How to Prove that a Sequence of Functions Converges Pointwise

[@limitsatinfinity4393]

Thank you for the explanation. Before watching the video, I spend almost an hour trying to solve the problem. I never realized that the inequality changes after dividing by ln(x). Thanks again

[@alejandrorodriguez3658]

Keep doing this man, u r saving my grades

[@TheMathSorcerer]

:)

[@berke-ozgen]

This is art. Thanks for sharing!

[@algorithmo134]

is there a playlist to this video? thanks

[@sunilrampuria9339]

hi, the convergence isn't uniform but i find the explanation to be a bit incomplete, your explanation works on this case, but not when the interval is [0,1). In this interval too the sequence of functions doesn't converge uniformly, and it's easy to prove via contradiction.

[@anuragseth4420]

the video is about pointwise

[@jairoselin5119]

Hai, How one can prove that?

[@Dil_pickles]

youre the best. your videos have helped me way too many times. I'd give this video 2 likes if i could

[@TheMathSorcerer]

ahh thanks man!

[@ned.5326]

IKR?????????

[@Saeed-Patel-01]

if fn defined on [0,3/4] can we say it coverges uniformly and how to prove that?

[@sirroccosquall]

Cheers for this you absolute legend!

[@TheMathSorcerer]

👍

[@codystene3022]

Is this not the definition of uniform convergence? I am pretty sure pointwise has a different definition.

[@funnywaves8765]

Super! Thank you.

[@TheMathSorcerer]

you are welcome:)

[@davibernardolima7869]

Thank you so much!

[@ДалерСаттаров-х2ю]

oh man U are great THANK U!!!!!!!!!!!!

[@TheMathSorcerer]

You are welcome!

[@cndler23]

this is really advanced

[@TheMathSorcerer]

Yeah hehe

[@danbrown6698]

Good job

[@michaelkievits7073]

crystal clear

[@christinabeeee]

By choosing N = ln epsilon / ln x, isn't that making N depend on x?

[@nickhaas7433]

Yeah, that's why it converges pointwise and not uniformly

[@official_minyoung]

@@nickhaas7433I do know that in the definition of pointwise convergence, the N depends on x. However, I’m still curious if that proof is sufficient enough to say it doesn’t converge uniformly. In the video, he chose N larger than lnε/lnx, and it came to my thought that there could be a N that is larger than lnε/lnx and is constant within x in (0,1). Shouldn’t we find a counterexample of N to prove that the sequence of function does not converge uniformly?

[@ned.5326]

THANKS DUDE UR GREAT

[@obasimatictutorial]

Nice one sir

[@TheMathSorcerer]

Thanks

[@lit22006]

what if it was the open set (0,1) ?

[@berke-ozgen]

then just focus on 3rd condition.

[@joshbolton2782]

Thank you Thank you Thankyou thank you Thank you Ty tytytytyttyyt

[@Pannafreestyle]

love you bro

[@ZeonLP]

Math is love

[@TheMathSorcerer]

👍

[@smoosami1024]

Can you explain(Q,+)is not cyclic?

[@garrettthompson3286]

If (Q, +) were cyclic, it would have a generator that generates all positive rationals. Is there a smallest positive rational number?

[@smoosami1024]

Quickly please i have exam tomorrow

[@nikitazamvar8819]

how did exam go