# Contradiction, law of

From Encyclopedia of Mathematics

The logical law stating that no proposition can be true simultaneously with its negation. In the language of propositional calculus the law of contradiction is expressed by

$$\neg(A\mathbin\&\neg A)$$

This formula is derivable in classical as well as in intuitionistic constructive propositional calculus (cf. also Propositional calculus).

**How to Cite This Entry:**

Contradiction, law of.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Contradiction,_law_of&oldid=43574

This article was adapted from an original article by V.N. Grishin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article