The Difference Between Pointwise Convergence and Uniform Convergence

[@uzmaimam8911]

this video deserves thousands of likes, thank you so much.

[@TheMathSorcerer]

Glad it helped!

[@whosyourdaddy25]

Your videos are saving my life right now

[@hector4818]

Bro I love you so much , I have no idea what I’m doing and your videos are legit saving me 🙏🙏💙💙

[@yosefgomgom225]

This video clear up much confusion that I have on difference between pointwise convergence and uniform convergence

[@bhavyakukkar]

Do you think there is any way that the difference between pointwise and uniform convergence can be visualized? I can understand the definitions with respect to the preservation of continuity, integrability, etc., but I still don't completely grasp what the difference in their primary definitions actually does (N being independent of x)

[@pizzakat]

there is a great video by @cmodgamma1091 visualizing the difference between both, I know this is a little too late but you never know i guess

[@mkwarlock]

In most of the resources on this topic, in the definition for uniform convergence, it was stated that n >= N instead of strictly n > N. Is this an oversight in the video or is this intentionally different, and how important is this distinction? Otherwise, thanks for the great videos, I love them!

[@mkwarlock]

Maybe it's tied to the fact theat we are choosing N from Z+ instead of the set of natural numbers, as in most other literature I've come across today while studying this topic. I think this distinction would make sense if we consider Z+ as containing 0.

[@TheMathSorcerer]

It's not a huge deal, different books do it different ways.

[@abdoulkarenzo3138]

Thx a lot my brother u helped me in my Exam

[@dtieck]

Just found your channel and I already know it is going to help a lot haha, nice video!

[@Mohammed138]

Thank you bro so satisfying

[@km-sc4kz]

this was a great help, thank you :)

[@TheMathSorcerer]

You are welcome😄

[@danbrown6698]

This video is quete helpful 👏

[@Jemapelbulgarel]

Thank you, great explanation

[@TheMathSorcerer]

You are welcome 😄

[@parastooazizi1447]

So much helpful! Thanks a lot!

[@GOODBOY-vt1cf]

thank you so much

[@TheMathSorcerer]

You are welcome 😀

[@shilpaprashar6]

Cool Video.

[@user-ke2rp4gz2c]

Thank you

[@TheMathSorcerer]

You're welcome

[@edwardqian4019]

you are so awesome. thanks for video a lot!

[@MuhammadAbdullah-lc4cc]

can you make a video lecture on these topics of complex analysis 2 weierstrass function . elliptic function in term of weierstrass functions with same periods. Jacobian elliptic function and it's properties ??

[@TheMathSorcerer]

Sure

[@kodysmediaarena8011]

Good explanation

[@TheMathSorcerer]

thank you!!

[@gaaraofddarkness]

Thanks a lot... could you pls explain now why arctan (nx) is UC/ PW convergent on [0,b]?

[@thawng9346]

The function of arctan is continuous, but the limit function is not. Hence, it is pointwise convergent. f(x) = arctan (nx) we know that arctan is continuous on [0,b]. But if x = 0 it will converge to 0. If x

[@rahrah527]

This video is a few years old at this point, but could one say that your example f_n(x) is pointwise convergent on [0,1] but uniformly convergent on only [0,1)?

[@frederickburke9944]

did you follow this up with the video proving x^n does not converge uniformly? I am not finding it

[@gonzaloprats2038]

how does x^n tend to 0 when n approaches infinity??

[@vinvic1578]

It does, assuming |x| < 1

[@MuhammadAbdullah-lc4cc]

or any link of complex analysis topics ?

[@TheMathSorcerer]

yeah I have a playlist kzbin.info/aero/PLO1y6V1SXjjOLpoC123XeiAX8hxbyY_2b

[@maskbakchodars2271]

This topic is covered under calculus 3 in our institute can you tell me. WHICH OF YOUR PLAYLIST CONTAINS VIDEO ON THIS TOPIC SO I CAN SEE WHOLE TOPIC

[@TheMathSorcerer]

Advanced calculus playlist has a few more

[@vanessamichaels9512]

'irregardless' is not a word

[@marcusjohnpeterson2302]

Why don't you write for pointwise conv "there is a N=N(\epsilon, x) \in Z^+" and for uniform conv "there is a N=N(\epsilon) \in Z^+..." It would be no confusion then if N depends or not on x...just sayin'... :)

[@TheMathSorcerer]

👍

[@anuphalder8839]

why pointwise convergence is called pointwise?

[@francescofoschins9964]

too bad i have no clue on how to solve this shit and my exam is the day after tomorrow