Imaginary numberAn imaginary number is a real number multiplied by the imaginary unit i, which is defined by its property i2 = −1. The square of an imaginary number bi is −b2. For example, 5i is an imaginary number, and its square is −25. By definition, zero is considered to be both real and imaginary. Originally coined in the 17th century by René Descartes as a derogatory term and regarded as fictitious or useless, the concept gained wide acceptance following the work of Leonhard Euler (in the 18th century) and Augustin-Louis Cauchy and Carl Friedrich Gauss (in the early 19th century).
Imaginary unitThe imaginary unit or unit imaginary number (i) is a solution to the quadratic equation . Although there is no real number with this property, i can be used to extend the real numbers to what are called complex numbers, using addition and multiplication. A simple example of the use of i in a complex number is . Imaginary numbers are an important mathematical concept; they extend the real number system to the complex number system , in which at least one root for every nonconstant polynomial exists (see Algebraic closure and Fundamental theorem of algebra).
ArtistAn artist is a person engaged in an activity related to creating art, practicing the arts, or demonstrating an art. The common usage in both everyday speech and academic discourse refers to a practitioner in the visual arts only. However, the term is also often used in the entertainment business, especially in a business context, for musicians and other performers (although less often for actors). "Artiste" (French for artist) is a variant used in English in this context, but this use has become rare.
Pragmaticism"Pragmaticism" is a term used by Charles Sanders Peirce for his pragmatic philosophy starting in 1905, in order to distance himself and it from pragmatism, the original name, which had been used in a manner he did not approve of in the "literary journals". Peirce in 1905 announced his coinage "pragmaticism", saying that it was "ugly enough to be safe from kidnappers" (Collected Papers (CP) 5.414). Today, outside of philosophy, "pragmatism" is often taken to refer to a compromise of aims or principles, even a ruthless search for mercenary advantage.
Nth rootIn mathematics, taking the nth root is an operation involving two numbers, the radicand and the index or degree. Taking the nth root is written as , where x is the radicand and n is the index (also sometimes called the degree). This is pronounced as "the nth root of x". The definition then of an nth root of a number x is a number r (the root) which, when raised to the power of the positive integer n, yields x: A root of degree 2 is called a square root (usually written without the n as just ) and a root of degree 3, a cube root (written ).
Grammatical numberIn linguistics, grammatical number is a feature of nouns, pronouns, adjectives and verb agreement that expresses count distinctions (such as "one", "two" or "three or more"). English and other languages present number categories of singular or plural, both of which are cited by using the hash sign (#) or by the numero signs "No." and "Nos." respectively. Some languages also have a dual, trial and paucal number or other arrangements.
Formal grammarIn formal language theory, a grammar (when the context is not given, often called a formal grammar for clarity) describes how to form strings from a language's alphabet that are valid according to the language's syntax. A grammar does not describe the meaning of the strings or what can be done with them in whatever context—only their form. A formal grammar is defined as a set of production rules for such strings in a formal language. Formal language theory, the discipline that studies formal grammars and languages, is a branch of applied mathematics.
Square rootIn mathematics, a square root of a number x is a number y such that ; in other words, a number y whose square (the result of multiplying the number by itself, or ) is x. For example, 4 and −4 are square roots of 16 because . Every nonnegative real number x has a unique nonnegative square root, called the principal square root, which is denoted by where the symbol "" is called the radical sign or radix. For example, to express the fact that the principal square root of 9 is 3, we write .
ResearchResearch is "creative and systematic work undertaken to increase the stock of knowledge". It involves the collection, organization and analysis of evidence to increase understanding of a topic, characterized by a particular attentiveness to controlling sources of bias and error. These activities are characterized by accounting and controlling for biases. A research project may be an expansion on past work in the field. To test the validity of instruments, procedures, or experiments, research may replicate elements of prior projects or the project as a whole.
GrammarIn linguistics, the grammar of a natural language is its set of structural rules on speakers' or writers' usage and creation of clauses, phrases, and words. The term can also refer to the study of such rules, a subject that includes phonology, morphology, and syntax, together with phonetics, semantics, and pragmatics. There are two different ways to study grammar right now: traditional grammar and theoretical grammar. Fluent speakers of a language variety or lect have internalised these rules.
