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Enumerative Definition
An enumerative definition of a concept or term is a special type of extensional definition that gives an explicit and exhaustive listing of all the objects that fall under the concept or term in question. Enumerative definitions are only possible for finite sets and only practical for relatively small sets. Example An example of an enumerative definition for the set extant monotreme species (for which the intensional definition is "species of currently-living mammals that lay eggs") would be: : platypuses : echidnae: :: short-beaked echidna :: long-beaked echidnae: ::: Sir David's long-beaked echidna ::: eastern long-beaked echidna ::: western long-beaked echidna See also * Definition * Extension * Extensional definition * Set notation * Enumeration An enumeration is a complete, ordered listing of all the items in a collection. The term is commonly used in mathematics and computer science to refer to a listing of all of the element (mathematics), elements of a Set ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extensional Definition
In logic, extensional and intensional definitions are two key ways in which the objects, concepts, or referents a term refers to can be defined. They give meaning or denotation to a term. An intensional definition gives meaning to a term by specifying necessary and sufficient conditions for when the term should be used. An extensional definition gives meaning to a term by specifying every object that falls under the definition of the term in question. For example, in set theory one would extensionally define the set of square numbers as , while an intensional definition of the set of the square numbers could be . Intensional definition An intensional definition gives meaning to a term by specifying necessary and sufficient conditions for when the term should be used. In the case of nouns, this is equivalent to specifying the properties that an object needs to have in order to be counted as a referent of the term. For example, an intensional definition of the word "bache ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eastern Long-beaked Echidna
The eastern long-beaked echidna (''Zaglossus bartoni''), also known as Barton's long-beaked echidna, is one of three species from the genus ''Zaglossus'' to occur in New Guinea. It is found mainly in the eastern half at elevations between . Description The eastern long-beaked echidna can be distinguished from other members of the genus by the number of claws on the fore and hind feet: it has five claws on its fore feet and four on its hind feet. Its weight varies from ; its body length ranges from ; it has no tail. It has dense black fur. It rolls into a spiny ball for defense. They have a lifespan of roughly 30 years. Like the closely related platypus, echidnas have spurs on their hind legs. Unlike the platypus, echidna spurs are not venomous. All eastern long-beaked echidnas start with spurs on their hind feet and spur sheaths that cover them. Females typically lose their spurs later in life while males keep them. Females are also generally larger than males. Body mass tends to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Enumeration
An enumeration is a complete, ordered listing of all the items in a collection. The term is commonly used in mathematics and computer science to refer to a listing of all of the element (mathematics), elements of a Set (mathematics), set. The precise requirements for an enumeration (for example, whether the set must be finite set, finite, or whether the list is allowed to contain repetitions) depend on the discipline of study and the context of a given problem. Some sets can be enumerated by means of a natural ordering (such as 1, 2, 3, 4, ... for the set of positive integers), but in other cases it may be necessary to impose a (perhaps arbitrary) ordering. In some contexts, such as enumerative combinatorics, the term ''enumeration'' is used more in the sense of ''counting'' – with emphasis on determination of the number of elements that a set contains, rather than the production of an explicit listing of those elements. Combinatorics In combinatorics, enumeration means cou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Set Notation
In mathematics and more specifically in set theory, set-builder notation is a notation for specifying a set by a property that characterizes its members. Specifying sets by member properties is allowed by the axiom schema of specification. This is also known as set comprehension and set abstraction. Sets defined by a predicate Set-builder notation can be used to describe a set that is defined by a predicate, that is, a logical formula that evaluates to ''true'' for an element of the set, and ''false'' otherwise. In this form, set-builder notation has three parts: a variable, a colon or vertical bar separator, and a predicate. Thus there is a variable on the left of the separator, and a rule on the right of it. These three parts are contained in curly brackets: :\ or :\. The vertical bar (or colon) is a separator that can be read as "such that", "for which", or "with the property that". The formula is said to be the ''rule'' or the ''predicate''. All values of for which th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extensional Definition
In logic, extensional and intensional definitions are two key ways in which the objects, concepts, or referents a term refers to can be defined. They give meaning or denotation to a term. An intensional definition gives meaning to a term by specifying necessary and sufficient conditions for when the term should be used. An extensional definition gives meaning to a term by specifying every object that falls under the definition of the term in question. For example, in set theory one would extensionally define the set of square numbers as , while an intensional definition of the set of the square numbers could be . Intensional definition An intensional definition gives meaning to a term by specifying necessary and sufficient conditions for when the term should be used. In the case of nouns, this is equivalent to specifying the properties that an object needs to have in order to be counted as a referent of the term. For example, an intensional definition of the word "bache ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extension (semantics)
