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?
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
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.
@@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
