Why are we justified in taking the limit delta --> 0? I understand the result flows nicely when we do, but are we indebted to the limit we took somehow? Thanks for your videos!
@@brightsideofmaths I mean in the sense of why is it useful to see what happens to this shape in the limit if we are trying to say something about the shape itself? I appreciate your response, I think I have a deeper misunderstanding I need to address before moving on!
With a zero delta, we cannot apply Cauchy's theorem as we have learnt in the former videos. I wanted to show a straightforward proof of this important fact :)
@@brightsideofmaths But why exactly we cannot use the version of the previous part? If delta is zero, we are still able to construct the polygon paths, right?
Great work! This helps one see beyond textbooks.
Glad you think so! :) And thank you for your support!
Man you are such a legend, as crystal clear as always!
Thanks! I appreciate that! :) And thanks for the support!
Can’t wait for Cauchy’s formula!
Superb understanding sir
The proof works exactly the same if g is holomorphic in a disk D-{z0} where z0 is not necessarily the center of the disk, am I right?
Amazing series, thank you!
Glad you enjoy it!
Thank you so much for having these series m(__)m I wouldn't otherwise have such a good master explain these concepts while trying to self study
Why are we justified in taking the limit delta --> 0? I understand the result flows nicely when we do, but are we indebted to the limit we took somehow? Thanks for your videos!
What do you mean by "justified" here? The limit exists and we can do the calculations. Do you prefer not taking the limit but doing it another way?
@@brightsideofmaths I mean in the sense of why is it useful to see what happens to this shape in the limit if we are trying to say something about the shape itself? I appreciate your response, I think I have a deeper misunderstanding I need to address before moving on!
@@skillick The delta was a helping variable from the beginning. So we want to get rid of it in the end.
@@brightsideofmaths Thank you!! That caused the penny to drop for me!
Why do we have to consider some non-zero delta and take the limit? Is not possible to choose directly delta equal to zero at the beginning?
With a zero delta, we cannot apply Cauchy's theorem as we have learnt in the former videos. I wanted to show a straightforward proof of this important fact :)
@@brightsideofmaths But why exactly we cannot use the version of the previous part? If delta is zero, we are still able to construct the polygon paths, right?
@@kayebennett7867 Yeah but the region is not the correct one then.
Whoa is this a face reveal
It's a least my face :D