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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.
In Jan Łukasiewicz's prefix notation for logic, the operator is , short for Polish alternatywa (English: alternative). [ 4 ] In mathematics, the disjunction of an arbitrary number of elements a 1 , … , a n {\displaystyle a_{1},\ldots ,a_{n}} can be denoted as an iterated binary operation using a larger ⋁ (Unicode U+22C1 ⋁ N-ARY LOGICAL ...
The symbol used for exclusive disjunction varies from one field of application to the next, and even depends on the properties being emphasized in a given context of discussion. In addition to the abbreviation "XOR", any of the following symbols may also be seen: + was used by George Boole in 1847. [6]
The stroke is named after Henry Maurice Sheffer, who in 1913 published a paper in the Transactions of the American Mathematical Society [10] providing an axiomatization of Boolean algebras using the stroke, and proved its equivalence to a standard formulation thereof by Huntington employing the familiar operators of propositional logic (AND, OR, NOT).
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 ′.
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 high-level computer programming and digital electronics, logical conjunction is commonly represented by an infix operator, usually as a keyword such as "AND", an algebraic multiplication, or the ampersand symbol & (sometimes doubled as in &&). Many languages also provide short-circuit control structures corresponding to logical conjunction.
An alternative notation for this usage is to typeset the letters "def" above an ordinary equality sign, =. [14] Similarly, another alternative notation for this usage is to precede the equals sign with a colon, :=. The colon notation has the advantage that it reflects the inherent asymmetry in the definition of one object from already defined ...