literally i was crying a few minutes ago because i couldn't do my analysis exercise sheet. You are the best teacher on youtube thank you so much, may god bless you have a beautiful day
@TheMathSorcerer3 жыл бұрын
Thank you!!
@keshavchaturvedi40153 жыл бұрын
U climbed the tower?
@tho_norlha3 жыл бұрын
@@keshavchaturvedi4015 still climbing but I know I can have everything at the top
@keshavchaturvedi40153 жыл бұрын
@@tho_norlha all the best climb it
@comuniunecuosho-campulbudi7611 Жыл бұрын
also check out John Gabriel's New Calculus
@ethanekat4 жыл бұрын
I read about this all over the internet for an hour and you clear it up in 10 minutes--thanks!
@TheMathSorcerer4 жыл бұрын
You are welcome!
@zachedwards5911Ай бұрын
I love that this video gives an intuitive explanation of the difference. Of course having the difference explained using the definition is important since it’s important to know that in uniform continuity, delta does not depend on the point and only depends on epsilon. However, this difference on the surface may seem unintuitive and unimportant. However, the rectangle demonstration perfectly encapsulates the intuitive idea behind why we care about uniformly continuous functions. For general continuous functions, there exists a rectangle that encloses the value of the function over some delta interval of x values, but the height of that box (and thus the area of the box) may depend on the specific point of the function that we are looking at. A given delta interval of x values does not always correspond to the same epsilon interval of function values due to the influence of the point itself. Uniformly continuous functions for a given delta interval for x have the same rectangle at every point of the function. The height of the rectangle, the epsilon interval for the image of the function, only depends on the given delta value. Hence the name uniform continuity.
@Nofxthepirate3 жыл бұрын
I just finished my (intro to) Real Analysis course for my Applied Math major, and uniform continuity was the last topic in the class. Thanks for helping me get an A!
@anthonykim527125 күн бұрын
this was the most intuitive explanation ever thank you so much for this
@simphiweyawa3970 Жыл бұрын
Thank you brother. I just realised i passed through Real analysis without intuitively understanding this. Sometimes we can just continually talk about the definition without intuitively understanding it. This intuition is the best. Continue the good work.
@katerinagk26813 жыл бұрын
Thank you so much!! I'm studing real analysis this semester and it all seems so theoritical, it's hard to draw a picture like that. Your videos really help with understanding the material, thanks again.
@kagayakuangel58284 жыл бұрын
You have a true gift. Thank you so much!! Now I just need to understand pointwise and uniform convergence!
@inesjesus45774 жыл бұрын
Hey there! Still need help with that?
@iHadar5 жыл бұрын
This is a GREAT explanation! thank you
@user-jc9kj7wt6j2 жыл бұрын
The rectangle really helps me to understand the concept. Thank you so much.
@johnlama78263 ай бұрын
best analysis teacher!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
@wanghaoyu8745 жыл бұрын
Good explanation!
@TheMathSorcerer5 жыл бұрын
Thank you!
@kaifalcone80253 жыл бұрын
I have spent the entire semester trying to figure this out. Thank goodness I found this video, thank you!!
@jasonthomas2908 Жыл бұрын
WOOOT, maths made clear, love it thanks
@muhitthemagician76512 жыл бұрын
Man! You're a lifesaver
@sharonnuri2 жыл бұрын
I am studying real analysis and this helped a lot to visualize uniform continious functions, Thank you sir.
@ydg_me2 жыл бұрын
Thank you very much, It was very helpful :)
@umarmuzzamil8559 Жыл бұрын
best explanation ever....thank you
@CheesyBread4 жыл бұрын
Pretty good video, but it seems like you call f(x) values “y values” which can be confusing given the definition. The definition states that both x and y lie in the domain of f. What that means for the definition is that you can think of x and y as 2 different “x values” (by x values I mean domain values, as in they are defined by their position on the x axis). For uniform continuity, we see that the difference between 2 points is arbitrarily small (less than delta) and thus the difference between f(x) and f(y) is also small (less than epsilon). By small, I mean small enough to satisfy the definition of uniform continuity. The rectangle visualization is still correct though. When an f value (escapes) the rectangle, that would mean that abs(f(x)-f(y)) is no longer less than epsilon and is therefore not uniformly continuous at the point (y,f(y)). I hope what I said can help anyone who might’ve been confused by that. If it was just me who was confused than oh well.
@TheMathSorcerer4 жыл бұрын
Hey good point and thanks for your comment. 😄
@CheesyBread4 жыл бұрын
The Math Sorcerer yeah man I was mostly just putting my thoughts here so I could better understand what’s going on. Appreciate the instant feedback to my comment as well that’s nice. Keep up the good work!
