequence
I am getting hungry hearing all this talk about lim soup!
Most tasty soup ever :)
Thank you for saving my exams!
Happy to help!
I wish all the best to you, will make sure my students stop by
00:31
how the the infinity is included? it is not define to included, is not it?
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?
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?
@@videogamemusicguy4208 We have liminf = limsup :)
@@videogamemusicguy4208 "divergent to infinity" is a notion you could also define with the property in (b),
@@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?
@@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.
In general I believe this property holds ,
inf { (a_n ) }
Nice sir. Keep it up. I love solving challenging calculus, algebra, trigonometry and geometry maths problems on my.....
real analysis exam in 2 days... yeah i got time!
You can do it!
Could you enable videos with subtitles for automatic translation?
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.
are u nadeking ?
No :D
@@brightsideofmaths haha joking but you have similar voice to him