Postulate 5
– a line contains at least 2 points- a plane contains at least 3 noncollinear points- Space contains 4 nonplanar points
Postulate 5, also known as the parallel postulate, states that if a straight line crossing two straight lines makes the interior angles on the same side less than two right angles, then the two straight lines, if produced indefinitely, will meet on that side where the angles are less than two right angles.
This postulate is one of the axioms of Euclidean geometry, which deals with the properties of flat space and is widely used in mathematics and physics. It essentially means that if two straight lines are parallel, they will never intersect, and if they are not parallel, they will eventually meet at some point.
The parallel postulate has been the subject of much debate and investigation in mathematics, as it is not immediately obvious whether or not it is necessary. In fact, many non-Euclidean geometries have been developed that do not obey this postulate, such as hyperbolic geometry and elliptic geometry.
Overall, the parallel postulate is an essential part of Euclidean geometry, but its validity and applicability in other contexts is a topic of ongoing research in the mathematical community.
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