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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.
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} .
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 "−".
Negation: the symbol appeared in Heyting in 1930 [2] [3] (compare to Frege's symbol ⫟ in his Begriffsschrift [4]); the symbol appeared in Russell in 1908; [5] 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 Boolean logic, logical NOR, [1] non-disjunction, or joint denial [1] is a truth-functional operator which produces a result that is the negation of logical or.That is, a sentence of the form (p NOR q) is true precisely when neither p nor q is true—i.e. when both p and q are false.
The corresponding logical symbols are "", "", [6] and , [10] and sometimes "iff".These are usually treated as equivalent. However, some texts of mathematical logic (particularly those on first-order logic, rather than propositional logic) make a distinction between these, in which the first, ↔, is used as a symbol in logic formulas, while ⇔ is used in reasoning about those logic formulas ...
In most logical systems, negation, material conditional and false are related as: ¬ p ⇔ (p → ⊥). In fact, this is the definition of negation in some systems, [8] such as intuitionistic logic, and can be proven in propositional calculi where negation is a fundamental connective.