What Is the Empty Set in Set Theory

When can nothing be something? It seems like a silly question, and quite paradoxical.   In the mathematical field of set theory, it is routine for nothing to be something other than nothing. How can this be? When we form a set with no elements, we no longer have nothing. We have a set with nothing in it. There is a special name for the set which contains no elements. This is called the empty or null set. A Subtle Difference The definition of the empty set is quite subtle and requires a little bit of thought. It is important to remember that we think of a set as a collection of elements. The set itself is different from the elements that it contains. For example, we will look at {5}, which is a set containing the element 5. The set {5} is not a number. It is a set with the number 5 as an element, whereas 5 is a number. In a similar way, the empty set is not nothing. Instead, it is the set with no elements. It helps to think of sets as containers, and the elements are those things that we put in them. An empty container is still a container and is analogous to the empty set. The Uniqueness of the Empty Set The empty set is unique, which is why it is entirely appropriate to talk about the empty set, rather than an empty set. This makes the empty set distinct from other sets. There are infinitely many sets with one element in them. The sets {a}, {1}, {b} and {123} each have one element, and so they are equivalent to one another.   Since the elements themselves are different from one another, the sets are not equal. There is nothing special about the examples above each having one element. With one exception, for any counting number or infinity, there are infinitely many sets of that size. The exception is for the number zero. There is only one set, the empty set, with no elements in it. The mathematical proof of this fact is not difficult. We first assume that the empty set is not unique, that there are two sets with no elements in them, and then use a few properties from set theory to show that this assumption implies a contradiction. Notation and Terminology for the Empty Set The empty set is denoted by the symbol ∅, which comes from a similar symbol in the Danish alphabet. Some books refer to the empty set by its alternate name of null set. Properties of the Empty Set Since there is only one empty set, it is worthwhile to see what happens when the set operations of intersection, union, and complement are used with the empty set and a general set that we will denote by X. It is also interesting to consider subset of the empty set and when is the empty set a subset. These facts are collected below: The intersection of any set with the empty set is the empty set. This is because there are no elements in the empty set, and so the two sets have no elements in common. In symbols, we write X ∠© ∅ ∅.The union of any set with the empty set is the set we started with. This is because there are no elements in the empty set, and so we are not adding any elements to the other set when we form the union. In symbols, we write X U ∅ X.The complement of the empty set is the universal set for the setting that we are working in. This is because the set of all elements that are not in the empty set is just the set of all elements.The empty set is a subset of any set. This is because we form subsets of a set X by selecting (or not selecting) elements from X. One option for a subset is to use no elements at all from X. This gives us the empty set.

The Effects Of Musical Instruments On Music - 890 Words

All noise making objects produce certain tones that help distinguish them from another item. For instance, when a child hears a cartoon playing in another room then they are residing in, the brain can tell if the voices they hear are from SpongeBob, or Looney Tunes. The same process happens with musical instruments, although the actual term to describe it is timbre. Timbre describes all characteristics of music that have nothing to do with pitch, loudness, or length. An example of timbre within music would be when a piccolo and a clarinet are playing a tone with dynamic levels identically, a trained ear can separate the two. Timbre is often referred to as tone color or tone quality. There are an unnumbered amount of expressions that are used to describe timbre such as, dim, nasally, mellow, brittle, and flat. Without changes in timbre an audience would quickly become uninterested in a piece. Therefore, composers often use timbre to affect mood of the audience. By changing dynamics, but keeping the timbre the same the musician can provoke different emotions onto the audience. In performing a piece with bright timbres, and loud dynamics the musician causes a disposition of conflict, but through varying the dynamic level to soft the audience moods suddenly shift to compassion. A composer creates musical landscapes in this way. Moreover, without the use of voices and instruments timbre would have not use in music. To further understand the use of voices and instruments inShow MoreRelatedCorrelation Between Music and IQ in Children Essay631 Words   |  3 Pages1. Introduction This project investigates the effect which the playing of a musical instrument – namely the drums – has on one’s intelligence and academic ability. A search of the literature reveals that studies of this kind have been conducted by other researchers in many parts of the world and has led to the conclusion that music is an extremely healthy activity to be involved in. 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Response To Beijing Games Book Free Essays