Singularity theoryIn mathematics, singularity theory studies spaces that are almost manifolds, but not quite. A string can serve as an example of a one-dimensional manifold, if one neglects its thickness. A singularity can be made by balling it up, dropping it on the floor, and flattening it. In some places the flat string will cross itself in an approximate "X" shape. The points on the floor where it does this are one kind of singularity, the double point: one bit of the floor corresponds to more than one bit of string.
Ambiguous grammarIn computer science, an ambiguous grammar is a context-free grammar for which there exists a string that can have more than one leftmost derivation or parse tree. Every non-empty context-free language admits an ambiguous grammar by introducing e.g. a duplicate rule. A language that only admits ambiguous grammars is called an inherently ambiguous language. Deterministic context-free grammars are always unambiguous, and are an important subclass of unambiguous grammars; there are non-deterministic unambiguous grammars, however.
PluralThe plural (sometimes abbreviated as pl., pl, or ), in many languages, is one of the values of the grammatical category of number. The plural of a noun typically denotes a quantity greater than the default quantity represented by that noun. This default quantity is most commonly one (a form that represents this default quantity of one is said to be of singular number). Therefore, plurals most typically denote two or more of something, although they may also denote fractional, zero or negative amounts.
ArtArt is a diverse range of human activity, and resulting product, that involves creative or imaginative talent expressive of technical proficiency, beauty, emotional power, or conceptual ideas. There is no generally agreed definition of what constitutes art, and its interpretation has varied greatly throughout history and across cultures. In the Western tradition, the three classical branches of visual art are painting, sculpture, and architecture.
Context-free grammarIn formal language theory, a context-free grammar (CFG) is a formal grammar whose production rules can be applied to a nonterminal symbol regardless of its context. In particular, in a context-free grammar, each production rule is of the form with a single nonterminal symbol, and a string of terminals and/or nonterminals ( can be empty). Regardless of which symbols surround it, the single nonterminal on the left hand side can always be replaced by on the right hand side.
Tree-adjoining grammarTree-adjoining grammar (TAG) is a grammar formalism defined by Aravind Joshi. Tree-adjoining grammars are somewhat similar to context-free grammars, but the elementary unit of rewriting is the tree rather than the symbol. Whereas context-free grammars have rules for rewriting symbols as strings of other symbols, tree-adjoining grammars have rules for rewriting the nodes of trees as other trees (see tree (graph theory) and tree (data structure)).
Singular valueIn mathematics, in particular functional analysis, the singular values, or s-numbers of a compact operator acting between Hilbert spaces and , are the square roots of the (necessarily non-negative) eigenvalues of the self-adjoint operator (where denotes the adjoint of ). The singular values are non-negative real numbers, usually listed in decreasing order (σ1(T), σ2(T), ...). The largest singular value σ1(T) is equal to the operator norm of T (see Min-max theorem).
Cube rootIn mathematics, a cube root of a number x is a number y such that y3 = x. All nonzero real numbers, have exactly one real cube root and a pair of complex conjugate cube roots, and all nonzero complex numbers have three distinct complex cube roots. For example, the real cube root of 8, denoted , is 2, because 23 = 8, while the other cube roots of 8 are and .
Virtual communityA virtual community is a social network of individuals who connect through specific social media, potentially crossing geographical and political boundaries in order to pursue mutual interests or goals. Some of the most pervasive virtual communities are online communities operating under social networking services. Howard Rheingold discussed virtual communities in his book, The Virtual Community, published in 1993. The book's discussion ranges from Rheingold's adventures on The WELL, computer-mediated communication, social groups and information science.
Women artistsThe absence of women from the canon of Western art has been a subject of inquiry and reconsideration since the early 1970s. Linda Nochlin's influential 1971 essay, "Why Have There Been No Great Women Artists?", examined the social and institutional barriers that blocked most women from entering artistic professions throughout history, prompted a new focus on women artists, their art and experiences, and contributed inspiration to the Feminist art movement.
