Comment by articulatepang
9 days ago
You can think of it as returning an equivalence class if you like. Then it's single-valued.
More explicitly, it returns an equivalence class whose members are complex numbers that differ by integer multiples of 2*pi*i.
When it's important to distinguish members of the class, we speak of branches of the logarithm.
Also note the very cool and fun topology connection here. The keyword to search for is Riemann surface.
> You can think of it as returning an equivalence class if you like. Then it's single-valued.
I can, but I still have to be very mindful of how I use the "=" sign. Sometimes it's an (in)equality, sometimes it's... the equivalence class thing. The ambiguity doesn't seem very elegant.
> Also note the very cool and fun topology connection here. The keyword to search for is Riemann surface.
I'll check that out, thanks.