query: who gave the first working definition of an element

pos: Chemical element element cannot be transformed into other chemical elements by chemical processes. Elements during this time were generally distinguished by their atomic weights, a property measurable with fair accuracy by available analytical techniques. The 1913 discovery by English physicist Henry Moseley that the nuclear charge is the physical basis for an atom's atomic number, further refined when the nature of protons and neutrons became appreciated, eventually led to the current definition of an element based on atomic number (number of protons per atomic nucleus). The use of atomic numbers, rather than atomic weights, to distinguish elements has greater predictive value (since

neg: Criticism of the Israeli government only special characteristic of Israel is that it is a Jewish state, hence there is an element of anti-Semitism. Delegitimization was a factor addressed by Abba Eban, who claimed that efforts to deny "the equal rights of the Jewish people its lawful sovereignty within the community of nations" constituted anti-Semitism. The European Monitoring Centre on Racism and Xenophobia (EUMC, recently renamed to Fundamental Rights Agency) published a draft of an operational definition of antisemitism called "Working Definition of Antisemitism" which accompanied a report by the EUMC on report that summarized antisemitism in Europe. The EUMC working definition included five kinds

neg: Abstract algebra for the composition of forms, but like Euler before him, he seems to have been more interested in concrete results than in general theory. In 1870, Leopold Kronecker gave a definition of an abelian group in the context of ideal class groups of a number field, generalizing Gauss's work; but it appears he did not tie his definition with previous work on groups, particularly permutation groups. In 1882, considering the same question, Heinrich M. Weber realized the connection and gave a similar definition that involved the cancellation property but omitted the existence of the inverse element, which was sufficient in

neg: Data element definition play. Fewer definitions in a chosen word's dictionary entry is preferable. This minimizes misinterpretation related to a reader's context and background. The process of finding a good meaning of a word is called Word sense disambiguation. Here is the definition of "person" data element as defined in the www.w3c.org Friend of a Friend specification *: Although most people do have an intuitive understanding of what a person is, the definition has much room for improvement. The first problem is that the definition is circular. Note that this definition really does not help most readers and needs to be clarified. Here

neg: 0.999... are rational numbers that can be written as with and . This implies and thus and since by the definition above, every element of 1 is also an element of 0.999..., and, combined with the proof above that every element of 0.999... is also an element of 1, the sets 0.999... and 1 contain the same rational numbers, and are therefore the same set, that is, 0.999... = 1. The definition of real numbers as Dedekind cuts was first published by Richard Dedekind in 1872. The above approach to assigning a real number to each decimal expansion is due to

neg: Working Definition of Antisemitism Select Committee reported on antisemitism in the UK. Its report included a long section on defining antisemitism, including a discussion of the working definition, noting that the President of the Board of Deputies of British Jews gave evidence describing the definition as "helpful, comprehensive and fit for purpose”, as well as a summary of some criticisms of the definition. Among the Committee's recommendations were "that the IHRA definition, with our additional caveats, should be formally adopted by the UK Government, law enforcement agencies and all political parties, to assist them in determining whether or not an incident or discourse can

neg: Involution (mathematics) with transpose as the involution. In ring theory, the word "involution" is customarily taken to mean an antihomomorphism that is its own inverse function. Examples of involutions in common rings: In group theory, an element of a group is an involution if it has order 2; i.e. an involution is an element "a" such that "a" ≠ "e" and "a" = "e", where "e" is the identity element. Originally, this definition agreed with the first definition above, since members of groups were always bijections from a set into itself; i.e., "group" was taken to mean "permutation group". By the end

neg: Data element definition Data element definition In metadata, a data element definition is a human readable phrase or sentence associated with a data element within a data dictionary that describes the meaning or semantics of a data element. Data element definitions are critical for external users of any data system. Good definitions can dramatically ease the process of mapping one set of data into another set of data. This is a core feature of distributed computing and intelligent agent development. There are several guidelines that should be followed when creating high-quality data element definitions. A good definition is: A data element definition is

neg: Model theory mark the fact that at most x is an unbound variable in φ) and ψ defined as follows: (Note that the equality symbol has a double meaning here.) It is intuitively clear how to translate such formulas into mathematical meaning. In the σ-structure formula_9 of the natural numbers, for example, an element "n" satisfies the formula φ if and only if "n" is a prime number. The formula ψ similarly defines irreducibility. Tarski gave a rigorous definition, sometimes called "Tarski's definition of truth", for the satisfaction relation formula_10, so that one easily proves: A set "T" of sentences is called

neg: Per Martin-Löf He wrote a 1966 article "On the definition of random sequences" that gave the first suitable definition of a random sequence. Earlier researchers such as Richard von Mises had attempted to formalize the notion of a test for randomness in order to define a random sequence as one that passed all tests for randomness; however, the precise notion of a randomness test was left vague. Martin-Löf's key insight was to use the theory of computation to define formally the notion of a test for randomness. This contrasts with the idea of randomness in probability; in that theory, no particular element

neg: Cipolla's algorithm non-zero element formula_72 has a multiplicative inverse, write down formula_73 and formula_74. In other words, So the two equalities formula_76 and formula_77 must hold. Working out the details gives expressions for formula_78 and formula_79, namely The inverse elements which are shown in the expressions of formula_78 and formula_79 do exist, because these are all elements of formula_4. This completes the first part of the proof, showing that formula_58 is a field. The second and middle part of the proof is showing that for every element formula_86. By definition, formula_87 is not a square in formula_4. Euler's criterion then says that

neg: Blockquote element languages, the semantics and effect of HTML codice_6 is different from the use of an initial colon in a paragraph, which may be translated into an HTML codice_13 element enclosed within a codice_14 element. (That is a "data definition" within a "definition list", without there being any preceding "data term" or codice_15 element). Blockquote element In HTML and XHTML, the blockquote element defines "a section [within a document] that is quoted from another source". The syntax is codice_1. The codice_2 element is used to indicate the quotation of a large section of text from another source. Using the default HTML

neg: History of chemistry Polytechnique, Louis Jacques Thénard, Gay-Lussac also participated in early electrochemical research, investigating the elements discovered by its means. Among other achievements, they decomposed boric acid by using fused potassium, thus discovering the element boron. The two also took part in contemporary debates that modified Lavoisier's definition of acids and furthered his program of analyzing organic compounds for their oxygen and hydrogen content. The element iodine was discovered by French chemist Bernard Courtois in 1811. Courtois gave samples to his friends, Charles Bernard Desormes (1777–1862) and Nicolas Clément (1779–1841), to continue research. He also gave some of the substance to Gay-Lussac

