Love your videos. I wish the YT Algorithm had introduced you earlier.

Thanks for doing all kinds of tutorials! Even ones that might be not as popular! Very appreciated 🙏❤️

In fact |√x-√y|≤√|x-y| for all non-negative x and y. So it's uniformly continuous.

Excellent lesson!

On the open set of ordinal integers between zeroth and second.

This is the information I was looking for, I had many doubts, thank you very much my friend.✨👍

Your videos helps me a lot to read U.A by Stephen Abott, thanks you so much

Great problem sir, waiting for more of your physics videos.

Thank you so so so much!

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

But sir what if we choose x in 0,1 and y in 1,+infinity how would your result hold in this case

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).

@watchaccount

3 жыл бұрын

what if epsilon = 1000000 and delta1 = delta2 = 10?

@jonathanjacobson7012

3 жыл бұрын

Daniel, what would you do with x=1.5

@charlottedarroch

3 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.

14:15

@bsuperbrain

3 жыл бұрын

Nope, the 'stop' was cut off. :D

@adned6281

3 жыл бұрын

The first good place to stop: kzread.info/dash/bejne/eJyVqMewe9zWXbQ.html

@goodplacetostop2973

3 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 : kzread.info/dash/bejne/Z4yfk7WMhdi1mrg.html

@adned6281

3 жыл бұрын

@@goodplacetostop2973 Wow, you do know your good places to stop. Guess my assumption about good place to stop continuity was not justified.

@goodplacetostop2973

3 жыл бұрын

Adned Actually I haven’t found the original good to place... yet. There’s A LOT of videos to go through lol

Is step function is uniformly continuous

What about f(x)=1/x

@rogerlie4176

3 жыл бұрын

Set y = x + ẟ/2 and see what happens with |f(x) - f(y)| when x -> 0⁺.

Creo que Mr.Penn debe ser más ordenado y escribir un poco más grandes las letras.

@zeravam

3 жыл бұрын

Michael escribe muy bien y claro, pon la pantalla completa para ver las letras más grandes

Sir I'm an 8th grader and having problems while factoring cubics and quartics, could you kindly help me

@ancientwisdom7993

3 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.

@chessematics

3 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

Consider going directly to absolute continuity, so a function can be recovered by integrating its derivative. Key for calculus.

@pierineri

3 жыл бұрын

Very bad

All of this complicated equations and dividing into those two cases is unnecessary. Just use delta = epsilon^2 and you're basically immediately done.

KZread unsubscribed me. Go figure.