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Adding to what Anand Mehta said, the negation of that statement has two interpretations.

(i) there are zero lines through that point that are parallel to the given line (this is called Elliptic or Reimannian Geometry)

(ii) there is an infinite number of lines that pass through the point and parallel to a given line (this is called Hyperbolic or Lobachevskian Geometry)

I might add that the study of non-Euclidean Geometries are absolutely fascinating.

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9y ago

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