neg: Random element definition of random variable. The definition of a random element formula_11 with values in a Banach space formula_12 is typically understood to utilize the smallest formula_13-algebra on "B" for which every bounded linear functional is measurable. An equivalent definition, in this case, to the above, is that a map formula_14, from a probability space, is a random element if formula_15 is a random variable for every bounded linear functional "f", or, equivalently, that formula_11 is weakly measurable. A "random variable" is the simplest type of random element. It is a map formula_17 is a measurable function from the set of

neg: Working Definition of Antisemitism manifests itself with regard to the State of Israel. According to both Ken Marcus and Antony Lerman, the novel element in Stern's draft definition was identifying certain forms of criticism of Israel and Zionism as antisemitic, and Marcus also highlights the "praxeological" nature of the definition and its examples, i.e. its focus on pragmatic identification rather than scholarly understanding. At the suggestion of the American Jewish Committee (AJC), the EUMC director organized a meeting of Jewish representatives to discuss the new definition of antisemitism which had been drafted by Kenneth Stern; the consultation involved representatives of the AJC and European

neg: Group (mathematics) the resulting definition is equivalent to the one given above. Two important consequences of the group axioms are the uniqueness of the identity element and the uniqueness of inverse elements. There can be only one identity element in a group, and each element in a group has exactly one inverse element. Thus, it is customary to speak of "the" identity, and "the" inverse of an element. To prove the uniqueness of an inverse element of "a", suppose that "a" has two inverses, denoted "b" and "c", in a group ("G", •). Then The term "b" on the first line above

neg: History of the function concept the well-known ordered pair definition of a function as a certain subset of the cartesian product E x F, gave the following: "Let E and F be two sets, which may or may not be distinct. A relation between a variable element x of E and a variable element y of F is called a functional relation in y if, for all x ∈ E, there exists a unique y ∈ F which is in the given relation with x. "We give the name of function to the operation which in this way associates with every element x ∈ E

neg: Data element definition as a Critical Data Element (CDE). This categorization provides focus for data governance and data quality. An organization often has various sub-categories of CDEs, based on use of the data. e.g., Standards such as the ISO/IEC 11179 Metadata Registry specification give guidelines for creating precise data element definitions. Specifically chapter four of the ISO/IEC 11179 metadata registry standard covers data element definition quality standards . Common words such as play or run frequently have many meanings. For example the WordNet database documents over 57 different distinct meanings for the word "play" but only a single definition for the term dramatic

neg: Normal subgroup groups from a given group. Évariste Galois was the first to realize the importance of the existence of normal subgroups. A subgroup of a group is called a normal subgroup if it is invariant under conjugation; that is, the conjugation of an element of by an element of is always in . The usual notation for this relation is formula_1, and the definition may be written in symbols as For any subgroup, the following conditions are equivalent to normality. Therefore, any one of them may be taken as the definition: The last condition accounts for some of the importance of

neg: Enumeration can also be stated as follows: We may also define it differently when working with finite sets. In this case an enumeration may be defined as follows: In the first definition it varies whether the mapping is also required to be injective (i.e., every element of "S" is the image of "exactly one" natural number), and/or allowed to be partial (i.e., the mapping is defined only for some natural numbers). In some applications (especially those concerned with computability of the set "S"), these differences are of little importance, because one is concerned only with the mere existence of some enumeration,

neg: Naive set theory is used for the ordered pair). If "A" and "B" are sets, then the Cartesian product (or simply product) is defined to be: That is, "A" × "B" is the set of all ordered pairs whose first coordinate is an element of "A" and whose second coordinate is an element of "B". This definition may be extended to a set "A" × "B" × "C" of ordered triples, and more generally to sets of ordered n-tuples for any positive integer "n". It is even possible to define infinite Cartesian products, but this requires a more recondite definition of the product.

neg: Semigroup with involution "x", where "H" is the Green’s relation "H". This defining property can be formulated in several equivalent ways. Another is to say that every "L"-class contains a projection. An axiomatic definition is the condition that for every "x" in "S" there exists an element "x"′ such that , , , . Michael P. Drazin first proved that given "x", the element "x′" satisfying these axioms is unique. It is called the Moore–Penrose inverse of "x". This agrees with the classical definition of the Moore–Penrose inverse of a square matrix. In the multiplicative semigroup "M"("C") of square matrices of order "n",

neg: Holocaust denial motivation of deniers more succinctly: In 2005, the European Monitoring Centre on Racism and Xenophobia (EUMC) published a working definition of antisemitism which gave as an example of the way that antisemitism might manifest itself. A definition based on the EUMC definition was later adopted by the U.S. Department of State. In November 2013 the Fundamental Rights Agency (FRA) the successor agency to the EUMC removed the definition from the organisation's website in 'a clear-out of non-official documents'. A spokesperson stated that the document had never been viewed as a valid definition and that "We are not aware of any

neg: Data element definition is the definition of the "Person" Data Element in the Global Justice XML Data Model 3.0 *: Note that once again the definition is still circular. Person should not reference itself. The definition should use terms other than person to describe what a person is. Here is a more precise but shorter definition of a person: Note that it uses the word "individual" to state that this is an instance of a class of things called human being. Technically you might use "homo sapiens" in your definition, but more people are familiar with the term "human being" than "homo sapiens,"

neg: Endevor a type / processor group / function, being generate delete or move, the default processor is invoked. The default process moves the element BASE, DELTA and SOURCE OUTPUT LIBRARY objects from the source libraries to the target libraries as defined by the element TYPE. Endevor maintains configuration control for each element registered in the system. Every element is distinguished by the element name, system, subsystem and type. The type definition determines how the element is stored and how subsequent changes, known as deltas, are handled. Example of an Endevor TYPE definition for COBOL objects. In this example the type is

neg: Finitary relation example, the constant element a = (a, …, a) or the variable element x = ("x", …, "x"). A statement of the form "a is in the relation "L" " or "a satisfies "L" " is taken to mean that a is in "L" under the first definition and that a is in "G"("L") under the second definition. The following considerations apply under either definition: As a rule, whatever definition best fits the application at hand will be chosen for that purpose, and anything that falls under it will be called a relation for the duration of that discussion. If