The field of sports has definitely gained an unquestionable significance and obvious implications among people and within societies. Such relevant characteristics concerning the sports discipline have resulted in making it as an important topic to be presented in a literary work. This is because facts and stories about sports are essential to be discussed in order for its underlying principles and messages to be learned and ultimately realized by the public. We will write a custom essay sample on Response To Beijing Games Book or any similar topic only for you Order Now Sports field in today’s contemporary setting has achieved an apparent prominence. The said fame is attributed to the success of the quintessential sports event – the Olympics. The advent and emergence of the Olympics have paved the way for recognition of various kinds of sports, their respective players or athletes and most importantly, the acknowledgement of the host countries where the said sports occasion is held every four years. The purpose, essence and valuable effects of Olympics to its host nation were what Susan Brownell (2008) effectively and successfully exemplified in her book â€Å"Beijing Games: What the Olympics Mean to China. † The Brownell material provided the public with clear insight about the meaning and effects of the 2008 summer Olympics to China. In the book, the author attained her goals and the narrative’s worth when they efficiently imparted to the readers the importance of hosting the Olympic Games to the country of China. In doing so, the â€Å"Beijing Games† book revealed that the meaning of Olympics to China lies on the reality that Olympics as Western civilization component can, in fact, possibly occur and affect the Far East culture. The attempt of Brownell and her book to emphasize the triumphant connection that transpired between Olympics and China led to the recognition of the beneficial impact of Olympic Games to China as well as the nation’s worldwide influence. The book therefore served as a very inspiring and awakening literary work where the effect and how Olympics change its host country as well as how China impacted and altered the Olympic were eventually realized. Written by Brownell months before the 2008 summer Olympic Games in Beijing, the book â€Å"Beijing Games† is evidently topical to China in showing the nation as one of the powerful and influential countries in Asia or the Far East part of the world. In general, the work acted as defender of the history and sports background of China as well as its political structure. This was carried out by the book with its specific criticism against the Western culture’s manner of interpreting and performing the Olympics (Brownell, 2008). â€Å"Beijing Games’ was not purely sports-oriented as several historical, political and social facts and events relating to China were discussed such as the 1989 Tiananmen Square tragic incident. Hence, in organizing the book, the author made seven chapters that talked about a number of issues. These include the disparities between the respective historical encounters with Olympic sports or the physical endeavors of China and the rest of Western countries (Brownell, 2008). The book also presented how Chinese regarded their affiliation with the International Olympic Committee or IOC, the coverage made by Western media concerning China as a nation and its sports. Foremost these topics, the Brownell book is to be significantly noted by its intriguing yet powerful presentation on whether Beijing is destined to change the Olympic’s history and nature or vice versa (Brownell, 2008). In order to understand and appreciate better the Beijing Games book, it is empirically essential to analyze how the material appeared and considered by the readers. Additionally, it is valuable to react to the book by discussing both its main and weak points. In responding to the book, the general concepts which pertain to China and the Olympics are first to be evaluated. On the whole, the book is to be commended for its efforts at disclosing the ability of the Far East civilization to hold a global sports event such as the Olympics thereby making people realize that the quintessential sports activity should not be made exclusive to Western countries. Since China embarked on what seemed like a remarkable sports undertaking, the book asserted that it is but just practical to praise and commend the country for its firm principle and practice of bringing Olympics to the other side of the world. Due to its emphasis on the capability of China, the book is to be equally acclaimed because the author has successfully disputed a misleading and incorrect notion about the sports history and background in China. The book then did well in making the world recognize that Beijing aspiration to host the 2008 summer Olympics is attributed to an enormous desire to overcome a lasting wrong impression about China’s inability towards sports or little or none at all connection with the said field. In asserting China’s power and influence in sports, the book’s notable criticism against the Western control of what is projected to be a global sports activity has worked to the advantage of China and the field of sports in general. This is because through the book, the international public was provided with the fact that the country has, in fact, rich and original sports background or nature. Based from the efforts of the author or the book, various political and social concerns that prevented sports from flourishing in China were presented, all aimed at ending the many forms of discriminations and misrepresentation on the function of Olympics sports in China and the apparent neglect done by Western cultures. Personally, I considered the book to be generally acceptable and commendable. While its organizational presentation appeared to be loosening, its principles and objectives made â€Å"Beijing Games† as one literary material worth reading and referred to other sectors of the public aside from sports. This is because the book is supposed to impart important messages or lessons to anyone. That is, the field of sports is a universal discipline which needs to be equally adhered to and uphold by worldwide audience. The realization of the meaning of Olympics to China showed how the book ultimately achieved its very essence and goals. Reference Brownell, S (2008). Beijing Games: What the Olympics Mean to China. New York: Rowman Littlefield How to cite Response To Beijing Games Book, Papers

