Projective Space Equation

An interesting equation with surprising consequences in projective space. Find all the functions f such that f(cx) = c f(x), where we can just pull the constant out.

Breaking the product: https://youtu.be/lqO3D5Kttjc
Multiplicative identity: https://youtu.be/Gjr7u2NI2_k
Cauchy's functional identity: https://youtu.be/WnglFnfjjFs
Another fun identity: https://youtu.be/s6jF5jPl_Z4

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Видео Projective Space Equation канала Dr Peyam