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β (other)
The symbol β, an upward pointing arrow, also called up arrow, uparrow, or upwards arrow, may refer to: Notation * β, a mathematical symbol for "undefined" * β, a mathematical symbol for " approaching from below" * β, a notation of Knuth's up-arrow notation for very large integers * β, a mathematical game theory position ''Up'' * β or Sheffer stroke, the logical connective "not both" or NAND * β, the APL function 'take' * "Increased" (and similar meanings), in medical notation * β, a chemical symbol for production of gas, which bubbles up. Character representations * β, upwards arrow, a Unicode arrow symbol * β, ↑, a HTML or XML character entity * β, codepoint 8A (hex) in EBCDIC Code page 293, used for writing APL * β, the glyph for character 94 (decimal) in ASCII until 1967, when it was replaced by the caret (^). See also * κ, an archaic Romanian Cyrillic letter * Arrow keys, on computer keyboards * Arrow (other) ** β (disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Undefined (mathematics)
In mathematics, the term undefined refers to a value, function, or other expression that cannot be assigned a meaning within a specific formal system. Attempting to assign or use an undefined value within a particular formal system, may produce contradictory or meaningless results within that system. In practice, mathematicians may use the term ''undefined'' to warn that a particular calculation or property can produce mathematically inconsistent results, and therefore, it should be avoided. Caution must be taken to avoid the use of such undefined values in a deduction or proof. Whether a particular function or value is undefined, depends on the rules of the formal system in which it is used. For example, the imaginary number \sqrt is undefined within the set of real numbers. So it is meaningless to reason about the value, solely within the discourse of real numbers. However, defining the imaginary number i to be equal to \sqrt, allows there to be a consistent set ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Limit (mathematics)
In mathematics, a limit is the value that a function (or sequence) approaches as the argument (or index) approaches some value. Limits of functions are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals. The concept of a limit of a sequence is further generalized to the concept of a limit of a topological net, and is closely related to limit and direct limit in category theory. The limit inferior and limit superior provide generalizations of the concept of a limit which are particularly relevant when the limit at a point may not exist. Notation In formulas, a limit of a function is usually written as : \lim_ f(x) = L, and is read as "the limit of of as approaches equals ". This means that the value of the function can be made arbitrarily close to , by choosing sufficiently close to . Alternatively, the fact that a function approaches the limit as approaches is sometimes denoted by a right arrow (β or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Knuth's Up-arrow Notation
In mathematics, Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976. In his 1947 paper, R. L. Goodstein introduced the specific sequence of operations that are now called ''hyperoperations''. Goodstein also suggested the Greek names tetration, pentation, etc., for the extended operations beyond exponentiation. The sequence starts with a unary operation (the successor function with ''n'' = 0), and continues with the binary operations of addition (''n'' = 1), multiplication (''n'' = 2), exponentiation (''n'' = 3), tetration (''n'' = 4), pentation (''n'' = 5), etc. Various notations have been used to represent hyperoperations. One such notation is H_n(a,b). Knuth's up-arrow notation \uparrow is another. For example: * the single arrow \uparrow represents exponentiation (iterated multiplication) 2 \uparrow 4 = H_3(2,4) = 2\times(2\times(2\times 2)) = 2^4 = 16 * the double arrow \uparrow\uparrow represents tetration (iterated ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Up (game Theory)
Combinatorial game theory is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information. Research in this field has primarily focused on two-player games in which a ''position'' evolves through alternating ''moves'', each governed by well-defined rules, with the aim of achieving a specific winning condition. Unlike economic game theory, combinatorial game theory generally avoids the study of games of chance or games involving imperfect information, preferring instead games in which the current state and the full set of available moves are always known to both players. However, as mathematical techniques develop, the scope of analyzable games expands, and the boundaries of the field continue to evolve. Authors typically define the term "game" at the outset of academic papers, with definitions tailored to the specific game under analysis rather than reflecting the fieldβs full scope. Combinatorial games include wel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sheffer Stroke
In Boolean functions and propositional calculus, the Sheffer stroke denotes a logical operation that is equivalent to the negation of the conjunction operation, expressed in ordinary language as "not both". It is also called non-conjunction, alternative denial (since it says in effect that at least one of its operands is false), or NAND ("not and"). In digital electronics, it corresponds to the NAND gate. It is named after Henry Maurice Sheffer and written as \mid or as \uparrow or as \overline or as Dpq in Polish notation by Εukasiewicz (but not as , , , often used to represent disjunction). Its dual is the NOR operator (also known as the Peirce arrow, Quine dagger or Webb operator). Like its dual, NAND can be used by itself, without any other logical operator, to constitute a logical formal system (making NAND functionally complete). This property makes the NAND gate crucial to modern digital electronics, including its use in computer processor design. Definition ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
APL Syntax And Symbols
The programming language APL is distinctive in being ''symbolic'' rather than ''lexical'': its primitives are denoted by ''symbols'', not words. These symbols were originally devised as a mathematical notation to describe algorithms. APL programmers often assign informal names when discussing functions and operators (for example, "product" for Γ/) but the core functions and operators provided by the language are denoted by non-textual symbols. Monadic and dyadic functions Most symbols denote ''functions'' or ''operators''. A ''monadic'' function takes as its argument the result of evaluating everything to its right. (Moderated in the usual way by parentheses.) A ''dyadic'' function has another argument, the first item of data on its left. Many symbols denote both monadic and dyadic functions, interpreted according to use. For example, β3.2 gives 3, the largest integer not above the argument, and 3β2 gives 2, the lower of the two arguments. Functions and operators APL uses ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Medical Abbreviations
