Subject:
All Disciplines Arts & Humanities Biology & Life Sciences Business & Economics Chemistry & Materials Science Computer Science & Mathematics Engineering Environmental & Earth Sciences Medicine & Pharmacology Physical Sciences Public Health & Healthcare Social Sciences
Sort:
Hottest Latest Alphabetical (A-Z) Alphabetical (Z-A)
Type:
All Topic Review Biography
Topic Review
Limit Point
In mathematics, a limit point (or cluster point or accumulation point) of a set [math]\displaystyle{ S }[/math] in a topological space [math]\displaystyle{ X }[/math] is a point [math]\displaystyle{ x }[/math] that can be "approximated" by points of [math]\displaystyle{ S }[/math] in the sense that every neighbourhood of [math]\displaystyle{ x }[/math] with respect to the topology on [math]\displaystyle{ X }[/math] also contains a point of [math]\displaystyle{ S }[/math] other than [math]\displaystyle{ x }[/math] itself. A limit point of a set [math]\displaystyle{ S }[/math] does not itself have to be an element of [math]\displaystyle{ S. }[/math] There is also a closely related concept for sequences. A cluster point or accumulation point of a sequence [math]\displaystyle{ (x_n)_{n \in \mathbb{N}} }[/math] in a topological space [math]\displaystyle{ X }[/math] is a point [math]\displaystyle{ x }[/math] such that, for every neighbourhood [math]\displaystyle{ V }[/math] of [math]\displaystyle{ x, }[/math] there are infinitely many natural numbers [math]\displaystyle{ n }[/math] such that [math]\displaystyle{ x_n \in V. }[/math] This definition of a cluster or accumulation point of a sequence generalizes to nets and filters. In contrast to sets, for a sequence, net, or filter, the term "limit point" is not synonymous with a "cluster/accumulation point"; by definition, the similarly named notion of a limit point of a filter (respectively, a limit point of a sequence, a limit point of a net) refers to a point that the filter converges to (respectively, the sequence converges to, the net converges to). The limit points of a set should not be confused with adherent points for which every neighbourhood of [math]\displaystyle{ x }[/math] contains a point of [math]\displaystyle{ S }[/math]. Unlike for limit points, this point of [math]\displaystyle{ S }[/math] may be [math]\displaystyle{ x }[/math] itself. A limit point can be characterized as an adherent point that is not an isolated point. Limit points of a set should also not be confused with boundary points. For example, [math]\displaystyle{ 0 }[/math] is a boundary point (but not a limit point) of set [math]\displaystyle{ \{ 0 \} }[/math] in [math]\displaystyle{ \R }[/math] with standard topology. However, [math]\displaystyle{ 0.5 }[/math] is a limit point (though not a boundary point) of interval [math]\displaystyle{ [0, 1] }[/math] in [math]\displaystyle{ \R }[/math] with standard topology (for a less trivial example of a limit point, see the first caption). This concept profitably generalizes the notion of a limit and is the underpinning of concepts such as closed set and topological closure. Indeed, a set is closed if and only if it contains all of its limit points, and the topological closure operation can be thought of as an operation that enriches a set by uniting it with its limit points.
  • 4.9K
  • 25 Oct 2022
Topic Review
Product Distribution
A product distribution is a probability distribution constructed as the distribution of the product of random variables having two other known distributions. Given two statistically independent random variables X and Y, the distribution of the random variable Z that is formed as the product is a product distribution.
  • 4.8K
  • 11 Nov 2022
Topic Review
The Sims 2 Stuff Packs
Stuff packs are minor expansion packs for The Sims 2 that add new items, clothing, and furniture to the game without implementing any significant changes to gameplay.
  • 4.8K
  • 17 Nov 2022
Topic Review
Fresh Fruit Supply Chain Optimization
The fresh fruit chain has been recognized as a very important and strategic part of the economic development of many countries. The planning framework for production and distribution is highly complex as a result. Mathematical models have been developed over the decades to deal with this complexity. This review focuses on the recent progress in mathematically based decision making to account for uncertainties in the fresh fruit supply chain
  • 4.8K
  • 27 Jul 2021
Topic Review
Feature Detection (Computer Vision)
In computer vision and image processing feature detection includes methods for computing abstractions of image information and making local decisions at every image point whether there is an image feature of a given type at that point or not. The resulting features will be subsets of the image domain, often in the form of isolated points, continuous curves or connected regions.
