In hyperbolic space, parallel lines do not behave in the same way as they do in Euclidean space. In fact, in hyperbolic geometry, there are no parallel lines that never meet. Instead, any two distinct lines in hyperbolic space will eventually intersect, no matter how far apart they initially appear to be. This phenomenon is due to the non-Euclidean curvature of hyperbolic space, which causes lines to curve and diverge in a way that is different from the behavior of lines in Euclidean space. Therefore, if two lines in hyperbolic space are defined as parallel, they will eventually intersect, unlike in Euclidean space where parallel lines never intersect.
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