President of India and Women Empowerment Essay Sample free essay sample

India. our state. is good known for its cultural heritage. civilization. faith and its geographical characteristics. Furthermore. India is besides popularly dubbed as a malechauvinistic state. We proudly portray our state as â€Å"Bharat-Mata† and raise mottos in congratulations of our integrity. unity and self-respect. While making so. we fail to gain that â€Å"Bharat-Mata† means female parent to every Indian. Even after six and a half decennaries of Independence. adult females in our state go on to be incapacitated victims of male jingoism and highhandedness in about every walk of life. Conventionally. adult females were compelled to play the 2nd violin in every domain. household or public life. But today. adult females have distinguished themselves and hold made their individuality and presence in all domains of life. Woman. today. are non merely confined to domestic jobs like upbringing of kids but they besides form an built-in portion of the society and do a impor tant part to the development of the state This essay attempts to concentrate on assorted combative issues. We will write a custom essay sample on President of India and Women Empowerment Essay Sample or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page Are all the adult females empowered in the county? Whether the advancement made by adult females in India is an across-the-board factor or is it limited to a few stray instances? Has the benefit of the assorted public assistance steps trickled down to every subdivision and category of the society? Women authorization has been a affair of argument for long and a meeting point of beliing subjects. Over theyears. the authoritiess have been underscoring adult females empowerment in true spirit. Even though. some subdivisions of adult females have benefited from this authorization. the huge bulk of them in rural sections have remained untasted. Womans in rural countries are still considered inferior to work forces in every domain of life. In world. adult females perform half of the work and work forces finally hard currency in on their good will and take all the recognition. Much demands to be done for the bulk of the adult females in rural countries. Paradoxically. the state is being rul ed by the UPA Government with Ms. Sonia Gandhi as its Chairperson. Other illustrations are that of Ms. Mamata Banerjee of Trinamool Congress. Mrs. Sushma Swaraj as a powerful Opposition leader. Ms. Tessy Thomas as a missile scientist of India. Ms. Meira Kumar as the first adult female Speaker of the Lok Sabha. etc. Besides political relations. adult females have distinguished themselves in the Fieldss of disposal. concern. medical specialties. technology. music. uranology. information engineering. athleticss. bench. banking. etc. It is a well-known adage that the fate of a kid is ever the work of the female parent. Then. how can we of all time neglect the importance of a adult female who. as a female parent rears and develops a worthy kid turning into great individuals like Guru Gobind Singh. Shaheed Bhagat Singh. Dr. A. P. J. Abdul Kalam. etc. Likewise. adult females like the late Indira Gandhi. the late Vijaya Lakshmi Pandit. Mother Teresa. Ms. Kiran Bedi. Ms. Lata Mangeshkar. Ms. Chanda Kochhar. the late Kalpana Chawla. Justice Fathima Beevi. Ms. Saina Nehwal and their like have scripted narratives of success in history. The inquiry that arises here is: Has the overall advancement of adult females been achieved at coveted degrees in the state? One would disconsolately acknowledge here: No. it has non. Women empowerment refers to supplying adult females with equal chances in all Fieldss. It is soon the demand of the hr. If equality of chances can be brought approximately in India. authorization could be easy done. Empowerment will enable Indian adult females to keep the same place in any field and be treated on a par with work forces. Unfortunately. it is still a dream in India. It is pertinent to observe here that merely a certain category of adult females have benefited from the push of authorization. In India. bulk of the rural adult females continue to be populating in the bonds of mediaeval orthodoxy with their male opposite numbers playing a dominant function in about everything that affairs. Gender equality plays a polar function in the upheaval of adult females. Inequality needs to be scrapped . Article 15 of the Constitution prohibits gender favoritism. Furthermore. Article 15 ( 3 ) permits the province to positively know apart in favor of adult females to do particular proviso. to present them societal. economic and political justness and agreements them para. Gender-based favoritism and disparity are witnessed in legion instances of sexual torment and dowry deceases that are really common in India even in the age of radical technological promotions. In some instances. adult females are still restricted from come ining temple premises. Womans must be encouraged to turn out their heart in every domain. The Government must open doors for them to turn out that they are equal to work forces. As per the latest study. the part of adult females in assorted sectors is as follows: Financial A ; Insurance ( 60 % ) . Media and Entertainment ( 42 % ) . Professional Services ( 56 % ) . The undermentioned sectors show battle of lowest per centum of adult females: Agribusiness and Mining ( 18 % ) and Automotive ( 21 % ) . In Indian Parliament an d Assemblies. adult females have neer represented more than 10 % . Most of the adult females workers in India are outside the organized sector.

