I was reading the Wikipedia article on equivalence relations and one section says that "the empty relation R on a non-empty set X is vacuosly symmetric and transitive but not reflexive."
What is the empty relation? And what is vacuosly symmetric?
Thank you very much.
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$\begingroup$A relation on a set $A$ is by definition a subset $R\subseteq A\times A$. Then "$a$ is related to $b$" means "$(a,b)\in R$. The empty relation is then just the empty set, so that "$a$ is related to $b$ is always false.
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