I'm trying to find the Mobius transformation of the intersection

>>7674993
No, you need to take the hyperbolic inverse Mellin transform, of the intersection, superimposing a supergeometric Riemann sum in dual (complete) Hilbert space, and then take the double reverse Fourier transform of the residue, and finally just dagger the result.

>>7675028
you don't know what you're talking about do you

>>7675653
Yeah because math majors are definitely the only ones who take a course in complex analysis.

>>7675663
>>7675653
2nd year uni undergrad, guess that corresponds to math major in amerifat speak?

>>7674993

It is not true in general that f(c1∩c2) = f(c1)∩f(c2)

For example suppose we have the set X = {1,2} the union of A = {1} and B = {2}
Define f(1) = f(2) = 0
Then f(X ∩ Y) = empty set
f(X) ∩ f(Y) = {0}

But [math]f^{-1}(X \cap Y) = f^{-1}(X) \cap f^{-1}(Y)[/math] and since Mobius transforms have inverses it is true for Mobius transforms.

>>7675665

Complex analysis appears not to be required for any major at MIT except for mathematics. (Applied complex analysis is 18.04, the version for pure math majors is 18.112) So yes, apparently complex analysis is nothing but autistic nonsense for silly mathfags according to amerifats.

>>7675907
this makes no sense

I don't see why you couldn't OP. Thinking about it geometrically as a stereographic projection, it seems obvious. Maybe I'm wrong, but I'll try to prove it from the definition.

>>7675653
>kilk

>>7675955

It is not true in general (for an arbitrary function f) that f(A∩B) = f(A)∩f(B).

It is true in general (for an arbitrary function f) that [math]f^{-1}(A \cap B) = f^{-1}(A) \cap f^{-1}(B)[/math].

Mobius transforms are in fact bijections from the Riemann sphere to itself. Since these maps are bijective, the latter statement implies that to find the image of the intersection of two disks you can take the intersection of the images of each disk.

>>7675965
oh shit I misread your post, this makes sense. I wasn't confused why you were giving an example of a function where that property didn't hold.

Your second statement is only true when f is bijective, right?

>>7675992
*was confused