neg: Data element definition so commonly used terms, if they are still precise, are always preferred. Sometimes your system may have cultural norms and assumptions in the definitions. For example if your "Person" data element tracked characters in a science fiction series that included aliens you may need a more general term other than "human being". Data element definition In metadata, a data element definition is a human readable phrase or sentence associated with a data element within a data dictionary that describes the meaning or semantics of a data element. Data element definitions are critical for external users of any data system. Good

neg: (ε, δ)-definition of limit (ε, δ)-definition of limit In calculus, the (ε, δ)-definition of limit ("epsilon–delta definition of limit") is a formalization of the notion of limit. The concept is due to Augustin-Louis Cauchy, who never gave an (formula_1) definition of limit in his "Cours d'Analyse", but occasionally used formula_1 arguments in proofs. It was first given as a formal definition by Bernard Bolzano in 1817, and the definitive modern statement was ultimately provided by Karl Weierstrass. It makes rigorous the following informal notion: the dependent expression "f"("x") approaches the value "L" as the variable "x" approaches the value "c" if "f"("x") can be

neg: Roseberry Topping walled enclosures and the remains of huts dating from the period are still visible in the hill's vicinity. The hill was perhaps held in special regard by the Vikings who settled in Cleveland during the early medieval period and gave the area many of its place names. They gave Roseberry Topping its present name: first attested in 1119 as "Othenesberg", its second element is accepted to derive from Old Norse "bjarg" ('rock'); the first element must be an Old Norse personal name, Authunn or Óthinn, giving 'Authunn's/Óthinn's rock'. If the latter, Roseberry Topping is one of only a handful of

neg: Package diagram A "package merge" is "a directed relationship between two packages, that indicates that the contents of the two packages are to be combined. It is very similar to Generalisation in the sense that the source element conceptually adds the characteristics of the target element to its own characteristics resulting in an element that combines the characteristics of both" In this relationship, if an element exists within both the source package and the target package, then the source element's definition will be expanded to include the target element's definition. Package diagrams can use packages containing use cases to illustrate the functionality

neg: Carl Schmitt it was "suspended" for four years, first with the 28 February 1933 Reichstag Fire Decree, with the suspension renewed every four years, implying a continual state of emergency). "On Dictatorship" was followed by another essay in 1922, titled ""Politische Theologie"" (political theology); in it, Schmitt, who at the time was working as a professor at the University of Bonn, gave further substance to his authoritarian theories, analysing the concept of "free will" influenced by Christian-Catholic thinkers. The book begins with Schmitt's famous, or notorious, definition: "Sovereign is he who decides on the exception." By "exception", Schmitt means the appropriate moment

neg: Quasigroup hold only for varieties. Quasigroups are varieties if left and right division are taken as primitive. A quasigroup is a type (2,2,2) algebra (i.e., equipped with three binary operations) satisfying the identities: In other words: Multiplication and division in either order, one after the other, on the same side by the same element, have no net effect. Hence if is a quasigroup according to the first definition, then is the same quasigroup in the sense of universal algebra. A loop is a quasigroup with an identity element; that is, an element, "e", such that It follows that the identity element,

neg: Relation (database) Relation (database) In relational database theory, a relation, as originally defined by E. F. Codd, is a set of tuples (d, d, ..., d), where each element d is a member of D, a data domain. Codd's original definition notwithstanding, and contrary to the usual definition in mathematics, there is no ordering to the elements of the tuples of a relation. Instead, each element is termed an attribute value. An attribute is a name paired with a domain (nowadays more commonly referred to as a type or data type). An attribute value is an attribute name paired with an element

neg: Carbon group of three elements the existence of which was predicted in 1869 by the Russian chemist Dmitri Mendeleev when he first devised his periodic table. However, the element was not actually discovered for some time. In September 1885, a miner discovered a mineral sample in a silver mine and gave it to the mine manager, who determined that it was a new mineral and sent the mineral to Clemens A. Winkler. Winkler realized that the sample was 75% silver, 18% sulfur, and 7% of an undiscovered element. After several months, Winkler isolated the element and determined that it was element 32.

neg: Inverse element inverse as defined in the previous section is strictly narrower than the definition given in this section. Only elements in the Green class "H" have an inverse from the unital magma perspective, whereas for any idempotent "e", the elements of "H" have an inverse as defined in this section. Under this more general definition, inverses need not be unique (or exist) in an arbitrary semigroup or monoid. If all elements are regular, then the semigroup (or monoid) is called regular, and every element has at least one inverse. If every element has exactly one inverse as defined in this section,

neg: Normal form for free groups and free product of groups formula_44 reduced, then formula_45. Let formula_46 be the free product of groups formula_47 and formula_48. Every element formula_12 is represented by formula_50 where formula_51 for formula_52. Definition. A "reduced sequence" is a sequence formula_53 such that for formula_52 we have formula_55 and formula_56 are not in the same factor formula_47 or formula_48. The identity element is represented by the empty set. Definition. A "normal form" for a free product of groups is a representation or choice of a reduced sequence for each element in the free product. The fact that the second statement implies the first is easy. Now suppose

neg: Theaetetus (dialogue) element by element'(207d). Socrates questions Theaetetus by drawing on his learning of how to write, and the idea that if you misplace individual elements (letters) of a name, that does not mean you have knowledge of it (208a). This finishes Socrates' second definition of an account as 'the way to the whole through the elements' (208c). The third definition Socrates offers is 'being able to tell some mark by which the object you are asked about differs from all other things' (208c), giving the example that the Sun is distinct for its brightness. However, this definition of an account fails

neg: Valence (chemistry) called bonds, representing a saturated valency for each element. The two tables below show some examples of different compounds, their valence diagrams, and the valences for each element of the compound. Valence only describes connectivity; it does not describe the geometry of molecular compounds, or what are now known to be ionic compounds or giant covalent structures. A line between atoms does not represent a pair of electrons as it does in Lewis diagrams. Valence is defined by the IUPAC as: An alternative modern description is: This definition differs from the IUPAC definition as an element can be said to

neg: Peter Lucas (computer scientist) to the IBM company, working at the IBM Laboratory Vienna, where he worked on the formal description of programming languages. Together with Hans Bekić, Kurt Walk, and Heinz Zemanek, he was responsible for the formal definition of the IBM programming language PL/I using the Vienna Definition Language (VDL), an important part of the formal method VDM. In addition, he worked together with Hans Bekić on a compiler for ALGOL 60. During this time, he gave lectures and lectures at the Vienna University of Technology and the Johannes Kepler University Linz, covering theoretical foundations of programming and the formal definition of