  • 4.7K
  • 10 Oct 2022
Topic Review
Home Economics
Home economics, or family and consumer sciences, is a subject concerning human development, personal and family finances, consumer issues, housing and interior design, nutrition and food preparation, as well as textiles and apparel. Home economics courses are offered around the world and across multiple educational levels. Internationally, it is coordinated by the International Federation for Home Economics. Historically, the purpose of these courses was to professionalize housework, to provide intellectual fulfillment for women, and to emphasize the value of "women's work" in society and to prepare them for the traditional roles of sexes. However, it has since evolved into family and consumer sciences to cover additional subject matter outside of just home life and wellness. Family and consumer sciences are taught as an elective or required course in secondary education, as a continuing education course in institutions, and at the primary level.   Beginning as home economics in the United States, the course was a key part of the education system for teaching one the art of taking care of a household. In the 19th and early 20th century, it was a woman-dominated course, teaching women to be homemakers and efficient household managers. The American Association of Family and Consumer Sciences was created as an answer to more Americans desiring youth to learn vocational skills. Politics played a role in home economics education, and it wasn’t until later in the century that the course shifted from being woman-dominated to now required for both sexes.   Now family and consumer science have been included in the broader subject of Career Technical Education, a program that teaches skilled trades, applied sciences, modern technologies, and career preparation. Despite the subjects over the past century, there has been a major decline in home economics courses offered by educational institutions.  
  • 4.7K
  • 09 Nov 2022
Topic Review
Major Applications of Smart Agriculture
With the rise of new technologies, such as the Internet of Things, raising the productivity of agricultural and farming activities is critical to improving yields and cost-effectiveness. IoT, in particular, can improve the efficiency of agriculture and farming processes by eliminating human intervention through automation. The fast rise of Internet of Things (IoT)-based tools has changed nearly all life sectors, including business, agriculture, surveillance, etc. These radical developments are upending traditional agricultural practices and presenting new options in the face of various obstacles.
  • 4.7K
  • 24 Jan 2022
Topic Review
Pentium FDIV Bug
The Pentium FDIV bug is a hardware bug affecting the floating point unit (FPU) of the early Intel Pentium processors. Because of the bug, the processor might return incorrect binary floating point results when dividing a number. The bug was discovered in 1994 by Professor Thomas R. Nicely at Lynchburg College. Intel attributed the error to missing entries in the lookup table used by the floating-point division circuitry. The severity of the FDIV bug is debated. Though rarely encountered by most users (Byte magazine estimated that 1 in 9 billion floating point divides with random parameters would produce inaccurate results), both the flaw and Intel's initial handling of the matter were heavily criticized by the tech community. In December 1994, Intel recalled the defective processors. In January 1995, Intel announced "a pre-tax charge of $475 million against earnings, ostensibly the total cost associated with replacement of the flawed processors."
  • 4.7K
  • 04 Nov 2022
Topic Review
Features New to Windows 7
Some of the new features included in Windows 7 are advancements in touch, speech and handwriting recognition, support for virtual hard disks, support for additional file formats, improved performance on multi-core processors, improved boot performance, and kernel improvements. Some of the features which are present in versions up to and including Windows Vista were removed or changed.
  • 4.7K
  • 15 Nov 2022
Topic Review
Prime Video
Prime Video, also marketed as Amazon Prime Video, is an American Internet video on demand service that is developed, owned, and operated by Amazon. It offers television shows and films for rent or purchase and Prime Video, a selection of Amazon Studios original content and licensed acquisitions included in the Amazon's Prime subscription. In the United Kingdom , United States , Germany , and many other territories, access to Prime Video is also available through a video-only membership, which does not require a full Prime subscription. In France and Italy, and other countries like Australia , Canada , India , etc. Prime Video content is only accessible through a dedicated Prime Video website. In some countries Prime Video additionally offers Amazon Channels, which allows viewers to subscribe to other suppliers' content, including HBO in the United States. Launched on September 7, 2006 as Amazon Unbox in the United States, the service grew with its expanding library, and added the Prime Video membership with the development of Prime. It was then renamed as Amazon Instant Video on Demand. After acquiring the local streaming and DVD-by-mail service LoveFilm in 2011, Prime Video was added to Prime in the United Kingdom, Germany and Austria in 2014, a move that angered some Prime UK members as the bundling was non-negotiable with a 61% increase in subscription fee. In the UK, Germany, and Austria, Prime Video has been available on a monthly subscription of £5.99 or €7.99 per month, continuing the plan of LoveFilm Instant. The service was previously available in Norway , Denmark and Sweden in 2012, but was discontinued in 2013. On April 18, 2016, Amazon split Prime Video from Amazon Prime in the US for $8.99 per month. The service also hosts Amazon Original content alongside titles on Video as well. On December 14, 2016, Prime Video launched worldwide (except for Mainland China, Cuba, Iran, North Korea, Syria) expanding its reach beyond the US, the UK, Germany, Austria, and Japan. Among the new territories, the service was included with Prime in Belgium, Canada , France , India , Italy, Spain , Poland , and Brazil , while for all other countries – for instance Bulgaria – it was made available for a monthly promotional price of $/€2.99 per month for the first six months and $/€5.99 per month thereafter.
  • 4.6K
  • 29 Nov 2022
  • Page
  • of
  • 371
Featured Entry Collections
>>

Featured Books

>>
Encyclopedia of Social Sciences
Encyclopedia of COVID-19
Encyclopedia of Fungi
Encyclopedia of Digital Society, Industry 5.0 and Smart City
Video Production Service
Feedback