Uniform Continuity (Example 3): Not Uniformly Continuous

Showing a function is not uniformly continuous
In this video, I demonstrate how to show that a function is not uniformly continuous. It's harder than it may seem at first, but super interesting, check it out!
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[@rajat1197]

You simplified it really well. Thank you.

[@user-yc5mw1ww2x]

Thank you so much for the explanation and mostly for slowing down cuz everyone seems in a rush ever since I got to college, including myself

[@Owain.Z]

Thank you sir💯🙌🏾

[@ahmetsimsek3128]

ty sirr , u are the best

[@juanmegias9147]

Thanks so much

[@nipurnshakya9312]

the work you did in this proof is good

[@milossidjak2019]

Case study of functions. First time delta, epsilon makes sense. Made sense before, but uniform continuity and fact how many points you need to properly approximate function. One point defines 1/x in proximity of 0.

[@dr.rahulgupta7573]

Thank you for this nice information.

[@wtt274]

Great video !

[@ABC-jq7ve]

I love your videos!!!

[@InOwnWorld01]

Respected Sir, May you suggest me best book for Real Analysis .Also Sir, which book you follow for Real Analysis?

[@shahinjahanlu2199]

سلام دکتر پیام .چرا از سورهای ریاضی برای نوشتن اثبات استفاده نمی کنید ؟

[@InOwnWorld01]

Respected Sir,, May you make video on topic " Lipschitz Continuity".
Because we know that every Lipschitz Continuous is Uniform continuous.
Sir, under which conditions either a given function is Lipschitz Continuous or not? By examples and counter examples.

[@drpeyam]

Already done

[@ahmadkalaoun3473]

I really wonder if there exist a uniformly continuous function over R other than the constant and the linear functions..what do you think?

[@drpeyam]

sin(x)

[@ahmadkalaoun3473]

@@drpeyam huh i really didn't think about it lol

[@puerulus]

I think any function that has a bounded derivative on R is uniformly continuous on R. So another example would be 1/(1+x^2).

[@MindcraftMax]

@@puerulus Yes, in fact such functions are even "more continuous" than uniformly continuous, they are Lipschitz continuous i.e. there exists some positive k such that for any (x,y) in ℝ² we get | f(x) - f(y) | < k | x-y |.
An example of another function that is still uniformly continuous but not Lipschitz continuous (because of unbounded derivative at 0) is square root of abs(x).

[@carlosalbertomonzonlozano4282]

oh... español,
genial

[@fade2black494]

Hey Peyam, how did you learn these proofs without learning by heart... I really need a better way of understanding formal proofs. Do you have, by chance any tips?

[@him21016]

You must simply read as many proofs and articles as you can; the more you're immersed, the more you'll learn

[@carlosalbertomonzonlozano4282]

mas videos en spanglish please

[@guill3978]

I have a very interesting doubt about mersenne divisors. Why every prime divisor of 2^p-1, where p is prime, must be congruent to 1mod(2p) and also congruent to 1mod(8) or -1mod(8)? Can you proove it in a video?

[@drpeyam]

I don’t do number theory

[@Priyam-wk1tf]

I can't understand intuitively why sin (x) is uniformly continuous??

[@drpeyam]

It doesn’t change that much to not be uniformly continuous

[@joefuentes2977]

Did you randomly just math in Spanish? 😂

[@aahaanchawla5393]

si, fue el.

[@aahaanchawla5393]

@@aashsyed1277 Because I saw the video.