In the present paper we argue that a symmetric picture of the relationships between equality and apartness can be attained by considering these notions on the background of bi-intuitionistic logic instead of the usual intuitionistic logic. In particular we show that, as the intuitionistic negation of a relation of apartness is an equality, the dualintuitionistic co-negation of an equality is a relation of apartness. At the same time, as the intuitionistic negation of equality is not an apartness, the co-intuitionistic negation of an apartness is not an equality.
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