In mathematics, defined and undefined are used to explain whether or not expressions have meaningful, sensible output. These are also known as "well-behaved" and respectively "ill-behaved". The following algebraic expressions are undefined: (see division by zero) 00 (however, it is often convenient to define the value of this expression to be 1, e.g. in combinatorics, in the context of power series, and in set theory) (however, in probability and measure theory ...

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The notion of definability treated in this article has been chosen primarily for definiteness, not on the grounds that it's more useful or interesting than other notions. Here we treat a few others: Definable number - Definability in other languages or structures. The language of arithmetic has symbols for 0, 1, the successor operation, addition, and multiplication, intended to be interpreted in the usual way over the natural numbers. Since no variables of this language range over the reals, we can ...

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Definable number, Definable number - General facts, Definable number - Notion does not exhaust unambiguously described numbers, Definable number - Other notions of definability, Definable number - Definability in other languages or structures, Definable number - Definability with ordinal parameters

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On the bus ride to school, Bart gives Milhouse one of a pair of Krusty walkie-talkies as a birthday present. Bart is crushed to discover that Milhouse had held a birthday party the previous Saturday, but he had not been invited. Milhouse seems unwilling to talk to Bart and avoids him for the rest of the day. Meanwhile, at the power plant, as Homer eats jelly donuts, one of them splatters onto a dial nearing the red zone. The plant is on the verge of a nuclear meltdown, and Homer seems to be the only person who can stop it. He has no s ...

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Homer Defined, Homer Defined - Synopsis, Homer Defined - Quotes

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The definable numbers form a field containing all the familiar real numbers such as 0, 1, π, e, et cetera. In particular, it contains all the numbers named in the mathematical constants article, and all algebraic numbers (and therefore all rational numbers). However, most real numbers are not definable: the set of all definable numbers is countably infinite (because the set of all logical formulas is) while the set of real numbers is uncountably infinite (see Cantor's diagonal argument). As a result, most real numbers have no description (in the same sense o ...

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Definable number, Definable number - General facts, Definable number - Notion does not exhaust unambiguously described numbers, Definable number - Other notions of definability, Definable number - Definability in other languages or structures, Definable number - Definability with ordinal parameters

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The list of statements determines a strong order among statements. Statements are labeled using the following conventions: s(i), where i is an integer in [1,n]; and n is the number of statements in the basic block Variables are identified in italic (e.g., v,u and t) Every variable is assumed to have a definition in the context or scope. (In static single assignment form, use-define chains are explicit because eac ...

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Use-define chain, Use-define chain - Purpose, Use-define chain - Setup, Use-define chain - Execution, Use-define chain - Method of building a use-def or ud chain

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The purpose of these data structures is to translate the physical representation of codes into a logical representation. The physical representation is "compressed" due to hardware limitations. The number of memory spaces, for instance, is limited, so a memory space (register, word in main memory, etc.) might take on multiple values over the course of its life. The physical location of the data is not interesting at to the compiler at this stage. However, the compiler needs to track the values, not the locations. Consequently, making ...

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Use-define chain, Use-define chain - Purpose, Use-define chain - Setup, Use-define chain - Execution, Use-define chain - Method of building a use-def or ud chain

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Ideal concept The ideal scheme would be to attach an analog to digital converter to an antenna. A computer would read the converter, and then software would transform the stream of data from the converter to any other form. An ideal transmitter would be similar. A computer program would generate a stream of numbers. These would be sent to a digital to analog converter connected to a radio ant ...

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Software-defined radio, Software-defined radio - How they work, Software-defined radio - History, Software-defined radio - SPEAKeasy phase I, Software-defined radio - SPEAKeasy phase II, Software-defined radio - Joint Tactical Radio System JTRS, Software-defined radio - Amateur software radios, Software-defined radio - Software Defined Radio & RFID Technology

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In his monumental dictionary, Samuel Johnson states that the original meaning of wit is "the powers of the mind; the mental faculties; the intellects"; he also defines wit as "quickness of fancy", among the nine definitions. In Webster's Dictionary, wit is subtly defined as "the association of ideas in a manner natural, but unusual and striking, so as to produce surprise joined with pleasure". The American television series The Simpsons defined wit, in a February 4, 1996 episode as "nothing more than an incisive observation, humorously phrased and ...