neg: Fair market value value." In concert with this decision, the Canada Revenue Agency (CRA) lists the following working definition in its on-line dictionary: Fair market value generally means the highest price, expressed in dollars, that a property would bring in an open and unrestricted market between a willing buyer and a willing seller who are both knowledgeable, informed, and prudent, and who are acting independently of each other. As the definition indicates, the Canadian and American concepts of fair market value are very similar. One obvious difference is that the Canadian working definition refers to "the highest price" whereas the American definition merely

neg: Steiner system Steiner system In combinatorial mathematics, a Steiner system (named after Jakob Steiner) is a type of block design, specifically a with λ = 1 and "t" ≥ 2. A Steiner system with parameters "t", "k", "n", written S("t","k","n"), is an "n"-element set "S" together with a set of "k"-element subsets of "S" (called blocks) with the property that each "t"-element subset of "S" is contained in exactly one block. In an alternate notation for block designs, an S("t","k","n") would be a "t"-("n","k",1) design. This definition is relatively modern, generalizing the "classical" definition of Steiner systems which in addition required that

neg: Absorbing element a magma). A zero element is an element "z" such that for all "s" in "S", . A refinement are the notions of left zero, where one requires only that , and right zero, where . Absorbing elements are particularly interesting for semigroups, especially the multiplicative semigroup of a semiring. In the case of a semiring with 0, the definition of an absorbing element is sometimes relaxed so that it is not required to absorb 0; otherwise, 0 would be the only absorbing element. Absorbing element In mathematics, an absorbing element is a special type of element of a set

neg: Kettle the 19th century. In 1893 the Crompton and Co. firm in the United Kingdom started featuring electric kettles in their catalogue. However, these first electric kettles were quite primitive as the heating element couldn't be immersed in the water. Instead, a separate compartment underneath the water storage area in the kettle was used to house the electric heating element. The design was inefficient even relative to the conventional stove-top kettles of the time. In 1922, the problem was finally solved by Leslie Large, an engineer working at Bulpitt & Sons of Birmingham who designed an element of wire wound around

neg: Inverse element Inverse element In abstract algebra, the idea of an inverse element generalises concepts of a negation (sign reversal) in relation to addition, and a reciprocal in relation to multiplication. The intuition is of an element that can 'undo' the effect of combination with another given element. While the precise definition of an inverse element varies depending on the algebraic structure involved, these definitions coincide in a group. The word 'inverse' is derived from that means 'turned upside down', 'overturned'. Let formula_1 be a set closed under a binary operation formula_2 (i.e., a magma). If formula_3 is an identity element of

neg: Batalin–Vilkovisky formalism condition for Δ may be written compactly as where it is understood that the pertinent operator acts on the unit element 1. In other words, formula_26 is a first-order (affine) operator, and formula_27 is a zeroth-order operator. The classical master equation for an even degree element "S" (called the [[Action (physics)|action]]) of a Batalin–Vilkovisky algebra is the equation The quantum master equation for an even degree element "W" of a Batalin–Vilkovisky algebra is the equation or equivalently, Assuming normalization Δ(1) = 0, the quantum master equation reads In the definition of a generalized BV algebra, one drops the second-order assumption

neg: Collective intelligence intelligence. Thus, a non-Turing model of computation is used. This theory allows simple formal definition of collective intelligence as the property of social structure and seems to be working well for a wide spectrum of beings, from bacterial colonies up to human social structures. Collective intelligence considered as a specific computational process is providing a straightforward explanation of several social phenomena. For this model of collective intelligence, the formal definition of IQS (IQ Social) was proposed and was defined as "the probability function over the time and domain of N-element inferences which are reflecting inference activity of the social structure".

neg: Electrical element and independent current sources can be considered non-linear resistors under this definition. The fourth passive element, the memristor, was proposed by Leon Chua in a 1971 paper, but a physical component demonstrating memristance was not created until thirty-seven years later. It was reported on April 30, 2008, that a working memristor had been developed by a team at HP Labs led by scientist R. Stanley Williams. With the advent of the memristor, each pairing of the four variables can now be related. There are also two special non-linear elements which are sometimes used in analysis but which are not the

neg: Interpersonal communication they experience negative emotional reactions to perceived disagreements and interference with the attainment of their goals" (p. 234). With this definition, conflict has three properties: The disagreement property demonstrates the element of perception in conflict. The negative emotion component demonstrates the affect characteristic. The behavioral element demonstrates the interference characteristic of conflict. Within this definition, conflict can be focused on task or relational issues. Task issues involve events, plans, behaviors, etc. Relational conflict involves dispute over personal issues, attitudes, values, beliefs, behaviors, relationship status, etc. Technology has provided the opportunity for quick worldwide access, but individuals who heavily depend on

neg: Transactinide element Transactinide element In chemistry, transactinide elements (also, transactinides, or super-heavy elements) are the chemical elements with atomic numbers from 104 to 120. Their atomic numbers are immediately greater than those of the actinides, the heaviest of which is lawrencium (atomic number 103). Glenn T. Seaborg first proposed the actinide concept, which led to the acceptance of the actinide series. He also proposed the transactinide series ranging from element 104 to 121 and the superactinide series approximately spanning elements 122 to 153. The transactinide seaborgium was named in his honor. By definition, transactinide elements are also transuranic elements, i.e. have an

neg: Pointer (computer programming) subtracting the number of elements required instead of the actual offset in bytes. (Pointer arithmetic with codice_88 pointers uses byte offsets, because codice_59 is 1 by definition.) In particular, the C definition explicitly declares that the syntax codice_91, which is the codice_92-th element of the array codice_7, is equivalent to codice_94, which is the content of the element pointed by codice_95. This implies that codice_96 is equivalent to codice_91, and one can write, e.g., codice_98 or codice_99 equally well to access the fourth element of an array codice_7. While powerful, pointer arithmetic can be a source of computer bugs. It

neg: Torsion (algebra) one annihilated by a non-zero element of the integral domain. Some authors use this as the definition of a torsion element but this definition does not work well over more general rings. A module "M" over a ring "R" is called a torsion module if all its elements are torsion elements, and torsion-free if zero is the only torsion element. If the ring "R" is an integral domain then the set of all torsion elements forms a submodule of "M", called the torsion submodule of "M", sometimes denoted T("M"). If "R" is not commutative, T("M") may or may not be

neg: Grothendieck universe "U" is an element of "U" and every element of "U" is a subset of "U". To see that it is regular, suppose that "c" is a collection of cardinals indexed by "I", where the cardinality of "I" and of each "c" is less than c("U"). Then, by the definition of c("U"), "I" and each "c" can be replaced by an element of "U". The union of elements of "U" indexed by an element of "U" is an element of "U", so the sum of the "c" has the cardinality of an element of "U", hence is less than c("U").

