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In light of the modern definition of what is a coordinate system, namely it's a pair (U, f) with U a region of a m-dimensional manifold, and f a bijection from U to ##\mathbb R^m##, can we say that the polar coordinates on ##\mathbb R^2## are a coordinate system?
I was thinking about this and the answer sounds to be a no, because the polar coordinates are not everywhere bijective to the cartesian coordinates, which we know, is a coordinate system that spans ##\mathbb R^2##.
I was thinking about this and the answer sounds to be a no, because the polar coordinates are not everywhere bijective to the cartesian coordinates, which we know, is a coordinate system that spans ##\mathbb R^2##.