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Nested Set Collection
A nested set collection or nested set family is a collection of sets that consists of chains of subsets forming a hierarchical structure, like Matryoshka doll, Russian dolls. It is used as reference concept in hierarchy, scientific hierarchy definitions, and many technical approaches, like the tree (data structure), tree in Data structure, computational data structures or nested set model of relational databases. Sometimes the concept is confused with a collection of sets with a hereditary property (like finiteness in a hereditarily finite set). Formal definition Some authors regard a nested set collection as a family of sets. Others prefer to classify it relation as an inclusion order. Let ''B'' be a empty set, non-empty set and C a collection of subsets of ''B''. Then C is a nested set collection if: * B \in \mathbf (and, for some authors, \empty \notin \mathbf) * \forall H,K \in \mathbf ~:~ H \cap K \neq \empty \implies H \subset K ~\lor~ K \subset H The first condition sta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer-Verlag
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in Berlin, it expanded internationally in the 1960s, and through mergers in the 1990s and a sale to venture capitalists it fused with Wolters Kluwer and eventually became part of Springer Nature in 2015. Springer has major offices in Berlin, Heidelberg, Dordrecht, and New York City. History Julius Springer founded Springer-Verlag in Berlin in 1842 and his son Ferdinand Springer grew it from a small firm of 4 employees into Germany's then second-largest academic publisher with 65 staff in 1872.Chronology ". Springer Science+Business Media. In 1964, Springer expanded its business internationally, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hereditarily Countable Set
In set theory, a set is called hereditarily countable if it is a countable set of hereditarily countable sets. Results The inductive definition above is well-founded and can be expressed in the language of first-order set theory. Equivalent properties A set is hereditarily countable if and only if it is countable, and every element of its transitive closure is countable. by . See also * * |
Object-oriented Programming
Object-oriented programming (OOP) is a programming paradigm based on the concept of '' objects''. Objects can contain data (called fields, attributes or properties) and have actions they can perform (called procedures or methods and implemented in code). In OOP, computer programs are designed by making them out of objects that interact with one another. Many of the most widely used programming languages (such as C++, Java, and Python) support object-oriented programming to a greater or lesser degree, typically as part of multiple paradigms in combination with others such as imperative programming and declarative programming. Significant object-oriented languages include Ada, ActionScript, C++, Common Lisp, C#, Dart, Eiffel, Fortran 2003, Haxe, Java, JavaScript, Kotlin, Logo, MATLAB, Objective-C, Object Pascal, Perl, PHP, Python, R, Raku, Ruby, Scala, SIMSCRIPT, Simula, Smalltalk, Swift, Vala and Visual Basic.NET. History The idea of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inheritance (object-oriented Programming)
In object-oriented programming, inheritance is the mechanism of basing an Object (computer science), object or Class (computer programming), class upon another object (Prototype-based programming, prototype-based inheritance) or class (Class-based programming, class-based inheritance), retaining similar implementation. Also defined as deriving new classes (#Subclasses and superclasses, sub classes) from existing ones such as super class or Fragile base class, base class and then forming them into a hierarchy of classes. In most class-based object-oriented languages like C++, an object created through inheritance, a "child object", acquires all the properties and behaviors of the "parent object", with the exception of: Constructor (object-oriented programming), constructors, destructors, operator overloading, overloaded operators and friend functions of the base class. Inheritance allows programmers to create classes that are built upon existing classes, to specify a new implementat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strict Subset
In mathematics, a set ''A'' is a subset of a set ''B'' if all elements of ''A'' are also elements of ''B''; ''B'' is then a superset of ''A''. It is possible for ''A'' and ''B'' to be equal; if they are unequal, then ''A'' is a proper subset of ''B''. The relationship of one set being a subset of another is called inclusion (or sometimes containment). ''A'' is a subset of ''B'' may also be expressed as ''B'' includes (or contains) ''A'' or ''A'' is included (or contained) in ''B''. A ''k''-subset is a subset with ''k'' elements. When quantified, A \subseteq B is represented as \forall x \left(x \in A \Rightarrow x \in B\right). One can prove the statement A \subseteq B by applying a proof technique known as the element argument:Let sets ''A'' and ''B'' be given. To prove that A \subseteq B, # suppose that ''a'' is a particular but arbitrarily chosen element of A # show that ''a'' is an element of ''B''. The validity of this technique can be seen as a consequence of univers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nested Hierarchy
