There are non-Euclidean geometries whose parallel postulates differ from the standard Euclidean parallel postulate in two ways,
i. Hyperbolic geometry is an example of a non- Euclidean geometry where given a line l and a point P not on the line, there is more than one line through P parallel to l.
ii. Elliptic geometry is a non-Euclidean geometry where given a line l and a point P not on the line, there are no lines through P parallel to l.
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