How to define Continuous functions of a Complex Variable? #complexanalysis #maths #mathshorts #compl

本站添加: 2026-05-25

[00:00:00]What does it mean for a complex valued function of a complex variable to be continuous? Well, if we are talking about a point, then it means that at that point, for any [clears throat] epsilon that are greater than zero, we can choose a small delta such that a delta neighborhood will be mapped inside the epsilon neighborhood of the value of the function.

[00:00:22]And here you can see that >> [music] >> in the blue color in the bottom we have the delta neighborhood, and here the delta is changing.

[00:00:30]And in the top you can see the epsilon neighborhood. And I can choose the epsilon here.

[00:00:36]We can see that the mapped neighborhood becomes some wiggly shape. However, it is [music] inside the epsilon neighborhood.

[00:00:44]So, here our function, which is z squared, is indeed continuous.

[00:00:50]Here you can drag around the point, and you can also change the function.

[00:00:57]The link to this Desmos file will be in the description.