law of double negation

Noun

 * 1)  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 $$ \neg A = (-\infty,0) \cup (2,\infty) $$, $$ \neg \neg A = (0,2) $$, $$ \neg \neg A \to A = (-\infty,1) \cup (1,\infty) \ne \mathbb{R} $$.