# Definition of Negation: Transforming a Term into its Negative

0.15 Definition of NegationThe introduction of the terms 0 and 1 makes it possible for us to define _negation_. This is a “uni-nary” operation which transforms a single term into another term called its _negative_.25 The negative of $a$ is called not-$a$ and is written $a^{\prime}$.26 Its formal definition implies the following postulate of existence27:[In French] the same word _negation_ denotes both the operation and its result, which becomes equivocal. The result ought to be denoted by another word, like [the English] “negative”. Some authors say, “supplementary” or “supplement”, [_e.g._ Boole and Huntington on ], Classical logic makes use of the term “contradictory” especially for propositions.We adopt here the notation of MacColl; Schröder indicates not-$a$ by $a_{1}$ which prevents the use of indices and obliges us to express them as exponents. The notation $a^{\prime}$ has the advantage of excluding neither indices nor exponents. The notation $\bar{a}$ employed by many authors is inconvenient for typographical reasons. When the negative affects a proposition written in an explicit form (with a copula ) it is applied to the copula \(