@TheMathSorcerer4 жыл бұрын
@@CheesyBread yup icould tell it's good to do that. I do the same thing sometimes writing down your thought process helps clarify stuff.
@TheMathSorcerer4 жыл бұрын
@@CheesyBread and thanks man😄
@randomprodigius9144 жыл бұрын
Really thank you I was confused on that to
@DankanXP3113 жыл бұрын
Wish my teacher had explained it this way, thank you very much!
@TheMathSorcerer3 жыл бұрын
You are welcome ❤️
@math61744 жыл бұрын
Now I got why the name uniform refer to. Big thanks, professor.
@TheMathSorcerer4 жыл бұрын
You are welcome!
@periclesstamatis75492 жыл бұрын
Thank you for this! Very helpful video!
@acdude5266 Жыл бұрын
Nice explanation. Very clear.
@TheMathSorcerer Жыл бұрын
Thank you!!!!
@official_minyoung5 ай бұрын
Best explanation ever
@Dusk4252 жыл бұрын
Thanks for this video. I found it really helpful. I completed my masters this year. But I still get confused between uniform continuity and continuity😭😭. Finally the confusion is gone. Thanks a lot.
@richardstone50962 жыл бұрын
Such a good way of explaining these concepts, thank you
@johnchan43712 жыл бұрын
I think a better way to understand Uniform Continuity (not sure if it's accurate) is that if a function is uniformly continuous on the real set of numbers, then the function is continuous and the slope of the tangent line of every point of the function is within a finite range.
@youngthug31243 жыл бұрын
yo man that's awesome have a great day
@Corellispinto3 жыл бұрын
Thank you for this. It was very helpful. I needed @Cheesy Bread’s explanation about the f(y) to fully understand what you were saying.
@charuniehansika11004 жыл бұрын
Awesome explanation .....Thank you very much!! :D
@TheMathSorcerer4 жыл бұрын
Np!
@kewalmohapatra44162 жыл бұрын
Love the idea of the rectangle!!
@PrajeeshMath2 жыл бұрын
That was a nice explanation
@TheMathSorcerer2 жыл бұрын
Thank you!
@Sofialovesmath2 жыл бұрын
What a fantastic video, can't thank you enough, cleared all my doubts!
@viveakkatochG3 жыл бұрын
You're a lifesaver!!!!! 👍🕺
@kxsteve20615 жыл бұрын
Great job man appreciate it
@-a56243 жыл бұрын
So helpful thank you!!
@independentmath2 жыл бұрын
Very helpful
@5180073a4 жыл бұрын
This is incredibly helpful !!! Thank you!!
@TheMathSorcerer4 жыл бұрын
Glad it was helpful!
@isaac58153 жыл бұрын
This is absolutely amazing!!
@TheMathSorcerer3 жыл бұрын
Thank you!!
@georgearapoglou28483 жыл бұрын
thank you !!!
@koratanadhanunjay92093 жыл бұрын
Awesome explaination 👍👍
@serracengiz86 Жыл бұрын
Thank you
@iagovieitez7738 Жыл бұрын
Amazing
@allanhenriques26943 жыл бұрын
so in one, delta is a function of epsilon, and in another, delta is a function of epsilon and the point
@aayala62203 жыл бұрын
amazing!!!
@sumittete28044 ай бұрын
Sir, If a function is uniformly continuous on a closed interval, could we refine the definition of uniform continuity by replacing the condition |x-y| < δ and |f(x) - f(y)| < ε with |x-y| ≤ δ implying |f(x) - f(y)| ≤ ε ?
@colaurier25945 жыл бұрын
Thank you !
@TheMathSorcerer5 жыл бұрын
np!
@sumittete28044 ай бұрын
Hello Sir...If a function is uniformly continuous on a closed interval, could we refine the definition of uniform continuity by replacing the condition |x-y| < δ and |f(x) - f(y)| < ε with |x-y| ≤ δ implying |f(x) - f(y)| ≤ ε ? Please sir, clarify it.
@S0M_DUBEY2 ай бұрын
Oh! now I understand,its all about that damn rectangle
@basmahina64143 жыл бұрын
Oh Thanks man!!
@ayeshaafzal27164 жыл бұрын
Very understandable 😍 But one point is making me confuse In the very last when u talk about rectangles ; in uniform continuity the size of rectangle should same at one place of graph when compared with continuity or at any point of graph size of rectangle should be same.?
@Maraq36911 ай бұрын
Does delta in non uniform definition depend on x also or just c and epsilon ?
