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Some of them but not all.

For example, uniqueness.

The rectangular coordinates (x, y) represent a different point if either x or y is changed. This is also true for polar coordinate (r, a) but only if r > 0. For r = 0 the coordinates represent the same point, whatever a is. Thus (x, y) has a 1-to-1 mapping onto the plane but the polar coordinates don't.

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Q: Do rectangular coordinates have the same property as polar coordinates?
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