|
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] |