Pegomastax - Facts and Figures

Pegomastax - Facts and Figures Name: Pegomastax (Greek for thick jaw); pronounced PEG-oh-MAST-ax Habitat: Woodlands of southern Africa Historical Period: Early Jurassic (200 million years ago) Size and Weight: About two feet long and five pounds Diet: Plants Distinguishing Characteristics: Prominent fangs; short bristles on body About Pegomastax Some of the most notable dinosaur discoveries dont involve going out into the field with a shovel and pickax, but examining long-forgotten fossil specimens that have been filed away in dank museum basements. Thats the case with Pegomastax, which was recently named by Paul Sereno after he examined a neglected collection of fossils from southern Africa, which had been discovered in the early 1960s and stashed in Harvard Universitys extensive archives. Pegomastax was certainly an odd-looking dinosaur, at least by the standards of the early Mesozoic Era. About two feet long from head to tail, this close relative of Heterodontosaurus was equipped with a parrot-like beak studded by two prominent canines. The porcupine-like bristles that covered its body are reminiscent of the short, stiff, feathery protrusions of another herbivorous dinosaur, the late Jurassic Tianyulong, which was also an early ornithopod of the heterodontosaur family. Given its presumed plant-eating diet, why did Pegomastax have such sizable canines? Sereno speculates that this feature evolved not because Pegoamastax snacked occasionally on insects or rotting carcasses, but because it needed to a) defend itself against larger theropod dinosaurs and b) compete for the right to mate. If longer-toothed males were more likely to survive predation, and also more likely to attract females, you can see why natural selection would have favored Pegomastaxs fangs.

