Limit Superior and Limit Inferior Explained (with Example Problems) | Real Analysis

We visualize what the lim sup of a sequence is, discuss the definitions of lim sup and lim inf, introduce two sequence theorems regaring lim sup and lim inf, and do several examples of finding the limit superior and limit inferior of a sequence. #realanalysis

◉Textbooks I Like◉

★DONATE★

Thanks to Petar, dric, Rolf Waefler, Robert Rennie, Barbara Sharrock, Joshua Gray, Karl Kristiansen, Katy, Mohamad Nossier, and Shadow Master for their generous support on Patreon!

Follow Wrath of Math on...

[krishnaks]

Thank you for explaining so clearly. It's not that easy to find graduate level maths content on youtube.

[hmingthansangavangchhia]

Very clear explanation. Even for beginners. I think it is much clearer than the one from 'The Bright Side of Mathematics'.

[Megane.Senpai]

thanks man, your explanations are crystal clear and are really helping me for my grad school preparations.

[cyrustaba]

hello great video i was wondering where the proofs are that you mentioned you would put in the description thank you again

[Joe-pjds]

Great video - thanks very much - your real analysis playlist has become my substitute for lacklustre lecturers.

[Maria-yxse]

This is great!!!! I was having a hard time understanding the defn from the textbook, turns out it only takes one search from yt to get this over with.

[ncebamaloka]

You the man🙏🏿 I hope you have a great day

[davidshi]

Your explanation is really helpful! Thanks again for taking my request, you're like a mathematical DJ :)
Just curious, where are these exercises from? Also, your sweater is excellent 🐸

[turokg]

Let's get to differentiation my man!

[Werner-slii]

@Wrath of Math I have looked in the description for a link to the videos with the proofs but I couldn't see any. I would love to watch them if you can kindly point out where I can can find them. I love your videos please keep them coming :)

[a.j.apalla]

Taking RA rn- this video helped a lot thanks! (Subbed)

[Bedoroski]

A dedicated explanation as usual. But I wonder, so can it be the case that: a sequence has all of its terms be less than (or =) some constant C, but C may not be limsup(seq).
It can be a graph where in the first N-th terms, it increases to a very value C . After that, it decreases to some value and then converge to some number D that's lower than C.
Is my interpretation valid?

I personally think we should include these confusing examples to strenghthen the understading of the material.

[severed_toast]

this was a great explanation, thank you. but i'm still stuck on how to work with limsup/liminf if it tends to something else other than infinity (e.g. 0 or 1) since I don't know where you would start 'cutting off' terms.

[davidporubic]

Is it ok to write for limes inferior=5 and limes superior =7 as an=5+2/n