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Numerosity
Numerosity may refer to: Cognitive science * Numerical cognition, a subdiscipline of cognitive science that studies the cognitive, developmental and neural bases of numbers and mathematics. Mathematics * Numerosity (mathematics), a theory for counting the number of elements of sets having infinite elements. It is a theory that refines Cantor's cardinality. Psychology * Number sense In psychology, number sense is the term used for the hypothesis that some animals, particularly humans, have a biologically determined ability that allows them to represent and manipulate large numerical quantities. The term was popularized by ..., a term used for the hypothesis that some animals, particularly humans, have a biologically determined ability that allows them to represent and manipulate large numerical quantities. [Baidu] |
Numerosity (mathematics)
The numerosity of an infinite set, as ininitally introduced by the Italian mathematician Vieri Benci and later on extended with the help of Mauro Di Nasso and Marco Forti, is a concept that develops Cantor’s notion of cardinality. While Cantor’s classical cardinality classifies sets based on the existence of a one-to-one correspondence with other sets (defining, for example, \aleph_0 for countable sets, \aleph_1 and so on for larger infinities), the idea of numerosity aims to provide an alternative viewpoint, linking to the common Euclidean notion that "the whole is greater than the part". All of this naturally leads to the hypernatural numbers. In short, Benci and his collaborators propose associating with an infinite set a numerical value that more directly reflects its “number of elements”, without resorting solely to one-to-one correspondences.Benci, V. (1995). "I Numeri e gli Insiemi Etichettati", Laterza, Bari, Italia. Conferenze del seminario di matematica dell' U ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cardinality
The thumb is the first digit of the hand, next to the index finger. When a person is standing in the medical anatomical position (where the palm is facing to the front), the thumb is the outermost digit. The Medical Latin English noun for thumb is ''pollex'' (compare ''hallux'' for big toe), and the corresponding adjective for thumb is ''pollical''. Definition Thumb and fingers The English word ''finger'' has two senses, even in the context of appendages of a single typical human hand: 1) Any of the five terminal members of the hand. 2) Any of the four terminal members of the hand, other than the thumb. Linguistically, it appears that the original sense was the first of these two: (also rendered as ) was, in the inferred Proto-Indo-European language, a suffixed form of (or ), which has given rise to many Indo-European-family words (tens of them defined in English dictionaries) that involve, or stem from, concepts of fiveness. The thumb shares the following with each of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Cognition
Numerical cognition is a subdiscipline of cognitive science that studies the cognitive, developmental and neural bases of numbers and mathematics. As with many cognitive science endeavors, this is a highly interdisciplinary topic, and includes researchers in cognitive psychology, developmental psychology, neuroscience and cognitive linguistics. This discipline, although it may interact with questions in the philosophy of mathematics, is primarily concerned with empirical questions. Topics included in the domain of numerical cognition include: *How do non-human animals process numerosity? *How do infants acquire an understanding of numbers (and how much is inborn)? *How do humans associate linguistic symbols with numerical quantities? *How do these capacities underlie our ability to perform complex calculations? *What are the neural bases of these abilities, both in humans and in non-humans? *What metaphorical capacities and processes allow us to extend our numerical understandi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number Sense
In psychology, number sense is the term used for the hypothesis that some animals, particularly humans, have a biologically determined ability that allows them to represent and manipulate large numerical quantities. The term was popularized by Stanislas Dehaene in his 1997 book "The Number Sense," but originally named by the mathematician Tobias Dantzig in his 1930 text Number: The Language of Science. Psychologists believe that the number sense in humans can be differentiated into the approximate number system, a system that supports the estimation of the magnitude, and the parallel individuation system, which allows the tracking of individual objects, typically for quantities below 4. There are also some differences in how number sense is defined in math cognition. For example, Gersten and Chard say number sense "refers to a child's fluidity and flexibility with numbers, the sense of what numbers mean and an ability to perform mental mathematics and to look at the world ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