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Wit, Wit - Famous wits, Wit - Forms of wit, Wit - Wit defined, Wit - Wit in poetry, Wit - Further meanings, Wit - Trivia

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It is difficult to define understanding. If we use the term concept as above, the question then arises as to what is a concept? Is it an abstract thing? Is it a brain pattern or a rule? Whatever definition is proposed, we can still ask how it is that we understand the thing that is featured in the definition: we can never satisfactorily define a concept, still less use it to explain understanding. It is more convenient to use an operational or behavioural definition, we can say that somebody who reacts appropriately t ...

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Understanding, Understanding - Examples, Understanding - Is understanding definable?, Understanding - Another definition

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Like Java, Ajile provides a Package directive for defining namespaces. Using the Package directive is trivial as demonstrated by the following example: Package ("com.iskitz.ajile.examples"); com.iskitz.ajile.examples.PackageExample = function() { alert("This is the PackageExample!"); }; In the above example a com.iskitz.ajile.examples namespace is created and a PackageExample module is added to it. A reversed domain name is used as ...

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AJILE, AJILE - Defining A Namespace, AJILE - Importing from a Namespace, AJILE - Example

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Functions whose domains can be recursively defined can be given recursive definitions patterned after the recursive definition of their domain. The canonical example of a recursively defined function is the following definition of the factorial function f(n): f(0) = 1 f(n) = n * f(n − 1) for any natural number n > 0 Given this definition, also called a recurrence relation, we wo ...

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Recursion, Recursion - Recursion in mathematics, Recursion - Functional Recursion, Recursion - Recursive Proofs, Recursion - Recursion in computing, Recursion - Recursion in language, Recursion - Recurrence relations or algorithms, Recursion - Recursively defined sets, Recursion - Example: the natural numbers, Recursion - Example: The set of true reachable propositions, Recursion - Recursively defined functions, Recursion - Recursive algorithms, Recursion - The recursion theorem, Recursion - Proof of uniqueness, Recursion - Proof of existence, Recursion - Recursion in plain English, Recursion - Recursive humour

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Breakcore is a loosely defined electronic music style that brings together elements of jungle, hardcore techno and IDM into a breakbeat-oriented sound that encourages speed, complexity, impact and maximum sonic density. Similar to Punk or Jazz music; Breakcore does not adhere to a predefined set of stylistic 'rules', instead following a looser set of musical ideals. The very nature of breakcore is anti-establishment, often using production techniques or sounds to intentionally alienate the non-breakcore listener. Musically, breakcore is centered around the deconstruction and creative reassembly of common breakb ...

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Breakcore, Breakcore - Breakcore Defined, Breakcore - Breakcore History, Breakcore - Breakcore artists, Breakcore - Breakcore record labels, Breakcore - Related Links

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Definitions of art and aesthetic arguments usually proceed from one of several possible perspectives. Art may be defined by the intention of the artist as in the writings of Dewey. Art may be seen as being in the response/emotion of the viewer as Tolstoy claims. In Danto's view, it can be defined as a character of the item itself or as a function of an object's context. Art - Plato. For Plato, art is a pursuit whose adherents are not to be trusted; given that their productions imitate the sensory world (it ...

