Limit Superior and Limit Inferior

Intermediate Analysis Spring 2015

[sho_cakes]

This was most helpful video that I found about liminf and limsup. Thank you!

[pqhai]

Much easier to understand than a textbook. Thank you so much!

[fernandoespinosa]

I couldn't find a video about this in my language. The explanation is very good. Thank you!

[loganhornberger]

*flips table* So it was this simple all along? Thank you so much!

[robertwilsoniii]

Really the best explanation of the concept I've ever seen.

[ericpttw]

Thanks for this. Great video when my university lectures didn't want to cover this, this semester.

[emlmm]

Thank you for the intuition, it's really helped my conceptualize this topic, however I still find it difficult to write rigorous proofs around these.

[alvinlepik]

So the definition is correct for limsup (and dually, for liminf), because we have a limit of a sequence of supremums, but we know the sequence is bounded from above (from below) by an upper bound (lower bound). ..but what makes the limit always exist? Is the sequence of supremums monotone ?

[rafaelferreira]

Thank you, thank you, for the first time I got some about it .

[akenny]

Such an incredibly helpful video, very well done!!!

[nievsbest]

Great concise video. I would like to be in your class.

[amybailon]

I am trying to prove that a shape with an infinite volume and limited surface area cannot exist. I have been unable to find a proof other than one on Wikipedia using limit superiors. Your video was very helpful, but I am still a little confused as to how I would apply it to this problem. Are there any other resources on limit superiors and inferiors or anything that would be helpful to solve this proof?

[sabanaser]

Great explanation. Where is other videos in real analysis?

[debendragurung]

Great video. The example of the sequences were very helpful. And also were the second theorem you mentioned. Thanks.
Are these subsequential limits also called the limit points?

[honerzawita]

this helps me to understand better than the book.

[jainmaria]

Thank you very much. It was really understandable.. Very good explanation.

[AlexButterfield]

What software are you using to make these videos?

btw. this was a great explanation. thanks.

[omkark]

you are best in world for explaining limsup ....

[kunalch.]

Thankyou for everything about lI'm sup and inf

[ricegoing]

I have to find an 'english' explanation to finally understand as in my country (France), it is really hard to find a good explanation, THANKS!!!