How and Why Guinea Pigs Were Domesticated

How and Why Guinea Pigs Were Domesticated Guinea pigs (Cavia porcellus) are small rodents raised in the South American Andes mountains not as friendly pets, but primarily for dinner. Called cuys, they reproduce rapidly and have large litters. Today guinea pig feasts are connected with religious ceremonies throughout South America, including feasts associated with Christmas, Easter, Carnival, and Corpus Christi. Modern domesticated adult Andean guinea pigs range from eight to eleven inches long and weigh between one and two pounds. They live in harems, approximately one male to seven females. Litters are generally three to four pups, and sometimes as many as eight; the gestation period is three months. Their lifespan is between five and seven years. Domestication Date and Location Guinea pigs were domesticated from the wild cavy (most likely Cavia tschudii, although some scholars suggest Cavia aperea), found today in the western (C. tschudii) or central (C. aperea) Andes. Scholars believe that domestication occurred between 5,000 and 7,000 years ago, in the Andes. Changes identified as the effects of domestication are increased body size and litter size, changes in behavior and hair coloration. Cuys are naturally gray, domesticated cuys have multicolored or white hair. Keeping Guinea Pigs in the Andes Since both wild and domestic forms of guinea pigs can be studied in a laboratory, behavioral studies of the differences have been completed. Differences between wild and domestic guinea pigs are in some part behavioral and part physical. Wild cuys are smaller and more aggressive  Ã¢â‚¬â€¹and pay more attention to their local environment than domestic ones and wild male cuys do not tolerate each other and live in harems with one male and several females. Domestic guinea pigs are larger and more tolerant of multi-male groups, and exhibit increased levels of social grooming of one another and increased courtship behavior. In traditional Andean households, cuys were (and are) kept indoors but not always in cages; a high stone sill at the entrance of a room keeps cuys from escaping. Some households built special rooms or cubby holes for cuys, or more typically keep them in the kitchens. Most Andean households kept at least 20 cuys; at that level, using a balanced feeding system, Andean families could produce at least 12 pounds of meat per month without decreasing their flock. Guinea pigs were fed barley and kitchen scraps of vegetables, and the residue from making chicha (maize) beer. Cuys were valued in folk medicines and its entrails were used to divine human illness. Subcutaneous fat from the guinea pig was used as a general salve. Archaeology and the Guinea Pig The first archaeological evidence of the human use of guinea pigs dates to about 9,000 years ago. They may have been domesticated as early as 5,000 BC, probably in the Andes of Ecuador; archaeologists have recovered burned bones and bones with cut marks from midden deposits beginning about that time. By 2500 BC, at sites such as the Temple of the Crossed Hands at Kotosh and at Chavin de Huantar, cuy remains are associated with ritual behaviors. Cuy effigy pots were made by the Moche (circa AD 500-1000). Naturally mummified cuys have been recovered from the Nasca site of Cahuachi and the late prehispanic site of Lo Demas. A cache of 23 well-preserved individuals was discovered at Cahuachi; guinea pig pens were identified at the Chimu site of Chan Chan. Spanish chroniclers including Bernabe Cobo and Garcilaso de la Vega wrote about the role of the guinea pig in Incan diets and ritual. Becoming a Pet Guinea pigs were introduced into Europe during the sixteenth century, but as pets, rather than food. Remains of one guinea pig were recently discovered within excavations at the town of Mons, Belgium, representing the earliest archaeological identification of guinea pigs in Europeand similar in time to the 17th-century paintings which illustrate the creatures, such as the 1612 Garden of Eden by Jan Brueghel the Elder. The excavations at the site of a proposed parking lot revealed a living quarter which had been occupied beginning in medieval times. The remains include eight bones of a guinea pig, all found within a middle-class cellar and adjacent cesspit, radiocarbon dated between AD 1550-1640, shortly after the Spanish conquest of South America. The recovered bones included a complete skull and the right part of the pelvis, leading Pigià ¨re et al. (2012) to conclude that this pig was not eaten, but rather kept as a domestic animal and discarded as a complete carcass. Sources History of the Guinea Pig  from archaeologist Michael Forstadt. Asher, Matthias. Large males dominate: Ecology, social organization, and mating system of wild cavies, the ancestors of the guinea pig. Behavioral Ecology and Sociobiology, Tanja Lippmann, Jà ¶rg Thomas Epplen, et al., Research Gate, July 2008. Gade DW. 1967.  The Guinea Pig in Andean Folk Culture.  Geographical Review  57(2):213-224. Kà ¼nzl C, and Sachser N. 1999.  The Behavioral Endocrinology of Domestication: A Comparison between the Domestic Guinea Pig (Cavia apereaf.porcellus) and Its Wild Ancestor, the Cavy (Cavia aperea).  Hormones and Behavior  35(1):28-37. Morales E. 1994.  The Guinea Pig in the Andean Economy: From Household Animal to Market Commodity.  Latin American Research Review 29(3):129-142. Pigià ¨re F, Van Neer W, Ansieau C, and Denis M. 2012.  New archaeozoological evidence for the introduction of the guinea pig to Europe.  Journal of Archaeological Science  39(4):1020-1024. Rosenfeld SA. 2008.  Delicious guinea pigs: Seasonality studies and the use of fat in the pre-Columbian Andean diet.  Quaternary International  180(1):127-134. Sachser, Norbert. Of Domestic and Wild Guinea Pigs: Studies in Sociophysiology, Domestication, and Social Evolution. Naturwissenschaften, Volume 85, Issue 7, SpringerLink, July 1998. Sandweiss DH, and Wing ES. 1997.  Ritual Rodents: The Guinea Pigs of Chincha, Peru.  Journal of Field Archaeology  24(1):47-58. Simonetti JA, and Cornejo LE. 1991.  Archaeological Evidence of Rodent Consumption in Central Chile.  Latin American Antiquity  2(1):92-96. Spotorno AE, Marin JC, Manriquez G, Valladares JP, Rico E, and Rivas C. 2006.  Ancient and modern steps during the domestication of guinea pigs (Cavia porcellus L.).  Journal of Zoology  270:57–62. Stahl PW. 2003.  Pre-columbian Andean animal domesticates at the edge of empire.  World Archaeology  34(3):470-483. Trillmich F, Kraus C, Kà ¼nkele J, Asher M, Clara M, Dekomien G, Epplen JT, Saralegui A, and Sachser N. 2004. Species-level differentiation of two cryptic species pairs of wild cavies, genera Cavia and Galea, with a discussion of the relationship between social systems and phylogeny in the Caviinae.  Canadian Journal of Zoology  82:516-524.