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Art, Art - Etymology, Art - Currently recognized forms of art, Art - Defining art, Art - General characteristics of art, Art - Skill, Art - Judgments of value, Art - Communicating emotion, Art - Creative impulse, Art - Differences in Defining Art, Art - Plato, Art - Aristotle, Art - Institutional definition, Art - Related Issues, Art - Social criticism, Art - The Issue of Utility, Art - History of Art, Art - Symbols

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Definitions of art and aesthetic arguments usually proceed from one of several possible perspectives. Art may be defined by the intention of the artist as in the writings of Dewey. Art may be seen as being in the response/emotion of the viewer as Tolstoy claims. In Danto's view, it can be defined as a character of the item itself or as a function of an object's context. Art - Plato. For Plato, art is a pursuit whose adherents are not to be trusted; given that their productions imitate the sensory world (it ...

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Art, Art - Etymology, Art - Art forms, Art - Defining art, Art - Characteristics of art, Art - Skill, Art - Judgments of value, Art - Communicating emotion, Art - Creative impulse, Art - Differences in defining art, Art - Plato, Art - Aristotle, Art - Institutional definition, Art - Related issues, Art - Social criticism, Art - Utility, Art - History of art, Art - Symbols

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While knowledge is a central part of daily life, the actual definition of knowledge is of great interest to philosophers, social scientists, and historians. Knowledge, according to most thinkers, must follow three defining criteria. It must be justified, true, and believed. Meeting these qualifications may be difficult or impossible. It is also common to weigh knowledge in how it can be applied or used. In this sense, knowledge consists of information augmented by intentionality (or direction). This model aligns with the DI ...

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Knowledge, Knowledge - Defining knowledge, Knowledge - Knowledge management, Knowledge - Situated knowledge, Knowledge - Sociology of knowledge, Knowledge - Other definitions

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Neurotheology defines spiritual experiences to include subjective reports of phenomena such as: The perception that time, fear or self-consciousness have dissolved Spiritual awe Oneness with the universe Ecstatic trance Sudden enlightenment Altered states of consciousness These subjective experiences are seen as the basis for many religious beliefs and behaviors. ...

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Neurotheology, Neurotheology - Terminology, Neurotheology - Defining and measuring spirituality, Neurotheology - Methdology, Neurotheology - Criticism, Neurotheology - Philosophical criticism, Neurotheology - Scientific criticism

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Recursion - Example: the natural numbers. The canonical example of a recursively defined set is given by the natural numbers: 0 is in N if n is in N, then n + 1 is in N The set of natural numbers is the smallest set satisfying the previous two properties. Here's an alternative recursive definition of N: 0, 1 are in N; if n and n + 1 are in N, then n + 2 is in N; N is the small ...

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Recursion, Recursion - Recursion in mathematics, Recursion - Functional Recursion, Recursion - Recursive Proofs, Recursion - Recursion in computing, Recursion - Recursion in language, Recursion - Recurrence relations or algorithms, Recursion - Recursively defined sets, Recursion - Example: the natural numbers, Recursion - Example: The set of true reachable propositions, Recursion - Recursively defined functions, Recursion - Recursive algorithms, Recursion - The recursion theorem, Recursion - Proof of uniqueness, Recursion - Proof of existence, Recursion - Recursion in plain English, Recursion - Recursive humour

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In the first edition (June 1979) of The Plantsman (a specialist journal published by the Royal Horticultural Society), Sandra Raphael (then a senior editor in the Dictionary Department of the Oxford University Press) contributed a short article on the history and meaning of the word. Her first example came from an issue of the Gardeners' Chronicle of 1881, when it seemed to mean "A nurseryman, a florist" (in the early sense of "florist" as a grower and breeder of flowers, rather than the more recent meaning of someone wh ...

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Plantsman, Plantsman - Defining the word, Plantsman - Some notable plantsmen and women, Plantsman - Other uses, Plantsman - Notes

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The annualized volatility σ is proportional to standard deviation σSD of the instrument's returns by the square-root of time period of the returns : , where P is time period in years of returns. The generalized volatility σT for time horizon ...

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Volatility, Volatility - Volatility for market players, Volatility - Volatility versus direction, Volatility - Volatility over time, Volatility - Defined

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