In fact |√x-√y|≤√|x-y| for all non-negative x and y. So it's uniformly continuous.
@neur3034 жыл бұрын
Thanks for doing all kinds of tutorials! Even ones that might be not as popular! Very appreciated 🙏❤️
@kinpatu4 жыл бұрын
Love your videos. I wish the YT Algorithm had introduced you earlier.
@ranitacab3 жыл бұрын
Your videos helps me a lot to read U.A by Stephen Abott, thanks you so much
@amadeutoletole67774 жыл бұрын
Excellent lesson!
@jimskea2244 жыл бұрын
On the open set of ordinal integers between zeroth and second.
@charlottedarroch4 жыл бұрын
You could have also picked δ = min{δ_1,δ_2,1} and that still confines x and y to one of [0,2] or [1,inf).
@watchaccount4 жыл бұрын
what if epsilon = 1000000 and delta1 = delta2 = 10?
@jonathanjacobson70124 жыл бұрын
Daniel, what would you do with x=1.5
@charlottedarroch4 жыл бұрын
@@jonathanjacobson7012 If x = 1.5 and |x-y| < δ = min{δ_1,δ_2,1}, then |x-y| < 1, so y is in (0.5,2.5). If y is in (0.5,2], then both x and y are in [0,2]. If instead y is in (2,2.5), then both x and y are in [1,inf). Either way, choosing δ = min{δ_1,δ_2,1} guarantees that for all positive real numbers x,y with |x-y| < δ, either both x,y are in [0,2], or both x,y in [1,inf), which is sufficient for Michael's argument.
@goodplacetostop29734 жыл бұрын
14:15
@bsuperbrain4 жыл бұрын
Nope, the 'stop' was cut off. :D
@adned62814 жыл бұрын
The first good place to stop: kzbin.info/www/bejne/fJnEd5itgN6jY7M
@goodplacetostop29734 жыл бұрын
@@adned6281 Nope, you haven't dug deep enough. Your video is from March 2020 but we can find earlier than that. Look this, this is from January 2020 : kzbin.info/www/bejne/a4nOYoaJitqCoLc
@adned62814 жыл бұрын
@@goodplacetostop2973 Wow, you do know your good places to stop. Guess my assumption about good place to stop continuity was not justified.
@goodplacetostop29734 жыл бұрын
Adned Actually I haven’t found the original good to place... yet. There’s A LOT of videos to go through lol
@juanfa982 жыл бұрын
at 6:22 in your scratch work, aren't you proving that sqrt(x) is a Lipschitz function? and all Lipschitz functions are uniformly continuos
@SalomonChing3 жыл бұрын
This is the information I was looking for, I had many doubts, thank you very much my friend.✨👍
@yazhineet.s37744 жыл бұрын
Great problem sir, waiting for more of your physics videos.
@greyforget691611 ай бұрын
Thank you so so so much!
@1tryhxrd.56710 ай бұрын
But sir what if we choose x in 0,1 and y in 1,+infinity how would your result hold in this case
@uniqueideas33143 жыл бұрын
Is step function is uniformly continuous
@josephhajj15704 жыл бұрын
What about f(x)=1/x
@rogerlie41764 жыл бұрын
Set y = x + ẟ/2 and see what happens with |f(x) - f(y)| when x -> 0⁺.
@leonardoavila8994 жыл бұрын
Creo que Mr.Penn debe ser más ordenado y escribir un poco más grandes las letras.
@zeravam4 жыл бұрын
Michael escribe muy bien y claro, pon la pantalla completa para ver las letras más grandes
@chessematics4 жыл бұрын
Sir I'm an 8th grader and having problems while factoring cubics and quartics, could you kindly help me
@ancientwisdom79934 жыл бұрын
When a prof is teaching university curriculum, it is not a proper place to ask for help for middle school stuff. There are literally hundreds of middle school math channels out there. If u want to badly ask questions to Michael, pose specific hard factorization problems on his vids where he posts competition math - have a basic sense of propriety.
@chessematics4 жыл бұрын
@@ancientwisdom7993 i am glad to see that you have the BASIC SENSE OF PROPRIETY, but if sir agrees then I don't think that your BASIC SENSE OF PROPRIETY will be of great worth
@backyard2822 жыл бұрын
All of this complicated equations and dividing into those two cases is unnecessary. Just use delta = epsilon^2 and you're basically immediately done.
@JB-ym4up4 жыл бұрын
KZbin unsubscribed me. Go figure.
@get21134 жыл бұрын
Consider going directly to absolute continuity, so a function can be recovered by integrating its derivative. Key for calculus.