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Verum
The tee (⊤, \top in LaTeX), also called down tack (as opposed to the up tack) or verum, is a symbol used to represent: * The top element in lattice theory. * The truth value of being true in logic, or a sentence (e.g., formula in propositional calculus) which is unconditionally true. By definition, every tautology is logically equivalent to the verum. * The top type in type theory. * Mixed radix encoding in the APL programming language. * A lowered phonic in the International Phonetic Alphabet and phonetics. In this usage, it is usually written under the primary IPA symbol. A similar-looking superscript T may be used to mean the transpose of a matrix. Encoding In Unicode, the tee character is encoded as . The symbol is encoded in LaTeX as \top. A large variant is encoded as in the Unicode block Miscellaneous Mathematical Symbols-A. See also * Turnstile (⊢) * Up tack (⊥) *List of logic symbols In logic, a set of symbols is commonly used to express logical repr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logic Symbols
In logic, a set of symbols is commonly used to express logical representation. 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, and the LaTeX symbol. Basic logic symbols Advanced or rarely used logical symbols The following symbols are either advanced and context-sensitive or very rarely used: See also * Glossary of logic * Józef Maria Bocheński * List of notation used in Principia Mathematica * List of mathematical symbols * Logic alphabet, a suggested set of logical symbols * * Logical connective * Mathematical operators and symbols in Unicode * Non-logical symbol * Polish notation * Truth function * Truth table * Wikipedia:WikiProject Logic/Standards for notation References Further reading * Józef Maria Bocheński (195 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Logic Symbols
In logic, a set of symbols is commonly used to express logical representation. 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, and the LaTeX symbol. Basic logic symbols Advanced or rarely used logical symbols The following symbols are either advanced and context-sensitive or very rarely used: See also * Glossary of logic * Józef Maria Bocheński * List of notation used in Principia Mathematica * List of mathematical symbols * Logic alphabet, a suggested set of logical symbols * * Logical connective * Mathematical operators and symbols in Unicode * Non-logical symbol * Polish notation * Truth function * Truth table * Wikipedia:WikiProject Logic/Standards for notation References Further reading * Józef Maria Bocheński ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truth Value
In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values ('' true'' or '' false''). Truth values are used in computing as well as various types of logic. Computing In some programming languages, any expression can be evaluated in a context that expects a Boolean data type. Typically (though this varies by programming language) expressions like the number zero, the empty string, empty lists, and null are treated as false, and strings with content (like "abc"), other numbers, and objects evaluate to true. Sometimes these classes of expressions are called falsy and truthy. For example, in Lisp, nil, the empty list, is treated as false, and all other values are treated as true. In C, the number 0 or 0.0 is false, and all other values are treated as true. In JavaScript, the empty string (""), null, undefined, NaN, +0, −0 and false are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Raising (sound Change)
In phonology and phonetics, raising is a sound change in which a vowel or consonant becomes higher or raised, meaning that the tongue becomes more elevated or positioned closer to the roof of the mouth than before. The opposite effect is known as lowering. Raising or lowering may be triggered by a nearby sound, when it is a form of assimilation, or it may occur on its own. In i-mutation, a front vowel is raised before or , which is assimilation. In the Attic dialect of Ancient Greek and in Koine Greek, close-mid were raised to . The change occurred in all cases and was not triggered by a nearby front consonant or vowel. Later, Ancient Greek was raised to become Koine Greek and then . For more information, see In Czech, the alveolar trill The voiced alveolar trill is a type of consonantal sound used in some spoken languages. The symbol in the International Phonetic Alphabet that represents dental consonant, dental, alveolar consonant, alveolar, and postalveolar co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Mathematical Symbols
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula or a mathematical expression. More formally, a ''mathematical symbol'' is any grapheme used in mathematical formulas and expressions. As formulas and expressions are entirely constituted with symbols of various types, many symbols are needed for expressing all mathematics. The most basic symbols are the decimal digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), and the letters of the Latin alphabet. The decimal digits are used for representing numbers through the Hindu–Arabic numeral system. Historically, upper-case letters were used for representing points in geometry, and lower-case letters were used for variables and constants. Letters are used for representing many other types of mathematical object. As the number of these types has increased, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Up Tack
"Up tack" is the Unicode name for a symbol (⊥, \bot in LaTeX, U+22A5 in Unicode) that is also called "bottom", "falsum", "absurdum", or "the absurdity symbol", depending on context. It is used to represent: * The truth value 'false', or a logical constant denoting a proposition in logic that is always false. (The names "falsum", "absurdum" and "absurdity symbol" come from this context.) * The bottom element in wheel theory and lattice theory, which also represents absurdum when used for logical semantics * The bottom type in type theory, which is the bottom element in the subtype relation. This may coincide with the empty type, which represents absurdum under the Curry–Howard correspondence * The "undefined value" in quantum physics interpretations that reject counterfactual definiteness, as in (r0,⊥) as well as * Mixed radix decoding in the APL programming language The glyph of the up tack appears as an upside-down tee symbol, and as such is sometimes called eet (t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turnstile (symbol)