neg: Dowling geometry "E". In his second paper (1973b) Dowling gave an intrinsic definition of the rank-"n" Dowling lattice of any finite group "G". Let "S" be the set {1...,"n"}. A "G"-labelled set ("T", α) is a set "T" together with a function α: "T" → "G". Two "G"-labelled sets, ("T", α) and ("T", β), are equivalent if there is a group element, "g", such that β = "g"α. An equivalence class is denoted ["T", α]. A partial "G"-partition of "S" is a set γ = {["B",α], ..., ["B",α]} of equivalence classes of "G"-labelled sets such that "B", ..., "B" are nonempty subsets

neg: Inverse element inverse, formula_46 By components it is computed as The left inverse doesn't exist, because which is a singular matrix, and cannot be inverted. Inverse element In abstract algebra, the idea of an inverse element generalises concepts of a negation (sign reversal) in relation to addition, and a reciprocal in relation to multiplication. The intuition is of an element that can 'undo' the effect of combination with another given element. While the precise definition of an inverse element varies depending on the algebraic structure involved, these definitions coincide in a group. The word 'inverse' is derived from that means 'turned upside

neg: Physis Hesiod "grow" out of primordial entities after the physical universe had been established. "Because those who use the term mean to say that nature is the first creative power; but if the soul turns out to be the primeval element, and not fire or air, then in the truest sense and beyond other things the soul may be said to exist "by" nature; and this would be true if you proved that the soul is older than the body, but not otherwise." Aristotle sought out the definition of "physis" to prove that there was more than one definition of "physis",

neg: History of video games any game played on a modern high definition display, and most handheld game systems. From a technical standpoint, these would more properly be called "electronic games" or "computer games." Today, however, the term "video game" has completely shed its purely technical definition and encompasses a wider range of technology. While still rather ill-defined, the term "video game" now generally encompasses any game played on hardware built with electronic logic circuits that incorporates an element of interactivity and outputs the results of the player's actions to a display. Going by this broader definition, the first video games appeared in the early

neg: Early history of video games a vector-scan monitor, any game played on a modern high definition display, and most handheld game systems. From a technical standpoint, these would more properly be called "electronic games" or "computer games". Today the term "video game" has completely shed its purely technical definition and encompasses a wider range of technology. While still rather ill-defined, the term "video game" now generally encompasses any game played on hardware built with electronic logic circuits that incorporates an element of interactivity and outputs the results of the player's actions to a display. Going by this broader definition, the first video games appeared in

neg: X Macro application consists of two parts: The list is defined by a macro or header file (named, codice_1) which generates no code by itself, but merely consists of a sequence of invocations of a macro (classically named "codice_2") with the elements' data. Each expansion of codice_1 is preceded by a definition of codice_2 with the syntax for a list element. The invocation of codice_1 expands codice_2 for each element in the list. This example defines a list of variables, and automatically generates their declarations and a function to print them out. First the list definition. The list entries could contain multiple

neg: Working Definition of Antisemitism Working Definition of Antisemitism The Working Definition of Antisemitism is a non-legally binding working definition of antisemitism adopted by the inter-governmental body the International Holocaust Remembrance Alliance (IHRA), and governmental and non-governmental organizations worldwide. The definition (which is published accompanied by illustrative examples) is: Antisemitism is a certain perception of Jews, which may be expressed as hatred toward Jews. Rhetorical and physical manifestations of antisemitism are directed toward Jewish or non-Jewish individuals and/or their property, toward Jewish community institutions and religious facilities. It was developed during 2003–04 and first published on 28 January 2005 on the website of the European

neg: Harry Friedman make television history by becoming the first syndicated television series to broadcast in high definition. Friedman was born in Omaha, Nebraska. He developed an early fascination with television programming and personalities, including Johnny Carson when he was a young local celebrity. Long before the conception of student internships, Friedman began working for Omaha's first television stations, doing whatever work management permitted. In 1971, Friedman moved to Los Angeles, and without contacts he gave himself six months to find a job in the business. With less than 24 hours remaining on his self-imposed deadline, Friedman became a part-time question writer on

neg: Document type definition within the <!ATTLIST ...> declaration of the element). For example: The example above shows a notation named "type-image-svg" that references the standard public FPI and the system identifier (the standard URI) of an SVG 1.1 document, instead of specifying just a system identifier as in the first example (which was a relative URI interpreted locally as a MIME type). This annotation is referenced directly within the unparsed "type" attribute of the "img" element, but its content is not retrieved. It also declares another notation for a vendor-specific application, to annotate the "sgml" root element in the document. In both cases,

neg: Group 3 element the current heaviest element known, oganesson. In 1787, Swedish part-time chemist Carl Axel Arrhenius found a heavy black rock near the Swedish village of Ytterby, Sweden (part of the Stockholm Archipelago). Thinking that it was an unknown mineral containing the newly discovered element tungsten, he named it ytterbite. Finnish scientist Johan Gadolin identified a new oxide or "earth" in Arrhenius' sample in 1789, and published his completed analysis in 1794; in 1797, the new oxide was named "yttria". In the decades after French scientist Antoine Lavoisier developed the first modern definition of chemical elements, it was believed that earths could

neg: Line element Line element In geometry, the line element or length element can be informally thought of as a line segment associated with an infinitesimal displacement vector in a metric space. The length of the line element, which may be thought of as a differential arc length, is a function of the metric tensor and is denoted by "ds" Line elements are used in physics, especially in theories of gravitation (most notably general relativity) where spacetime is modelled as a curved Pseudo-Riemannian manifold with an appropriate metric tensor. The coordinate-independent definition of the square of the line element "ds" in an "n"-dimensional