@JhaaJii4 жыл бұрын
And................ the sorcerer does magic !
@TheMathSorcerer4 жыл бұрын
yes!!
@sadnesswoder32834 жыл бұрын
hi I have some comments: firstly, thanks for the video and explanation ;) second, you should work the voice for next videos some parts it's very low then goes up suddenly. the most important comment is about uniform continuity I didn't get the drawing of a rectangle what if it goes like a wave but not down. when can we decide whether it goes away from the rectangle or not? I like that you have explained analytically and geometrically !! thanks again
@tomislavvinkovic8272 жыл бұрын
Just a second... If it says for EVERY Epsilon, cant the epsilon change, hence the rectangle changes as well?
@bestofyoutube55903 жыл бұрын
Thanksss🔥❤️
@TheMathSorcerer3 жыл бұрын
You are welcome!
@suup4k754 жыл бұрын
In your example with the red function near the end of uniform continuity, why could we not change the rectange to be taller so that we capture all of f(x) and f(y)? If it the rectangle is tall enough for the "worst case", shouldn't it be tall enough for the whole function and then be uniform continuous?
@TheDetonadoBR4 жыл бұрын
read this math.stackexchange.com/questions/2283008/uniform-continuity-of-function
@randomprodigius9144 жыл бұрын
@@TheDetonadoBR thanks
@randomdude91354 жыл бұрын
Still don't understand the uniform continuity part :/ Guess I've got a low IQ. But I'll think about this visual intuition for some time and hopefully I get it
@adam-does4 жыл бұрын
Random Dude Natural language helps me: A function is continuous means... Choose any input value for the function. Whatever you like. And choose any distance epsilon. Then I can find you a distance delta such that just so long as I keep my input values within delta *of the input you chose* , I’ll keep the correponding outputs within epsilon. A function is uniformly continuous means... Choose any distance epsilon. Then I can find you a distance delta such that just so long as I keep *any pair* of input values within delta, I’ll keep the outputs within epsilon. Where does the difference emerge? In the case of continuity, depending on which input you choose, I might need to keep my other input values within *different* distances (some may need to be really small, I might be safe keeping some fairly large) to keep their outputs within epsilon. Whereas in the case of uniform continuity, no matter what input you choose, I can always find the *same* distance delta between other input values which keeps their outputs within epsilon.
@maximchowdhury96902 жыл бұрын
isnt it 'for all x in dom(f)" not "for all x in R"?
@ts.nathan7786 Жыл бұрын
Go through the video ( URL ) given below for best explanation for the difference between continous function and uniform continous function: kzbin.info/www/bejne/nonOgqR5d7GFppo
@ajsdoa62825 жыл бұрын
I don't see a difference in the definitions except for the order they're written. It says for continuous, it's dependent on c but in uniformly continuous it's dependent on y, but y and c are both just real numbers, you just changed the name of the variables, they're still just in R doesn't matter what you call them, so no difference there.
@Sudhanshux007x5 жыл бұрын
It's the order only that matters. Go to page 2 of this pdf www.math.wisc.edu/~robbin/521dir/cont.pdf
@IssamZeinoun4 жыл бұрын
I was confused with this as well... but then I noticed what he said: that Delta in the Uniform Continuity can only depend on Epsilon, not on x. The language used to define this is specific, as follows: Whereas the first definition mentions the existence of "c" before it mentions that Delta exists, the second definition does not mention X or Y before it mentions that Delta exists. It's a subtle difference in linguistics, but is intentional. It's the mathematicians way of saying that Delta can depend on "C" in the first definition but cannot depend on X or Y in the second.
@reenarai19274 жыл бұрын
In case of continuity delta depends on c so - that value is constant. While in case of uniform con.. delta depends only on epsilon so no matter what c is that's why that is choosed like a variable y, we can take any no. Of our choices In place of y.
@jonatangarcia92854 жыл бұрын
It's very different, in Continuity definition, the "c" is constant, that means that just "x" changes in |x - c| < d, in another terminology, it's a neighborhood with radius 'd' and center 'c' B_d(c), and if 'x' belongs to that neighborhood, then ocurrs that |f(x) - f(c)| < e. or in other terminology, f(x) belongs to B_e(f(c)). In Uniformly contininuity, we have that |x - y| < d, both changes, it can be any number whose distance is less than 'd'. In ths case, there are not center, not neighborhood, just distane between two numbers
@randomprodigius9144 жыл бұрын
@@Sudhanshux007x Thanks a lot
@independentmath2 жыл бұрын
I spent a long time to feel the difference between continuity and uniform continuity....