I believe your reasoning for why k must be an integer has a defect. You say Phi(phi+2pi)=Phi(phi). All well and good; Phi is periodic. But When you consider Phi(kphi), kphi as a whole is the argument, and for Phi(kphi) to be periodic, all that is required is Phi(kphi+2pi), not Phi(kphi+2kpi). Of course, Phi(kphi+2kpi)=Phi(kphi) if k is an integer, but k is not REQUIRED to be an integer for Phi(kphi) to be periodic, since again, all that is required is for Phi(kphi+2pi)=Phi(kphi), in which case k can take on any value at all.
Thankyou Greg!
thanks man u rlly saved my life hope that ferrari is treating you well
I believe your reasoning for why k must be an integer has a defect. You say Phi(phi+2pi)=Phi(phi). All well and good; Phi is periodic. But When you consider Phi(kphi), kphi as a whole is the argument, and for Phi(kphi) to be periodic, all that is required is Phi(kphi+2pi), not Phi(kphi+2kpi). Of course, Phi(kphi+2kpi)=Phi(kphi) if k is an integer, but k is not REQUIRED to be an integer for Phi(kphi) to be periodic, since again, all that is required is for Phi(kphi+2pi)=Phi(kphi), in which case k can take on any value at all.
It's not three point twenty four... it's three point two four