A hierarchy (from Greek: , from , 'president of sacred rites') is an arrangement of items (objects, names, values, categories, etc.) that are represented as being "above", "below", or "at the same level as" one another. Hierarchy is an important concept in a wide variety of fields, such as architecture, philosophy, design, mathematics, computer science, organizational theory, systems theory, systematic biology, and the social sciences (especially political science). A hierarchy can link entities either directly or indirectly, and either vertically or diagonally. The only direct links in a hierarchy, insofar as they are hierarchical, are to one's immediate superior or to one of one's subordinates, although a system that is largely hierarchical can also incorporate alternative hierarchies. Hierarchical links can extend "vertically" upwards or downwards via multiple links in the same direction, following a path. All parts of the hierarchy that are not linked vertically to one anothe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Biological Classification
In biology, taxonomy () is the scientific study of naming, defining ( circumscribing) and classifying groups of biological organisms based on shared characteristics. Organisms are grouped into taxa (singular: taxon), and these groups are given a taxonomic rank; groups of a given rank can be aggregated to form a more inclusive group of higher rank, thus creating a taxonomic hierarchy. The principal ranks in modern use are domain, kingdom, phylum (''division'' is sometimes used in botany in place of ''phylum''), class, order, family, genus, and species. The Swedish botanist Carl Linnaeus is regarded as the founder of the current system of taxonomy, having developed a ranked system known as Linnaean taxonomy for categorizing organisms. With advances in the theory, data and analytical technology of biological systematics, the Linnaean system has transformed into a system of modern biological classification intended to reflect the evolutionary relationships among organisms, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stockholm
Stockholm (; ) is the Capital city, capital and List of urban areas in Sweden by population, most populous city of Sweden, as well as the List of urban areas in the Nordic countries, largest urban area in the Nordic countries. Approximately 1 million people live in the Stockholm Municipality, municipality, with 1.6 million in the Stockholm urban area, urban area, and 2.5 million in the Metropolitan Stockholm, metropolitan area. The city stretches across fourteen islands where Mälaren, Lake Mälaren flows into the Baltic Sea. Outside the city to the east, and along the coast, is the island chain of the Stockholm archipelago. The area has been settled since the Stone Age, in the 6th millennium BC, and was founded as a city in 1252 by Swedish statesman Birger Jarl. The city serves as the county seat of Stockholm County. Stockholm is the cultural, media, political, and economic centre of Sweden. The Stockholm region alone accounts for over a third of the country's Gros ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Systema Naturae
' (originally in Latin written ' with the Orthographic ligature, ligature æ) is one of the major works of the Sweden, Swedish botanist, zoologist and physician Carl Linnaeus (1707–1778) and introduced the Linnaean taxonomy. Although the system, now known as binomial nomenclature, was partially developed by the Bauhin brothers, Gaspard Bauhin, Gaspard and Johann Bauhin, Johann, Linnaeus was the first to use it consistently throughout his book. The first edition was published in 1735. The full title of the 10th edition (1758), which was the most important one, was ', which appeared in English in 1806 with the title: "A General System of Nature, Through the Three Grand Kingdoms of Animals, Vegetables, and Minerals, Systematically Divided Into their Several Classes, Orders, Genera, Species, and Varieties, with their Habitations, Manners, Economy, Structure and Peculiarities". The 10th edition of Systema Naturae, tenth edition of this book (1758) is considered the starting point of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linnaean Taxonomy
Linnaean taxonomy can mean either of two related concepts: # The particular form of biological classification (taxonomy) set up by Carl Linnaeus, as set forth in his ''Systema Naturae'' (1735) and subsequent works. In the taxonomy of Linnaeus there are three kingdoms, divided into ''classes'', and the classes divided into lower ranks in a hierarchical order. # A term for rank-based classification of organisms, in general. That is, taxonomy in the traditional sense of the word: rank-based scientific classification. This term is especially used as opposed to cladistic systematics, which groups organisms into clades. It is attributed to Linnaeus, although he neither invented the concept of ranked classification (it goes back to Plato and Aristotle) nor gave it its present form. In fact, it does not have an exact present form, as "Linnaean taxonomy" as such does not really exist: it is a collective (abstracting) term for what actually are several separate fields, which use similar a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taxonomy (general)
280px, Generalized scheme of taxonomy Taxonomy is a practice and science concerned with classification or categorization. Typically, there are two parts to it: the development of an underlying scheme of classes (a taxonomy) and the allocation of things to the classes (classification). Originally, taxonomy referred only to the classification of organisms on the basis of shared characteristics. Today it also has a more general sense. It may refer to the classification of things or concepts, as well as to the principles underlying such work. Thus a taxonomy can be used to organize species, documents, videos or anything else. A taxonomy organizes taxonomic units known as "taxa" (singular "taxon"). Many are hierarchies. One function of a taxonomy is to help users more easily find what they are searching for. This may be effected in ways that include a library classification system and a search engine taxonomy. Etymology The word was coined in 1813 by the Swiss botanist A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
