limsup and liminf of Sequences Simple Explanation with Examples [Real Analysis]

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[dragomirdespard]

You have made an error.. Sn is a non increasing sequence while In is non decreasing sequence..

[ujjwalroy]

This video was really helpful. Thank you Sir 🙏

[tomkamikaze]

The sequence of suprema s_n is non decresing and the sequence of infima i_n is non increasing. The suprema of a given set in your will be greater than or equal to that of the succeeding sets because the succeeding sets are the subsets of the given sets hence its supremum will be greater than or equal to that of the succeeding sets hence a non increasing sequence, similarly its infimum will be less than or equal to that of the infima of the succeeding sets hence a non decreasing sequence. This confusion has led to a mixup in your explanation

[autumntemplin]

Not only was the explanation great, the style humorous, but also...the handwriting is so beautiful! I want you as my professor!!!

[karengomez]

This explanation was very helpful. Thank you for taking the time to write things out because it really helped me follow along.

[aali]

Thank you very much about the explanation really helped me out.

[AllemandInstable]

should be the opposite right ? limsup is a decreasing sequence
if the max value of my sequence was the first term and is unique then the second term of the limsup sequence would be lower than the first value

[CosmicTutoring]

This video is solving Problem 2.12 on Page 52 of the aforementioned .pdf document.
The comments below are another great asset for you guys. I will try to redo this video as soon as I get time.
Thank you! :)

[thanasisdompazis]

very good explanation really helped me out! Ι also like to think of lim sup an as the greatest and lim inf an as the lowest limit point of a sequence

[shubhammeenadeshwali]

Thankyou so much sir for easy explanation

[witness]

wait, you mess up, the s_n=sup {a_n, a_{n+1}, ...} is monotonic decreasing and bounded below.

[vandadghiassi]

I believe you would make a good teacher IF first you learnt what is limsup...

[jj-wn]

É disso que a literatura brasileira precisa. Não dizer: É fácil ver... --"

[vatsaljingar]

Thank you very much sir🙏🙏🙏🙏🙏🙏🥺🥺🥺🥺🥺🥺🥺🥺🥺🥺🥺

[gabrielrdonald]

hey Cosmic tutor, any chance u can guide me how to convert the same understanding to limsup and liminf of sets? I have my exam in 5 days, stochastic probabilities, and I cant wrap my head around the same concept in terms of sets.

[spacecomunication]

you don't prove why they are increasing/decreasing

[نوارةالبيت-ذف]

At first the line was clear, and after a short stretch of the video, the line becomes unclear (I mean the clarity of the line, not the explanation) 😑💔

[casualBob]

the guy doesnt know what he i talking about, dont bother to get a deep understanding

[FatBitches]

How this guy only has 750 subscribers is beyond me