Abbreviations are used very frequently in medicine. They boost efficiency as long as they are used intelligently. The advantages of brevity should be weighed against the possibilities of obfuscation (making the communication harder for others to understand) and ambiguity (having more than one possible interpretation). Certain medical abbreviations are avoided to prevent mistakes, according to best practices (and in some cases regulatory requirements); these are flagged in the list of abbreviations used in medical prescriptions. Orthographic styling Periods (stops) Periods (stops) are often used in styling abbreviations. Prevalent practice in medicine today is often to forgo them as unnecessary. * Example: ** ''Less common:'' The diagnosis was ''C.O.P.D.'' hronic obstructive pulmonary disease** ''More common:'' The diagnosis was ''COPD'' Plurals The prevalent way to represent plurals for medical acronyms and initialisms is simply to affix a lower ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arrow (symbol)
An arrow is a graphical symbol, such as β, β or β, or a pictogram, used to point or indicate direction. In its simplest form, an arrow is a triangle, chevron, or concave kite, usually affixed to a line segment or rectangle, and in more complex forms a representation of an actual arrow (e.g. β΅ U+27B5). The direction indicated by an arrow is the one along the length of the line or rectangle toward the single pointed end. History An older (medieval) convention is the manicule (pointing hand, β). Pedro Reinel in c. 1505 first used the fleur-de-lis as indicating north in a compass rose; the convention of marking the eastern direction with a cross is older (medieval). Use of the arrow symbol does not appear to pre-date the 18th century. An early arrow symbol is found in an illustration of Bernard Forest de BΓ©lidor's treatise ''L'architecture hydraulique'', printed in France in 1737. The arrow is here used to illustrate the direction of the flow of water and of the wa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of XML And HTML Character Entity References
In SGML, HTML and XML documents, the logical constructs known as ''character data'' and ''attribute values'' consist of sequences of characters, in which each character can manifest directly (representing itself), or can be represented by a series of characters called a ''character reference'', of which there are two types: a ''numeric character reference'' and a ''character entity reference''. This article lists the character entity references that are valid in HTML and XML documents. A character entity reference refers to the content of a named entity. An entity declaration is created in XML, SGML and HTML documents (before HTML5) by using the syntax in a document type definition (DTD). Character reference overview In HTML and XML, a ''numeric character reference'' refers to a character by its Universal Coded Character Set/Unicode ''code point'', and uses the format: &#x''hhhh''; or &#''nnnn''; where the x must be lowercase in XML documents, ''hhhh'' is the code po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Code Page 293
The programming language APL uses a number of symbols, rather than words from natural language, to identify operations, similarly to mathematical symbols. Prior to the wide adoption of Unicode, a number of special-purpose EBCDIC and non-EBCDIC code pages were used to represent the symbols required for writing APL. Character sets Due to its origins on IBM Selectric-based teleprinters, APL symbols have traditionally been represented on the wire using a unique, non-standard character set. In the 1960s and 1970s, few terminal devices existed which could reproduce them, the most popular ones being the IBM 2741 and IBM 1050 fitted with a specific APL print head. Over time, with the universal use of high-quality graphic display, printing devices and Unicode support, the APL character font problem has largely been eliminated. Character repertoire IBM assigns the following character IDs (GCGIDs) to APL syntax, which are used in the definitions of its code pages. EBCDIC code pages Cod ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Caret
Caret () is the name used familiarly for the character provided on most QWERTY keyboards by typing . The symbol has a variety of uses in programming and mathematics. The name "caret" arose from its visual similarity to the original proofreader's caret, , a mark used in proofreading to indicate where a punctuation mark, word, or phrase should be inserted into a document. The ASCII standard (X3.64.1977) calls it a "circumflex"; the Unicode standard calls it a "circumflex accent", although it is no longer practicable for that purpose. History Typewriters On typewriters designed for languages that routinely use diacritics (accent marks), there are two possible ways to type these: keys can be dedicated to precomposed characters (with the diacritic included); alternatively a dead key mechanism can be provided. With the latter, a mark is made when a dead key is typed but, unlike normal keys, the paper carriage does not move on and thus the next letter to be typed is printed under ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arrow Keys
Arrow keys or cursor movement keys are keys on a computer keyboard that are either programmed or designated to move the cursor (computers), cursor in a specified direction. The term "cursor movement key" is distinct from "arrow key" in that the former term may refer to any of various keys on a computer keyboard designated for cursor movement, whereas "arrow keys" generally refers to one of four specific keys, typically marked with arrows. Arrow keys are typically located at the bottom of the keyboard to the left side of the numeric keypad, usually arranged in an inverted-T layout but also found in diamond shapes and linear shapes. Arrow keys are commonly used for navigating around documents and for playing games. The inverted-T layout was popularized by the Digital Equipment Corporation LK201 keyboard from 1982. Historical development Before the computer mouse was widespread, arrow keys were the primary way of moving a cursor on screen. Mouse keys is a feature that allows c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