In any of several fields of study that treat the use of signs — for example, in linguistics, logic, mathematics, semantics, semiotics, and philosophy of language — the extension of a concept, idea, or sign consists of the things to which it applies, in contrast with its comprehension (logic), comprehension or intension, which consists very roughly of the ideas, properties, or corresponding signs that are implied or suggested by the concept in question. In philosophical semantics or the philosophy of language, the 'extension' of a concept or expression is the set of things it extends to, or applies to, if it is the sort of concept or expression that a single object by itself can satisfy. Concepts and expressions of this sort are monad (Greek philosophy), monadic or "one-place" concepts and expressions. So the extension of the word "dog" is the set of all (past, present and future) dogs in the world: the set includes Fido, Rover, Lassie, Rex, and so on. The extension of the ph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Definition
A definition is a statement of the meaning of a term (a word, phrase, or other set of symbols). Definitions can be classified into two large categories: intensional definitions (which try to give the sense of a term), and extensional definitions (which try to list the objects that a term describes).Lyons, John. "Semantics, vol. I." Cambridge: Cambridge (1977). p.158 and on. Another important category of definitions is the class of ostensive definitions, which convey the meaning of a term by pointing out examples. A term may have many different senses and multiple meanings, and thus require multiple definitions. In mathematics, a definition is used to give a precise meaning to a new term, by describing a condition which unambiguously qualifies what the mathematical term is and is not. Definitions and axioms form the basis on which all of modern mathematics is to be constructed. Basic terminology In modern usage, a definition is something, typically expressed in words, that at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Western Long-beaked Echidna
The western long-beaked echidna (''Zaglossus bruijnii'') is one of the four Extant taxon, extant echidnas and one of three species of ''Zaglossus'' that occurs in New Guinea. Originally described as ''Tachyglossus bruijnii'', this is the type species of ''Zaglossus''. Description The western long-beaked echidna is an egg-laying mammal. Unlike the short-beaked echidna, which eats ants and termites, the long-beaked species eats earthworms. The long-beaked echidna is also larger than the short-beaked species, reaching up to ; the snout is longer and turns downward; and the spines are almost indistinguishable from the long fur. It is distinguished from the other ''Zaglossus'' species by the number of claws on the fore and hind feet: three (rarely four). It is the Largest mammals#Monotreme mammals .28Monotremata.29, largest extant monotreme. Distribution and habitat The species is found in the Bird's Head Peninsula, Bird's Head and Bomberai Peninsulas in Western New Guinea of Indo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sir David's Long-beaked Echidna
''Zaglossus attenboroughi'', also known as Attenborough's long-beaked echidna or locally as Payangko, is one of three species from the genus ''Zaglossus'' that inhabits the island of New Guinea. It lives in the Cyclops Mountains, which are near the cities of Sentani and Jayapura in the Indonesian province of Papua in Western New Guinea. It is named in honour of naturalist Sir David Attenborough. It is currently classified as critically endangered by the IUCN, and there had been no confirmed sightings between its initial collection in 1961 and November 2023, when the first video footage of a living individual was recorded. Taxonomy The early taxonomy of ''Zaglossus'' saw several different specimens described as separate species or subspecies, but by the late 1960s, the genus was considered to be monotypic, pending a comprehensive evaluation of collected specimens. Subsequent systematic revision of ''Zaglossus'' by Flannery & Groves in 1998 identified three allopatric species ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Object (philosophy)
The distinction between subject and object is a basic idea of philosophy. *A subject is a being that exercises Agency (philosophy), agency, undergoes conscious experiences, and is situated in relation to other things that exist outside itself; thus, a subject is any individual, person, or observer. *An object is any of the things observed or experienced by a subject, which may even include other beings (thus, from their own points of view: other subjects). A simple common differentiation for ''subject'' and ''object'' is: an observer versus a thing that is observed. In certain cases involving personhood, subjects and objects can be considered interchangeable where each label is applied only from one or the other point of view. Subjects and objects are related to the philosophical distinction between Subjectivity and objectivity (philosophy), subjectivity and objectivity: the existence of knowledge, ideas, or information either dependent upon a subject (subjectivity) or independent f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Short-beaked Echidna
The short-beaked echidna (''Tachyglossus aculeatus''), also called the short-nosed echidna, is one of four living species of echidna, and the only member of the genus ''Tachyglossus'', from Ancient Greek (), meaning "fast", and (), meaning "tongue". It is covered in fur and spines and has a distinctive snout and a specialised tongue, which it uses to catch its insect prey at a great speed. Like the other extant monotremes, the short-beaked echidna lays eggs; the monotremes are the only living group of mammals to do so. The short-beaked echidna has extremely strong front limbs and claws, which allow it to burrow quickly with great power. As it needs to be able to survive underground, it has a significant tolerance to high levels of carbon dioxide and low levels of oxygen. It has no weapons or fighting ability but deters predators by curling into a ball and protecting itself with its spines. It cannot sweat or deal well with heat, so it tends to avoid daytime activity in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Platypus
The platypus (''Ornithorhynchus anatinus''), sometimes referred to as the duck-billed platypus, is a semiaquatic, egg-laying mammal endemic to eastern Australia, including Tasmania. The platypus is the sole living representative or monotypic taxon of its family Ornithorhynchidae and genus ''Ornithorhynchus'', though a number of related species appear in the fossil record. Together with the four species of echidna, it is one of the five extant species of monotremes, mammals that lay eggs instead of giving birth to live young. Like other monotremes, the platypus has a sense of electrolocation, which it uses to detect prey in cloudy water. It is one of the few species of venomous mammals, as the male platypus has a spur on the hind foot that delivers an extremely painful venom. The unusual appearance of this egg-laying, duck-billed, beaver-tailed, otter-footed mammal at first baffled European naturalists. In 1799, the first scientists to examine a preserved platypus bod ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
