law of double negation

Definitions

The statement that the negation of the negation of A implies A, for any proposition A. Stated symbolically: ¬¬A→A.

Examples

“The law of double⟳ negation is not valid intuitionistically. To show⟳ this with Heyting algebra semantics, let⟳ A#61;(0,1)#92;cup(1,2). Then #92;negA#61;(-#92;infty,0)#92;cup(2,#92;infty), #92;neg#92;negA#61;(0,2), #92;neg#92;negA#92;toA#61;(-#92;infty,1)#92;cup(1,#92;infty)#92;ne#92;mathbb#123;R#125;.”

CEFR level