neg: Symbolic method (combinatorics) classes formula_51 and formula_57 is specified by defining the size of an ordered pair as the sum of the sizes of the elements in the pair. Thus we have for formula_72 and formula_73, formula_74. This should be a fairly intuitive definition. We now note that the number of elements in formula_75 of size n is Using the definition of the OGF and some elementary algebra, we can show that The "sequence construction", denoted by formula_79 is defined as In other words, a sequence is the neutral element, or an element of formula_57, or an ordered pair, ordered triple, etc. This

neg: Relation (database) codice_2 syntax is used to define a derived relation variable. The following is an example. Relation (database) In relational database theory, a relation, as originally defined by E. F. Codd, is a set of tuples (d, d, ..., d), where each element d is a member of D, a data domain. Codd's original definition notwithstanding, and contrary to the usual definition in mathematics, there is no ordering to the elements of the tuples of a relation. Instead, each element is termed an attribute value. An attribute is a name paired with a domain (nowadays more commonly referred to as a

neg: Algebra over a field 1 (the identity element), "a" and "b". Taking into account the definition of an identity element, it is sufficient to specify The fourth algebra is non-commutative, others are commutative. In some areas of mathematics, such as commutative algebra, it is common to consider the more general concept of an algebra over a ring, where a commutative unital ring "R" replaces the field "K". The only part of the definition that changes is that "A" is assumed to be an "R"-module (instead of a vector space over "K"). A ring "A" is always an associative algebra over its center, and over

neg: Knowledge worker point to the most narrow and defined definition of knowledge work, such as Florida's view of it as specifically, "the direct manipulation of symbols to create an original knowledge product, or to add obvious value to an existing one", which limits the definition of knowledge work to mainly creative work. They then contrast this view of knowledge work with the notably broader view which includes the handling and distribution of information, arguing that workers who play a role in the handling and distribution of information add real value to the field, despite not necessarily contributing a creative element. Thirdly, one

neg: Transition metal groups (4 to 11), with some authors including some elements in groups 3 or 12. The elements in group 3 have an "ns"("n" − 1)"d" configuration. The first transition series is present in the 4th period, and starts after Ca ("Z" = 20) of group-2 with the configuration [Ar]4"s", or scandium (Sc), the first element of group 3 with atomic number "Z" = 21 and configuration [Ar]4"s"3"d", depending on the definition used. As we move from left to right, electrons are added to the same "d"-sub-shell till it is complete. The element of group 11 in the first transition series

neg: N-ary group not reducible does not contain such elements. There exist "n"-ary groups with more than one neutral element. If the set of all neutral elements of an "n"-ary group is non-empty it forms an "n"-ary subgroup. Some authors include an identity in the definition of an "n"-ary group but as mentioned above such "n"-ary operations are just repeated binary operations. Groups with intrinsically "n"-ary operations do not have an identity element. The axioms of associativity and unique solutions in the definition of an "n"-ary group are stronger than they need to be. Under the assumption of "n"-ary associativity it suffices to

neg: Malaysian Standard (MS) 1722:2011 its representative or other person who are appropriate. So, any necessary action can be taken to improve the OSH management systems in the organisation. The second element of OSHMS is organizing which consists of element of establishment of OSH responsibilities, accountabilities, structures, a training system, competency definition, documentation practices and communication system. According to MS 1722:2011 – Occupational Safety and Health Management System – Requirement (First Revision), the involved clauses are as follows: 3.2.1.1 The employer shall have overall responsibility for the protection of employees’ safety and health and provide leadership for OSH activities in the organization. 3.2.1.2 The employer

neg: Document type definition set of attributes for each declared element, including the type of each attribute value, if not an explicit set of valid values. DTD markup declarations declare which element types, attribute lists, entities, and notations are allowed in the structure of the corresponding class of XML documents. An element type declaration defines an element and its possible content. A valid XML document contains only elements that are defined in the DTD. Various keywords and characters specify an element’s content: For example: Note that element type declarations are ignored by "non-validating" SGML and XML parsers (in which cases, any elements are accepted

neg: History of the function concept by equations involving real or complex numbers, and tacitly assumed they were continuous: Nikolai Lobachevsky and Peter Gustav Lejeune Dirichlet are traditionally credited with independently giving the modern "formal" definition of a function as a relation in which every first element has a unique second element. Lobachevsky (1834) writes that while Dirichlet (1837) writes Eves asserts that "the student of mathematics usually meets the Dirichlet definition of function in his introductory course in calculus. Dirichlet's claim to this formalization has been disputed by Imre Lakatos: However, Gardiner says "...it seems to me that Lakatos goes too far, for example, when

neg: Zorn ring Zorn ring In mathematics, a Zorn ring is an alternative ring in which for every non-nilpotent "x" there exists an element "y" such that "xy" is a non-zero idempotent . named them after Max August Zorn, who studied a similar condition in . For associative rings, the definition of Zorn ring can be restated as follows: the Jacobson radical J("R") is a nil ideal and every right ideal of "R" which is not contained in J("R") contains a nonzero idempotent. Replacing "right ideal" with "left ideal" yields an equivalent definition. Left or right Artinian rings, left or right perfect rings,

neg:
Recursive definition complex for the general case. An outline of the general proof and the criteria can be found in Munkres' 'Topology'.However,a specific case(domain is restricted to the positive integers instead of any well-ordered set) of the general recursive definition will be given below. Let formula_4 be a set and let formula_5 be an element of formula_6.If formula_7 is a function which assigns to each function formula_8 mapping a nonempty section of the positive integers into formula_6,an element of formula_6,then there exists a unique function formula_11 such that
 formula_12
 formula_13 for formula_14 Addition is defined recursively based on counting Multiplication is

neg: Set (mathematics) are equal (one and the same) if and only if every element of each set is an element of the other; this property is called the "extensionality of sets". There are two ways of describing, or specifying the members of, a set. One way is by intensional definition, using a rule or semantic description: The second way is by extension – that is, listing each member of the set. An extensional definition is denoted by enclosing the list of members in curly brackets: One often has the choice of specifying a set either intensionally or extensionally. In the examples above,

neg: Enhanced interrogation techniques fall within this new definition advocated by the U.S. The Bush administration told the CIA in 2002 that its interrogators working abroad would not violate US prohibitions against torture unless they "have the specific intent to inflict severe pain or suffering", according to a previously secret US Justice Department memo released on July 24, 2008. The interrogator's "good faith" and "honest belief" that the interrogation will not cause such suffering protects the interrogator, the memo adds. "Because specific intent is an element of the offense, the absence of specific intent negates the charge of torture", Jay Bybee, then the Assistant