In mathematical logic and computer science the symbol ⊢ (\vdash) has taken the name turnstile because of its resemblance to a typical turnstile. It is also referred to as tee and is often read as "yields", "proves", "satisfies" or "entails". Interpretations The turnstile represents a binary relation. It has several different interpretations in different contexts: * In epistemology, Per Martin-Löf (1996) analyzes the \vdash symbol thus: "... e combination of Frege's , judgement stroke and , content stroke �� came to be called the assertion sign." Frege's notation for a judgement of some content ::\vdash A :can then be read ::''I know is true''. :In the same vein, a conditional assertion ::P \vdash Q :can be read as: ::''From , I know that '' * In metalogic, the study of formal languages; the turnstile represents syntactic consequence (or "derivability"). This is to say, that it shows that one string can be derived from another in a single step, according to t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Miscellaneous Mathematical Symbols-A
Miscellaneous Mathematical Symbols-A is a Unicode block containing characters for mathematical, logical, and database notation. Character table Compact table History The following Unicode-related documents record the purpose and process of defining specific characters in the Miscellaneous Mathematical Symbols-A block: See also * Mathematical operators and symbols in Unicode The Unicode Standard encodes almost all standard characters used in mathematics. Unicode Technical Report #25 provides comprehensive information about the character repertoire, their properties, and guidelines for implementation. Mathematical op ... References {{Mathematical symbols notation language Unicode blocks ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unicode
Unicode or ''The Unicode Standard'' or TUS is a character encoding standard maintained by the Unicode Consortium designed to support the use of text in all of the world's writing systems that can be digitized. Version 16.0 defines 154,998 Character (computing), characters and 168 script (Unicode), scripts used in various ordinary, literary, academic, and technical contexts. Unicode has largely supplanted the previous environment of a myriad of incompatible character sets used within different locales and on different computer architectures. The entire repertoire of these sets, plus many additional characters, were merged into the single Unicode set. Unicode is used to encode the vast majority of text on the Internet, including most web pages, and relevant Unicode support has become a common consideration in contemporary software development. Unicode is ultimately capable of encoding more than 1.1 million characters. The Unicode character repertoire is synchronized with Univers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transpose
In linear algebra, the transpose of a Matrix (mathematics), matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of the matrix by producing another matrix, often denoted by (among other notations). The transpose of a matrix was introduced in 1858 by the British mathematician Arthur Cayley. Transpose of a matrix Definition The transpose of a matrix , denoted by , , , A^, , , or , may be constructed by any one of the following methods: #Reflection (mathematics), Reflect over its main diagonal (which runs from top-left to bottom-right) to obtain #Write the rows of as the columns of #Write the columns of as the rows of Formally, the -th row, -th column element of is the -th row, -th column element of : :\left[\mathbf^\operatorname\right]_ = \left[\mathbf\right]_. If is an matrix, then is an matrix. In the case of square matrices, may also denote the th power of the matrix . For avoiding a possibl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phonetics
Phonetics is a branch of linguistics that studies how humans produce and perceive sounds or, in the case of sign languages, the equivalent aspects of sign. Linguists who specialize in studying the physical properties of speech are phoneticians. The field of phonetics is traditionally divided into three sub-disciplines on questions involved such as how humans plan and execute movements to produce speech (articulatory phonetics), how various movements affect the properties of the resulting sound (acoustic phonetics) or how humans convert sound waves to linguistic information (auditory phonetics). Traditionally, the minimal linguistic unit of phonetics is the phone (phonetics), phone—a speech sound in a language which differs from the phonological unit of phoneme; the phoneme is an abstract categorization of phones and it is also defined as the smallest unit that discerns meaning between sounds in any given language. Phonetics deals with two aspects of human speech: production ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Phonetic Alphabet
The International Phonetic Alphabet (IPA) is an alphabetic system of phonetic notation based primarily on the Latin script. It was devised by the International Phonetic Association in the late 19th century as a standard written representation for the sounds of speech. The IPA is used by linguists, lexicography, lexicographers, foreign language students and teachers, speech–language pathology, speech–language pathologists, singers, actors, constructed language creators, and translators. The IPA is designed to represent those qualities of speech that are part of lexical item, lexical (and, to a limited extent, prosodic) sounds in oral language: phone (phonetics), phones, Intonation (linguistics), intonation and the separation of syllables. To represent additional qualities of speechsuch as tooth wikt:gnash, gnashing, lisping, and sounds made with a cleft lip and cleft palate, cleft palatean extensions to the International Phonetic Alphabet, extended set of symbols may be used ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
