Logical Relation
In synthetic, affine geometry the relation of two parallel lines is a fundamental concept that is modified from the usage in Euclidean geometry. It is clear that the relation of parallelism is a symmetric relation and a transitive relation. These are two properties of an equivalence relation. In Euclidean geometry a line is not considered to be parallel to itself, but in affine geometry it is convenient to hold a line as parallel to itself, thus yielding parallelism as an equivalence relation.
Read more about this topic: Parallel (geometry)
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