In mathematics, the cardinality of a set is a measure of the "number of elements of the set". For example, the set A = contains 3 elements, therefore A has a cardinality of 3. Beginning in the late 19th century, this concept was generalized to infinite sets, allowing to distinguish several stages of infinity, to perform arithmetic on them. There are two approaches to cardinality – one which compares sets directly using bijections and injections, another which uses cardinal numbers; the cardinality of a set is called its size, when no confusion with other notions of size is possible. The cardinality of a set A is denoted | A |, with a vertical bar on each side. Alternatively, the cardinality of a set A may be denoted by n, A, card ⁡, or # A. While the cardinality of a finite set is just the number of its elements, extending the notion to infinite sets starts with defining the notion of comparison of arbitrary sets. Two sets A and B have the same cardinality if there exists a bijection from A to B, that is, a function from A to B, both injective and surjective.

Such sets are said to be equipollent, or equinumerous. This relationship can be denoted A ≈ B or A ~ B. For example, the set E = of non-negative numbers has the same cardinality as the set N = of natural numbers, since the function f = 2n is a bijection from N to E, see picture. A has cardinality less than or equal to the cardinality of B if there exists an injective function from A into B. A has cardinality less than the cardinality of B if there is an injective function, but no bijective function, from A to B. For example, the set N of all natural numbers has cardinality less than its power set P, because g = is an injective function from N to P, it can be shown that no function from N to P can be bijective, see picture. By a similar argument, N has cardinality less than the cardinality of the set R of all real numbers, see Cantor's diagonal argument or Cantor's first uncountability proof. If |A| ≤ |B| and |B| ≤ |A| |A| = |B|; the axiom of choice is equivalent to the statement that |A| ≤ |B| or |B| ≤ |A| for every A, B.

Above, "cardinality" was defined functionally. That is, the "cardinality" of a set was not defined as a specific object itself. However, such an object can be defined; the relation of having the same cardinality is called equinumerosity, this is an equivalence relation on the class of all sets. The equivalence class of a set A under this relation consists of all those sets which have the same cardinality as A. There are two ways to define the "cardinality of a set": The cardinality of a set A is defined as its equivalence class under equinumerosity. A representative set is designated for each equivalence class; the most common choice is the initial ordinal in that class. This is taken as the definition of cardinal number in axiomatic set theory. Assuming the axiom of choice, the cardinalities of the infinite sets are denoted ℵ 0 < ℵ 1 < ℵ 2 < …. For each ordinal α, ℵ α + 1 is the least cardinal number greater than ℵ α; the cardinality of the natural numbers is denoted aleph-null, while the cardinality of the real numbers is denoted by " c ", is referred to as the cardinality of the continuum.

Cantor showed, using the diagonal argument, that c > ℵ 0. We can show that c = 2 ℵ 0, this being the cardinality of the set of all subsets of the natural numbers; the continuum hypothesis says that ℵ 1 = 2 ℵ 0, i.e. 2 ℵ 0 is the smallest cardinal number bigger than ℵ 0, i.e. there is no set whose cardinality is between that of the integers and that of the real numbers. The continuum hypothesis is independent of a standard axiomatization of set theory. See below for more details on the cardinality of the continuum. If the axiom of choice holds, the law of trichotomy holds for cardinality, thus we can make the following definitions: Any set X with cardinality less than that of the natural numbers, or | X | < | N |, is said to be a finite set. Any set X that has the same cardinality as the set of the natural num

Knabs Ridge Wind Farm is an electricity generating site just south of the A59 road near to Felliscliffe, North Yorkshire, England. It was the first wind farm to be built in North Yorkshire in over 15 years, was believed to be the first time that civilian air traffic was considered in the planning permission process; the proposal to build a wind farm on the site was first unveiled in 2003 when 6,000 homes in the area were leafleted with information about the wind farm. At that early stage, many objections were registered, including one from the Campaign for the Protection of Rural England. Planning consent for the wind farm was rejected by Harrogate Borough Council in November 2004; the management team at Leeds Bradford Airport, whose runway is only 10 miles south of the site, stated that the farm would have a detrimental effect on air traffic control as it could create false indications of aircraft. Other objectors pointed out that the site of was only 50 feet away from the Nidderdale AONB. Npower appealed against the decision and the application went before a public enquiry, which gained government consent in September 2005.

