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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 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 (⊥) *Falsum *List of logic symbols *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 objec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Up Tack
The up tack or falsum (⊥, \bot in LaTeX, U+22A5 in Unicode) is a constant symbol used to represent: * The truth value 'false', or a logical constant denoting a proposition in logic that is always false (often called "falsum" or "absurdum"). * 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 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 (the word "tee" in reverse). Tee plays a complementary or dual role in many of these theories. The similar-looking perpendicular symbol (⟂, \perp in LaTeX, U+27C2 in Unicode) is a binary relation symbol used to represent: * Perpendicularity of lines in geometry * Ortho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Falsum
The up tack or falsum (⊥, \bot in LaTeX, U+22A5 in Unicode) is a constant symbol used to represent: * The truth value 'false', or a logical constant denoting a proposition in logic that is always false (often called "falsum" or "absurdum"). * 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 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 (the word "tee" in reverse). Tee plays a complementary or dual role in many of these theories. The similar-looking perpendicular symbol (⟂, \perp in LaTeX, U+27C2 in Unicode) is a binary relation symbol used to represent: * Perpendicularity of lines in geometry * O ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Up Tack
The up tack or falsum (⊥, \bot in LaTeX, U+22A5 in Unicode) is a constant symbol used to represent: * The truth value 'false', or a logical constant denoting a proposition in logic that is always false (often called "falsum" or "absurdum"). * 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 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 (the word "tee" in reverse). Tee plays a complementary or dual role in many of these theories. The similar-looking perpendicular symbol (⟂, \perp in LaTeX, U+27C2 in Unicode) is a binary relation symbol used to represent: * Perpendicularity of lines in geometry * Ortho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
LaTeX
Latex is an emulsion (stable dispersion) of polymer microparticles in water. Latexes are found in nature, but synthetic latexes are common as well. In nature, latex is found as a milky fluid found in 10% of all flowering plants (angiosperms). It is a complex emulsion that coagulates on exposure to air, consisting of proteins, alkaloids, starches, sugars, oils, tannins, resins, and gums. It is usually exuded after tissue injury. In most plants, latex is white, but some have yellow, orange, or scarlet latex. Since the 17th century, latex has been used as a term for the fluid substance in plants, deriving from the Latin word for "liquid". It serves mainly as defense against herbivorous insects. Latex is not to be confused with plant sap; it is a distinct substance, separately produced, and with different functions. The word latex is also used to refer to natural latex rubber, particularly non-vulcanized rubber. Such is the case in products like latex gloves, latex condoms ... [...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 and rarely used logical symbols These symbols are sorted by their Unicode value: Usage in various countries Poland and Germany in Poland, the universal quantifier is sometimes written ∧, and the existential quantifier as ∨. The same applies for Germany. Japan The ⇒ symbol is often used in text to mean "result" or "conclusion", as in "We examined whether to sell the product ⇒ We will not sell it". Also, the → symbol is often used to denote "changed to", as in the sentence "The interest rate changed. March 20% → April 21%". See also * Józef ... [...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 if viewed from above. 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, acc ... [...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 ope ... References {{Mathematical symbols notation language Unicode blocks ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unicode
Unicode, formally The Unicode Standard,The formal version reference is is an information technology Technical standard, standard for the consistent character encoding, encoding, representation, and handling of Character (computing), text expressed in most of the world's writing systems. The standard, which is maintained by the Unicode Consortium, defines as of the current version (15.0) 149,186 characters covering 161 modern and historic script (Unicode), scripts, as well as symbols, emoji (including in colors), and non-visual control and formatting codes. Unicode's success at unifying character sets has led to its widespread and predominant use in the internationalization and localization of computer software. The standard has been implemented in many recent technologies, including modern operating systems, XML, and most modern programming languages. The Unicode character repertoire is synchronized with Universal Coded Character Set, ISO/IEC 10646, each being code-for-code id ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transpose
In linear algebra, the transpose of a 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. In the case of a logical matrix representing a binary relation R, the transpose corresponds to the converse relation RT. Transpose of a matrix Definition The transpose of a matrix , denoted by , , , A^, , , or , may be constructed by any one of the following methods: # 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, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
APL (programming Language)
APL (named after the book ''A Programming Language'') is a programming language developed in the 1960s by Kenneth E. Iverson. Its central datatype is the Array data type#Multi-dimensional arrays, multidimensional array. It uses a large range of APL syntax and symbols, special graphic symbols to represent most functions and operators, leading to very concise code. It has been an important influence on the development of concept modeling, spreadsheets, functional programming, and computer math packages. It has also inspired several other programming languages. History Mathematical notation A mathematical notation for manipulating arrays was developed by Kenneth E. Iverson, starting in 1957 at Harvard University. In 1960, he began work for IBM where he developed this notation with Adin Falkoff and published it in his book ''A Programming Language'' in 1962. The preface states its premise: This notation was used inside IBM for short research reports on computer systems, such as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mixed Radix
Mixed radix numeral systems are non-standard positional numeral systems in which the numerical radix, base varies from position to position. Such numerical representation applies when a quantity is expressed using a sequence of units that are each a multiple of the next smaller one, but not by the same factor. Such units are common for instance in measuring time; a time of 32 weeks, 5 days, 7 hours, 45 minutes, 15 seconds, and 500 milliseconds might be expressed as a number of minutes in mixed-radix notation as: ... 32, 5, 7, 45; 15, 500 ... ∞, 7, 24, 60; 60, 1000 or as :32∞577244560.15605001000 In the tabular format, the digits are written above their base, and a semicolon indicates the radix point. In numeral format, each digit has its associated base attached as a subscript, and the radix point is marked by a full stop, full stop or period. The base for each digit is the number of corresponding units that make up the next larger unit. As a consequence there is no b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Top Type
In mathematical logic and computer science, some type theories and type systems include a top type that is commonly denoted with top or the symbol ⊤. The top type is sometimes called also ''universal type'', or ''universal supertype'' as all other types in the type system of interest are subtypes of it, and in most cases, it contains every possible object of the type system. It is in contrast with the bottom type, or the ''universal subtype'', which every other type is supertype of and it is often that the type contains no members at all. Support in programming languages Several typed programming languages provide explicit support for the top type. In statically-typed languages, there are two different, often confused, concepts when discussing the top type. # A ''universal base class'' or other item at the top of a run time ''class hierarchy'' (often relevant in object-oriented programming) or ''type hierarchy''; it is often possible to create objects with this (run time) type, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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