neg: Philosophical methodology not fully justified, even our most basic beliefs about the world. Another element of philosophical method is to formulate questions to be answered or problems to be solved. The working assumption is that the more clearly the question or problem is stated, the easier it is to identify critical issues. A relatively small number of major philosophers prefer not to be quick, but to spend more time trying to get extremely clear on what the problem is all about. Another approach is to enunciate a theory, or to offer a definition or analysis, which constitutes an attempt to solve a

neg: Suicidology in a needful individual who defines an issue for which suicide is perceived as the best solution. He thought of suicide as psychache or intolerable psychological pain. Another notable person in the field of suicidology is Emile Durkheim. To Durkheim the word suicide is applied to all cases of death resulting directly or indirectly from a positive or negative act of the victim himself, which he knows will produce this result. Basically he saw suicide as an external and constraining social fact independent of individual psychopathology. In David J. Mayo's definition there were four elements to suicide. The first element:

neg: American Beauty (1999 film) added leaves on the ground. Mendes was satisfied by the way the wall gave definition to the outline of the bag. Mendes avoided using close-ups, as he believed the technique was overused; he also cited Spielberg's advice that he should imagine an audience silhouetted at the bottom of the camera monitor, to keep in mind that he was shooting for display on a screen. Spielberg—who visited the set a few times—also advised Mendes not to worry about costs if he had a "great idea" toward the end of a long working day. Mendes said, "That happened three or four times,

neg: Division algebra Division algebra In the field of mathematics called abstract algebra, a division algebra is, roughly speaking, an algebra over a field in which division, except by zero, is always possible. Formally, we start with an algebra "D" over a field, and assume that "D" does not just consist of its zero element. We call "D" a division algebra if for any element "a" in "D" and any non-zero element "b" in "D" there exists precisely one element "x" in "D" with "a" = "bx" and precisely one element "y" in "D" such that . For associative algebras, the definition can

neg: Free module of integers. For a ring formula_1 and an formula_1-module formula_3, the set formula_4 is a basis for formula_3 if: A free module is a module with a basis. An immediate consequence of the second half of the definition is that the coefficients in the first half are unique for each element of "M". If formula_1 has invariant basis number, then by definition any two bases have the same cardinality. The cardinality of any (and therefore every) basis is called the rank of the free module formula_3. If this cardinality is finite, the free module is said to be "free of

neg: Binomial coefficient factors are first cancelled (in particular since factorial values grow very rapidly). The formula does exhibit a symmetry that is less evident from the multiplicative formula (though it is from the definitions) which leads to a more efficient multiplicative computational routine. Using the falling factorial notation, The multiplicative formula allows the definition of binomial coefficients to be extended by replacing "n" by an arbitrary number "α" (negative, real, complex) or even an element of any commutative ring in which all positive integers are invertible: With this definition one has a generalization of the binomial formula (with one of the variables

neg: Working Definition of Antisemitism inquiry concerning the working definition thusly. "[…] The Plenary of the International Holocaust Remembrance Alliance (IHRA) adopted the working definition of antisemitism under the Romanian Chairmanship on 26 May 2016. The working definition, like all IHRA decision, is non-legally binding. The working definition is the text in the box…"<ref name ="ECCAP"> Working Definition of Antisemitism The Working Definition of Antisemitism is a non-legally binding working definition of antisemitism adopted by the inter-governmental body the International Holocaust Remembrance Alliance (IHRA), and governmental and non-governmental organizations worldwide. The definition (which is published accompanied by illustrative examples) is: Antisemitism is a certain perception

neg: Limit of a function a function. Although implicit in the development of calculus of the 17th and 18th centuries, the modern idea of the limit of a function goes back to Bolzano who, in 1817, introduced the basics of the epsilon-delta technique to define continuous functions. However, his work was not known during his lifetime . Cauchy discussed variable quantities, infinitesimals, and limits and defined continuity of formula_1 by saying that an infinitesimal change in "x" necessarily produces an infinitesimal change in "y" in his 1821 book "Cours d'analyse", while claims that he only gave a verbal definition. Weierstrass first introduced the epsilon-delta definition

neg: Elliptic Curve Digital Signature Algorithm verification step 5, formula_82 Collecting the common term formula_83, formula_84 Expanding the definition of formula_32 from signature step 6, formula_86 Since the inverse of an inverse is the original element, and the product of an element's inverse and the element is the identity, we are left with formula_87 From the definition of formula_61, this is verification step 6. This shows only that a correctly signed message will verify correctly; many other properties are required for a secure signature algorithm. In December 2010, a group calling itself "fail0verflow" announced recovery of the ECDSA private key used by Sony to sign software

neg: SAML 2.0 metadata. SAML 2.0 provides a well-defined, interoperable metadata format that entities can leverage to bootstrap the trust process. An identity provider publishes data about itself in an codice_101 element: Note the following details about this entity descriptor: By definition, an identity provider manages an SSO service that supports the SAML Web Browser SSO profile specified in SAMLProf. See, for example, the identity provider described in the codice_107 element shown in the next section. The SSO service at the identity provider is described in an codice_107 element: The previous metadata element describes the SSO service at the identity provider. Note the

neg: The Fifth Element (video game) adventure/action game does what all of the other games in the genre do, but not in any way better." The only positive reviews came from "GamePro", which gave the game three-and-a-half stars out of five, and from "Game Informer", which gave the game 7 out of 10, but quipped that "Unfortunately, the control is cumbersome, the camera sometimes jumps or sticks, and the enemies prove to be rather dumb. Rent it first, but if you really like the movie, you'll probably like the game too." The Fifth Element (video game) The Fifth Element is an action-adventure video game that is

neg: Exact solutions in general relativity Einstein also recognized another element of the definition of an exact solution: it should be a Lorentzian manifold (meeting additional criteria), i.e. a smooth manifold. But in working with general relativity, it turns out to be very useful to admit solutions which are not everywhere smooth; examples include many solutions created by matching a perfect fluid interior solution to a vacuum exterior solution, and impulsive plane waves. Once again, the creative tension between elegance and convenience, respectively, has proven difficult to resolve satisfactorily. In addition to such local objections, we have the far more challenging problem that there are very