The objection by LBA towards the wind farm is believed to be the first time that civilian air traffic paths have featured in an onshore wind farm consent inquiry. The planning inspector rejected the idea of affixing red lights to each tower as it was thought that they could interfere with drivers concentration on the adjacent A59 road. Building of the £13 million wind farm 3 miles west of Harrogate in Felliscliffe by the A59 road, was started in March 2007, completed by the summer of 2008 with full commissioning of the site starting in November of the same year; the wind farm consists of eight towers which are 190 feet high, with the addition of the rotors, the full height that they extend to is 305 feet. The site covers an area of 197 acres at an elevation of 708 feet above sea level, so they can be seen from some distance away; each generating unit was constructed by Senvion and is capable of generating 2 mW of power with the whole farm itself generating 16 mW in total. This provides enough electricity per year to power 7,000 homes and offsets over 23,000 tonnes of carbon dioxide going into the environment on an annual basis.

One of the turbines caught fire in January 2017 and had to be extinguished by North Yorkshire fire service. Each unit operates in tandem with three others which resulted in all four generating units being turned off. Seven months after the fire, the owners were seeking to overturn a condition in the planning permission of the site, set in 2005. If a turbine was to not generate power in over twelve months the owners are required to remove the tower and return the land to grazing purposes for cattle. By October 2017, the tower was still not active. List of onshore wind farms in the United Kingdom Key facts PDF sheet

Terral is the third studio album by Spanish singer-songwriter Pablo Alborán, scheduled to be released 11 November 2014 through Warner Music. The album was composed and produced by Eric Rosse. Terral earned a nomination for Best Contemporary Pop Vocal Album at the 16th Latin Grammy Awards and for Best Latin Pop Album at the 58th Annual Grammy Awards. A "French Version" of the album was released on 29 January 2016. "Por Fin" was released as the album's lead single on September 16, 2014. The song debuted at number 1 on the Spanish Singles Chart, it has so far spent two consecutive weeks at number one. "Pasos de cero" was the second single released as a pre-order single on October 7, 2014. On January 21, 2015 the song was released as the second single, with the music video for the song premiering the same day. "Recuérdame" was released on May 31, 2015 as the third official single, along with the music video for the song. "La Escalera" was released on October 28, 2015 as the fourth and final single, along with the music video.

Terral – French edition All tracks are written by Pablo Alborán

Violence against women is an entrenched social problem in Ukrainian culture engendered by traditional male and female stereotypes. It was not recognized during Soviet era, but in recent decades the issue became an important topic of discussion in Ukrainian society and among academic scholars. Nuzhat Ehsan, UN Population Fund representative in Ukraine, stated in February 2013 “Ukraine has an unacceptable level of violence by men and due to high level of alcohol consumption”, he blamed loopholes in the legislation contribute to the problem of domestic violence, “You can violate women and still if you are a high-level official or from a high-level official family, you can get away with it”. In the view of traditional morale norms the Ukrainian women are supposed "to be beautiful and to be a mother". Moreover, the gender traditions in Ukraine tend to restrict women from holding positions of political power, while standards of male behaviour include being protective of women; the ongoing War in Donbass in Ukraine's Donbass region is believed to have reinforced the separation of gender responsibilities.

But the UN reports the Ukrainian women living in the conflict zone are at significant risk due to weak law enforcement, high concentration of military groups and proliferation of weapons. In 2015 the Office of the United Nations High Commissioner for Human Rights expressed a deep concern about worsening situation with violence against women in Ukraine. According to the estimation of OSCE the violence towards women is widespread in Ukraine and it is associated with three times more deaths than the ongoing War in Donbass in the Donbass region of Ukraine. According to latest UN Report around 45 percent of Ukraine’s population suffers violence – physical, sexual or mental – and most of them are women. From the historical point of view the problem of violence against women in Ukraine was always surrounded by silence. There are not too many sources of official statistics to estimate; this fact brings understanding that the mass media is unsure how to approach the issue, the authorities do not know how to deal with the manifestations of the violence and the nation doesn't know how to mobilize the public to end the violence.

