Uniform Continuity (Example 3): Not Uniformly Continuous
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- Опубліковано 19 сер 2024
- 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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You simplified it really well. Thank you.
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
Thank you sir💯🙌🏾
ty sirr , u are the best
Thanks so much
the work you did in this proof is good
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.
Thank you for this nice information.
Great video !
I love your videos!!!
Respected Sir, May you suggest me best book for Real Analysis .Also Sir, which book you follow for Real Analysis?
سلام دکتر پیام .چرا از سورهای ریاضی برای نوشتن اثبات استفاده نمی کنید ؟
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.
Already done
I really wonder if there exist a uniformly continuous function over R other than the constant and the linear functions..what do you think?
sin(x)
@@drpeyam huh i really didn't think about it lol
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).
@@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).
oh... español,
genial
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?
You must simply read as many proofs and articles as you can; the more you're immersed, the more you'll learn
mas videos en spanglish please
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?
I don’t do number theory
I can't understand intuitively why sin (x) is uniformly continuous??
It doesn’t change that much to not be uniformly continuous
Did you randomly just math in Spanish? 😂
si, fue el.
@@aashsyed1277 Because I saw the video.