Antisymmetry
A homogeneous binary relation $R$ is antisymmetric if and only if $(a, b) \in R$ and $a \ne b \implies (b, a) \notin R$, for all $(a, b) \in R.$
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Despite its name, this is not the negation of symmetry.
A homogeneous binary relation $R$ is antisymmetric if and only if $(a, b) \in R$ and $a \ne b \implies (b, a) \notin R$, for all $(a, b) \in R.$
Despite its name, this is not the negation of symmetry.