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text: 'An antisymmetric relation is a relation where no two distinct elements are related in both directions. In other words. $R$ is antisymmetric iff\n\n$(aRb ∧ bRa) → a = b$\n\nor, equivalently, $a ≠ b → (¬aRb ∨ ¬bRa)$\n\nAntisymmetry isn't quite the [set_theory_compliment compliment] of [symmetric_relation Symmetry]. Due to the fact that $aRa$ is allowed in an antisymmetric relation, the equivalence relation, $\\{(0,0), (1,1), (2,2)...\\}$ is both symmetric and antisymmetric.\n\nExamples of antisymmetric relations also include the successor relation, $\\{(0,1), (1,2), (2,3), (3,4)...\\}$, or this relation linking numbers to their prime factors $\\{...(9,3),(10,5),(10,2),(14,7),(14,2)...)\\}$\n\n',
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