English
law of double negation
Noun

law of double negation

1. (logic) The statement that the negation of the negation of A implies A, for any proposition A. Stated symbolically: \neg \neg A \to A .
The law of double negation is not valid intuitionistically. To show this with Heyting algebra semantics, let A = (0,1) \cup (1,2) . Then \neg A = (-\infty,0) \cup (2,\infty) , \neg \neg A = (0,2) ,   \neg \neg A \to A = (-\infty,1) \cup (1,\infty) \ne \mathbb{R} .

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