As a result all national anti-violence efforts rely on considerable support from Western donors A few available statistics indicate that the violence inherent in the poverty where most part of Ukrainian women live. The recorded data demonstrate that the observed value is just a minor fraction of a real figure due to a combined influence of traditions and personal shame. In Ukraine domestic violence towards women has a long history. There are evidences that the model of male aggressiveness directed towards women is transferred from generation to generation. Recent studies reveal that violence against women is not limited to any particular segment of the Ukrainian population and occurs across all social layers. There are not many Ukrainian women who are have achieved economic independence and own their own home. According to recent research violence against women remains a hidden problem, but it is clear that the ongoing War in Donbass in Ukraine leads to an increase in its prevalence. In early 2020 there were any women's shelters in Ukraine.

The sexual exploitation of women is a broad and serious problem in Ukrainian society. This issue consists of women's trafficking on the transnational markets and coercive prostitution, it comes up as a result of many factors including the impoverishment of significant part of population, soft pornography used by Ukrainian mass media to catch an attention of customers, so on. Statistical data reported by NGOs state that up to one third of young jobless Ukrainian women have been involved to some degree in illegal sex business activities. A survey of young Ukrainian girls performed by All-Ukrainian Committee for the Protection of Children reveals that a sexual abuse of them accounts for high proportion of the abuse victims. For example, it was reported that one Ukrainian girl out of three had experienced sexual harassment, one out of five had suffered physical sexual abuse, one out of ten had been raped. Criminal statistics reports that 55% of registered sexual assaults in Ukraine are directed towards youth under 18, 40% of them or 22% in total - towards children under 14.

In February 2019 domestic violence was made a criminal offense in Ukraine meaning perpetrators could be fined, or sentenced to community service or a prison sentence. Perpetrators could be subjected to a maximum of administrative punishment. According to The Ukrainian Week about 5% of victims report violence to the Ukrainian police. Kobelyanska, Larysa. "Violence and Trafficking in Women in Ukraine". Making the Transition Work for Women in Europe and Central Asia. World Bank Publications. ISBN 0-8213-4662-8. Hrycak, Alexandra. "Global Campaigns to Combat Violence against Women:Theorizing Their Impact in Post-Communist Ukraine". Gender and Society in Ukraine. University of Toronto Press. ISBN 978-1-4426-4064-1. Lucas, Brian. "Gender and conflict in Ukraine". Www.gsdrc.org. K4D Knowledge and Learning for Development. Retrieved 6 September 2018. Ukrainian National Hotline for Prevention of Domestic Violence, Trafficking in Persons and Gender Discrimination: 0 800 500 335 or 116 123

Informatics for Consumer Health is a government initiative coordinated by the National Cancer Institute within the National Institutes of Health. ICH focuses on a coordination of health information and health care delivery that empowers providers to manage care and increases the ability of consumers to gain mastery over their own health; the ICH online initiative involved stakeholders from various sectors—commercial IT, health care, education and advocacy—exchanging ideas and resources to bridge information technology and health care with the goal of improving behavioral support for all consumers. The Informatics for Consumer Health field is related to health informatics, medical informatics, consumer health informatics, eHealth, health information technology. Changing health behaviors is key to improving health outcomes. Research indicates that changes in basic preventive behavior - smoking cessation, better diet and exercise, routine screenings—can lead to potential reductions in disability and death due to cancer, heart disease, diabetes.

Effective consumer health information technology applications hold great promise for encouraging and supporting behavior change. With the behavioral and population health evidence-base as a backdrop, the “Informatics for Consumer Health” came out of to two events that occurred in 2009; the first event occurred in early 2009, when the U. S.-based National Research Council released a report titled “Computational Technology for Effective Healthcare: Immediate Steps and Future Directions”. This report concluded that many of the current deployments of health information technology had become disconnected from their primary objectives: to ensure the health of real consumers in real world settings; the research portfolio in health systems should be rebalanced, authors of the report argued, to emphasize cognitive support for providers and their families over technology development for its own sake. The second event occurred in March 2009, when the U. S. Congress passed the American Recovery and Reinvestment Act of 2009.

