Please do not stop with these series, you helped me through LA and now in Analysis.. you are single handedly leading me toward my cs degree .. Thank you
So this is my informal paraphrase of the delta epsilon definition: "if the limit L exists at x = A, no matter how small epsilon is, there will exist a set of x values, which satisfies the condition |x - A| ≤ delta (where delta is a value we have to find but we know it exists) so that |f(x) - L| ≤ epsilon"....is that correct or close to correct?
Could you plz upload a video on the uniform and absolute continuity and their difference along with continuity? I am struggling to see any video on them. It will be helpful to many I believe
Hey guys! Greetings froms Colombia. I'm fan of your channel. I love all videos. Thanks a lot for this invaluable knowledge. I'll know what tools do you use to write and record the videos?
Sorry, my question is why it is the sequence be an element of I \{x_0} instead of just I? Why exclude the point x_0? I thought we want it x_0 to be in the domain of f.
Referring to the last example in Video 27: is there continuity for irrational numbers by using the epsilon-delta definition? I read in Sutherland (2009) that a function as such would be discontinuous at Q but continuous at R\Q. 🤔
I was referring to your last example in Video 27, in which you said the function (=0 if irrational, =1 if rational) is discontinuous everywhere. @@brightsideofmaths
Thanks! But if you have the book Sutherland (2009), could you look at Exercise 4.16? It seems to suggest f is continuous on irrational, but discontinuous on rational. So I'm confused.@@brightsideofmaths
@@brightsideofmathswow thanks for the quick reply. So does that mean you can pick any decreasing convergent sequence with limit 0 for delta? Such as 2^-n?
@@brightsideofmaths ahh well let me be the first one haha. You sound like him in his early days. Are you swedish by any chance? Also, thank you so much for these videos. Really helping me out in my math for econ course :D
This guy might just single handedly carry me through real analysis
this guy is great! highest quality, math content. Keep up the amazing job!
Thank you :)
Please do not stop with these series, you helped me through LA and now in Analysis.. you are single handedly leading me toward my cs degree .. Thank you
I will never stop producing math videos :)
@fermisurface2616 Most of the universities in Europe. They don't have calculus here.
Ive looked through 10 videos now and yours is the first that properly visualizes what delta and epsilon mean. Thx man
Could not visualize when I read this theorem in my textbook. Thanks a lot for the clear explanation
finding you has made my homework grade go from D to A- no joke, thank you king
Happy to help :)
We used this not as a theorem, but rather as a definition of continuous function. Interesting.
So this is my informal paraphrase of the delta epsilon definition: "if the limit L exists at x = A, no matter how small epsilon is, there will exist a set of x values, which satisfies the condition |x - A| ≤ delta (where delta is a value we have to find but we know it exists) so that |f(x) - L| ≤ epsilon"....is that correct or close to correct?
Really great! Very interesting proof and short proof, wonderful 😍
Glad you liked it!
Could you plz upload a video on the uniform and absolute continuity and their difference along with continuity? I am struggling to see any video on them. It will be helpful to many I believe
Useful video. Keep it up.
Hey guys! Greetings froms Colombia. I'm fan of your channel. I love all videos. Thanks a lot for this invaluable knowledge. I'll know what tools do you use to write and record the videos?
Thank you very much! I use the nice free program Xournal :)
Why exclude x_0 with regards to the sequence ? Isn’t x_0 required to be in the domain of said function.
Maybe you can specify what you are referring to.
Sorry, my question is why it is the sequence be an element of I \{x_0} instead of just I? Why exclude the point x_0? I thought we want it x_0 to be in the domain of f.
@@jronirons5666 What is the timestamp of the question?
Usually the point x_0 is not the interesting one but what happens around it.
5:36
@@jronirons5666 How should x=x_0 satisfy the inequality with "greater or equal than epsilon" in the line above?
Referring to the last example in Video 27: is there continuity for irrational numbers by using the epsilon-delta definition? I read in Sutherland (2009) that a function as such would be discontinuous at Q but continuous at R\Q. 🤔
We have a continuity for all real numbers. So I don't understand your question completely.
I was referring to your last example in Video 27, in which you said the function (=0 if irrational, =1 if rational) is discontinuous everywhere. @@brightsideofmaths
Yes, it's discontinuous on rational numbers and on irrational numbers.@@demaskoh6921
Thanks! But if you have the book Sutherland (2009), could you look at Exercise 4.16? It seems to suggest f is continuous on irrational, but discontinuous on rational. So I'm confused.@@brightsideofmaths
As a function from R to R, the function cannot be continuous at irrational numbers but discontinuous at rational numbers.@@demaskoh6921
Why do you pick delta to be 1/n. That is not exhaustive of real > 0?
But for the proof it is sufficient :)
@@brightsideofmathswow thanks for the quick reply. So does that mean you can pick any decreasing convergent sequence with limit 0 for delta? Such as 2^-n?
@@lwuquh6732 For every epsilon how have to find a delta. If 2^{-n} works, then you can use it :)
why can't my math teacher be this good
Thanks :D
has anyone ever told you, you sound an awful lot like PewDiePie?
No, no one ever told me that :D
@@brightsideofmaths ahh well let me be the first one haha. You sound like him in his early days. Are you swedish by any chance? Also, thank you so much for these videos. Really helping me out in my math for econ course :D
6/10 good video
Why such a low score?