neg: Public history embrace a mission to make their special insights accessible and useful to the public." However, this draft definition prompted some challenges on the H-Public listserv from people in the field, who raised questions about whether public history is solely an endeavor by professional or trained historians, or if shared historical authority should be a key element of the field. Others have pointed out that the existence of many "publics" for public history complicates the task of definition. For example, historian Peter Novick has questioned whether much of what is termed public history should actually be called "private" history (for example,

neg: World War I prisoners of war in Germany due to their lack of qualifications or their unsuitability as workers on behalf of the enemy. For example, an imprisoned bureaucrat finding himself working in a field gave less results than if a civilian farmer had been given the work. Prisoners far from their country were, by definition, easy prey for propaganda which, partly oriented toward them, could be classed into two types: that made among the German population; and that distributed inside the camps, which was meant to take effect in France. When the first prisoners of war were captured, the German Army’s superiority was put on display by

neg: E. B. Ford Genetics Laboratory, 1952–1969, and Professor of Ecological Genetics 1963–1969. Ford was one of the first scientists to be elected a Fellow of All Souls College since the seventeenth century. Ford had a long working relationship with R.A. Fisher. By the time Ford had developed his formal definition of genetic polymorphism, Fisher had got accustomed to high selection values in nature. He was most impressed by the fact that polymorphism concealed powerful selective forces (Ford gave human blood groups as an example). Like Fisher, he continued the natural selection versus genetic drift debate with Sewall Wright, whom Ford believed put too

neg: Euclid–Mullin sequence Euclid–Mullin sequence The Euclid–Mullin sequence is an infinite sequence of distinct prime numbers, in which each element is the least prime factor of one plus the product of all earlier elements. They are named after the ancient Greek mathematician Euclid, because their definition relies on an idea in Euclid's proof that there are infinitely many primes, and after Albert A. Mullin, who asked about the sequence in 1963. The first 51 elements of the sequence are These are the only known elements . Finding the next one requires finding the least prime factor of a 335-digit number (which is known

neg: Twisted K-theory a ring. It has an addition, but it is no longer closed under multiplication. However, the direct sum of the twisted K-theories of formula_3 with all possible twists is a ring. In particular, the product of an element of K-theory with twist formula_24 with an element of K-theory with twist formula_45 is an element of K-theory twisted by formula_46. This element can be constructed directly from the above definition by using adjoints of Fredholm operators and construct a specific 2 x 2 matrix out of them (see the reference 1, where a more natural and general Z/2-graded version is also

neg: Rotation formalisms in three dimensions stores quaternion as an array following the convention used in (Wertz 1980) and (Markley 2003). An alternative definition used for example in (Coutsias 1999) and (Schmidt 2001) defines the "scalar" term as the first quaternion element, with the other elements shifted down one position. In terms of the Euler axis and angle this versor's components are expressed as follows: Inspection shows that the quaternion parametrization obeys the following constraint: The last term (in our definition) is often called the scalar term, which has its origin in quaternions when understood as the mathematical extension of the complex numbers, written as and

neg: Coxeter matroid a unique minimal element with respect to the "w"-Bruhat order. Suppose that the Coxeter group "W" is the symmetric group "S" and "P" is the parabolic subgroup "S"×"S". Then "W"/"P" can be identified with the "k"-element subsets of the "n"-element set {1,2...,"n"} and the elements "w" of "W" correspond to the linear orderings of this set. A Coxeter matroid consists of "k" elements sets such that for each "w" there is a unique minimal element in the corresponding Bruhat ordering of "k"-element subsets. This is exactly the definition of a matroid of rank "k" on an "n"-element set in terms

neg: Document type definition specifies that the document has a single top-level element (this is an implicit requirement for all valid XML and HTML documents, but not for document fragments or for all SGML documents, whose top-level elements may be different from the implied root element), and it indicates the type name of the root element: DTDs describe the structure of a class of documents via element and attribute-list declarations. Element declarations name the allowable set of elements within the document, and specify whether and how declared elements and runs of character data may be contained within each element. Attribute-list declarations name the allowable

neg: Standard atomic weight Standard atomic weight The standard atomic weight ("A", a relative atomic mass) is the atomic weight ("A") of a chemical element, as appearing and met in the earthly environment. It reflects the variance of natural isotopes (and so weight differences) of an element. Values are defined by (restricted to) the IUPAC (CIAAW) definition of natural, stable, terrestrial sources. It is the most common and practical atomic weight used, for example to determine molar mass. The specified definition is to use many representative sources (samples) from the Earth, so that the value can widely be used as 'the' atomic weight for

neg: 75th Ranger Regiment (United States) but no precise meaning.' For the want of a definition of who and what is a Ranger, integrity was lost. As a result of Grenada, circumstances have changed. Since 1983, men have had the opportunity to earn and wear an authorized Ranger unit scroll or an authorized Ranger Tab or both. But there is a need for a firm definition of who and what constitutes a RANGER. Without that definition, we face the likelihood of future controversy. In June 2001, Army Chief of Staff General Eric Shinseki gave the order to issue black berets to regular soldiers. At the time,

neg: Zero object (algebra) is a terminal object of any algebraic structure where it exists, like it was described for examples above. But its existence and, if it exists, the property to be an initial object (and hence, a "zero object" in the category-theoretical sense) depend on exact definition of the multiplicative identity 1 in a specified structure. If the definition of requires that , then the object cannot exist because it may contain only one element. In particular, the zero ring is not a field. If mathematicians sometimes talk about a field with one element, this abstract and somewhat mysterious mathematical object is

neg: OMG Business Architecture Special Interest Group blueprint of the enterprise that provides a common understanding of the organization and is used to align strategic objectives and tactical demands The definition was first published on the working groups homepage "bawg.omg.org," and first cited in Solaimani et al. (2010) In the Business Architecture Working Group (BAWG) wiki (2010) there was a further discussion on the definition, which was presented as: A formal blueprint of governance structures, business semantics and value streams across the extended enterprise. In order to develop an integrated view of an enterprise, many different views of an organization are typically developed. Each "view" is typically

neg: Inverse element binary operation satisfies the associative law is a group. Just like formula_4 can have several left identities or several right identities, it is possible for an element to have several left inverses or several right inverses (but note that their definition above uses a "two-sided" identity formula_3). It can even have several left inverses "and" several right inverses. If the operation formula_2 is associative then if an element has both a left inverse and a right inverse, they are equal. In other words, in a monoid (an associative unital magma) every element has at most one inverse (as defined in