Title XIII of the Act referred to as the Health Information Technology for Economic and Clinical Health Act, gave authority to the Department of Health and Human Services to offer incentives. “Meaningful use”, rather than “use” measured in technological terms, was to be gauged in terms of outcomes for patients and their families. In this context, a number of Federal agencies came together to convene the “Informatics for Consumer Health: Summit on Communication and Quality,” in November 2009; the summit brought together nearly 200 leaders from commercial IT, health care, education and advocacy organizations to open a dialogue and begin creating a blueprint for improving health care quality through enhanced behavioral support for consumers across the healthcare spectrum. Key Summit objectives to foster collaborations and spur innovation led to the publication of a special supplement on cyberinfrastructure for consumer health in the American Journal of Preventive Medicine and the development of the online Informatics for Consumer Health platform in 2010.

For three years the platform, informaticsforconsumehealth.org, served as a rallying place for summit stakeholders representing a wide range of sectors to exchange resources that bridge information technology and health care, improve behavioral support for all consumers. By sharing news and funding opportunities the ICH community helped disseminate information for facilitating collaboration among the public and research communities to improve consumer health. Goals of the ICH platform included: Serving as a clearinghouse of knowledge for use in the development of high-quality evidence based consumer and clinical health IT products. Creating an interactive portal where stakeholders could communicate and stay up to date on health IT research innovations and opportunities for collaboration and partnership. Learning from key stakeholders about available resources, projects and partnerships in consumer and clinical health IT to disseminate on the ICH platform. Providing a platform for conversation and collaboration around informatics for consumer health.

In 2013, the ICH platform was retired and all original content is now archived on the National Cancer Institute’s Health Communication and Informatics Research Branch website. As the science and practice of behavioral and public health informatics evolve, the activities and initiatives aggregated and posted on the ICH platform continue to be a priority for the public and private sector; the Informatics for Consumer Health initiative is led by a collaboration of Federal agencies with active intramural and extramural programs focused on aspects of consumer health IT. Agency for Healthcare Research and Quality Centers for Disease Control and Prevention National Cancer Institute National Institute of Standards and Technology National Library of Medicine National Science Foundation Office of the National Coordinator for Health Information Technology HCIRB website

The 2018 Donegal Senior Football Championship was the 96th official edition of Donegal GAA's premier Gaelic football tournament for senior graded clubs in County Donegal. Sixteen teams compete with the winner representing Donegal in the Ulster Senior Club Football Championship; the championship continues with a knock-out format. The draws were made on 24 March 2018. Kilcar were the defending champions after they defeated Naomh Conaill of Glenties 0-7 to 0-4 in the 2017 final. However, the club had to play the competition without two of its county stars, Patrick McBrearty and Ryan McHugh. On 26 September 2018, it was announced that McHugh had accepted medical advice and would be sidelined for the remainder of the year due to concussion, his injury came while playing for his club in a challenge match against Dublin champions St Vincents in Cavan in late August 2018 - he received a blow to the head during that match. Concussion had caused McHugh to spend six weeks on the sideline following a 2018 National Football League game earlier that year.

The injury meant he could take no part in the 2018 Donegal Senior Football Championship, news, worsened when taken in the context of the earlier loss of McHugh's club and county teammate McBrearty to a cruciate ligament injury. This was Milford's return to the senior grade after relegation in the mid-1990s after claiming the 2017 Donegal I. F. C. Title. On 21 October 2018, Gaoth Dobhair claimed their 15th S. F. C. Title when defeating Naomh Conaill of Glenties by 0-17 to 1-7 at MacCumhaill Park. Burt were relegated back to the 2019 I. F. C. after just two seasons in the top-flight when losing their Relegation Final to newly promoted Milford. The following teams changed division since the 2017 championship season; the 2018 County Championship took the same format as previous championships in which there was four groups of four with the top two qualifying for the quarter-finals. Bottom of each group play in relegation play-offs to decide which team is relegated the 2019 Intermediate championship. All 16 teams entered the competition at this stage.

The top 2 teams in each group advanced to the Quarter-Finals while the bottom team of each group entered a Relegation Playoff. This year, all teams played one home match, one away match and one match at a neutral venue