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Within a system of classical logic, double negation, that is, the negation of the negation of a proposition , is logically equivalent to . Expressed in symbolic terms, ¬ ¬ P ≡ P {\displaystyle \neg \neg P\equiv P} .
The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, [ 1 ] and the LaTeX symbol.
A special case of unary negation occurs when it operates on a positive number, in which case the result is a negative number (as in −5). The ambiguity of the "−" symbol does not generally lead to ambiguity in arithmetical expressions, because the order of operations makes only one interpretation or the other possible for each "−".
The symbol is used to denote negation. For example, if P ( x ) is the predicate " x is greater than 0 and less than 1", then, for a domain of discourse X of all natural numbers, the existential quantification "There exists a natural number x which is greater than 0 and less than 1" can be symbolically stated as:
The closely related code point U+2262 ≢ NOT IDENTICAL TO (≢, ≢) is the same symbol with a slash through it, indicating the negation of its mathematical meaning. [ 1 ] In LaTeX mathematical formulas, the code \equiv produces the triple bar symbol and \not\equiv produces the negated triple bar symbol ≢ {\displaystyle \not ...
Negation: the symbol appeared in Heyting in 1930 [3] [4] (compare to Frege's symbol ⫟ in his Begriffsschrift [5]); the symbol appeared in Russell in 1908; [6] an alternative notation is to add a horizontal line on top of the formula, as in ¯; another alternative notation is to use a prime symbol as in ′.
In mathematical logic, a literal is an atomic formula (also known as an atom or prime formula) or its negation. [1] [2] The definition mostly appears in proof theory (of classical logic), e.g. in conjunctive normal form and the method of resolution. Literals can be divided into two types: [2] A positive literal is just an atom (e.g., ).
In mathematics and physics, the phrase "change of sign" is associated with exchanging an object for its additive inverse (multiplication with −1, negation), an operation which is not restricted to real numbers. It applies among other objects to vectors, matrices, and complex numbers, which are not prescribed to be only either positive ...