The Extended Complex Plane (Riemann Sphere)

[@shishirsanjeev4051]

Very clear and concise. Great job!

[@shayanrezaei-z2c]

thank you :) it was really helpful

[@DrMcCrady]

Glad it was helpful!

[@bantix9902]

This is so cool!!!! I love math

[@DrMcCrady]

Math is pretty great!

[@hora-azul]

I'm in high school, so this might be a dumb doubt because I know basically nothing about advanced math. I was discussing with a friend whether 0⁰ equals 1 or undefined. I said it can be undefined because lim(0ˣ) as x -> 0 from the left is undefined. He said this doesn't make sense because the left side of the graph of f(x) = 0ˣ doesn't exist. Then, I went on WolframAlpha and it said the limit from the left equals "complex infinity". I spent some time reading about it and about the Riemann Sphere, but I still don't get how I could apply the limit of 0ˣ to that, or how to fit 0ˣ in the equations shown in this video.

[@DrMcCrady]

I want to clarify we’re talking about limits here. The expression 0^0 is an “indeterminate form”. It can be different values, or undefined, or properly diverge. For example x^x as x->0 from the right is 1. But (e^(-x))^(1/x) as x->infty is 1/e. My point is that something of the form 0^0 need not evaluate to the same number each time. Hope that helps!