Maori Identity Expression and Development in Once Were Warriors Essay

Maori Identity Expression and Development in Once Were Warriors - Essay Example I used the concepts and arguments from the following major theorists: Murray and Conrich (2008), Barclay (1990), Pihama (1996), Alia and Bull (2005) and Mita (1996). Murray and Conrich (2008) explore the meaning of ‘indigenous self-expression,’ while Barclay (1990) describes the process and effects of ‘talking in’ for indigenous people. Pihama (1996) emphasises the importance of contextualising Maori violence in order to avoid ethnic stereotyping. Alia and Bull (2005, p.64) argue that as indigenous groups internalise outsider views and develop their own internal understanding of their societies, they are involved in the ‘invention of tradition.’ Mita (1996) asserts that films provide the opportunity of decolonising themes. For this essay, I ask: How does Once Were Warriors reflect the ideas of the ‘indigenous self-expression’ (Murray and Conrich 2008), ‘our own image’ and ‘talking in’ (Barclay 1990), and â €˜decolonising the screen’ (Mita 1996)? Once Were Warriors reflects ‘indigenous self-expression’ (Murray and Conrich 2008), ‘our own image’ and ‘talking in’ (Barclay 1990) through emphasising the remaking and reclaiming of the warrior Maori culture in different ways and ‘decolonising the screen’ (Mita 1996) through reducing Western influences and focusing on the legitimacy of the hybrid Maori-modern culture. The paper concludes that Once Were Warriors signifies the remaking of Maori identity through the process of reclaiming their warriorhood status that simultaneously decolonises Maori identity development. ii. Reflexive Introduction I chose this film because it represents the breakdown of the indigenous social fabric, after colonisation has eroded the cultural fabric of the colonised. As a person who has a strong sense of colonisation history and who values family and clan ties, I can relate to the impacts of colonisati on and urbanisation on the social ties and identity-making of the Maori. Colonisation and its subsequent urbanisation and commercialisation effects have eroded the Maoris’ sense of identity, affecting not only their ethnic group as a whole, but also their family roots and individual personalities. I am then interpreting the film, not only from the views and concepts of the aforementioned theorists, but also from my own family and social values and experiences, because I am someone who deeply respects and values collectivistic societies, of which I am also a proud part of. I continue to strongly ground my analysis on scholarly research, nonetheless, through using textual analysis and semiotics that can help me attain a balanced perspective. iii. Background Introduction Since the early 1970s, a significant cultural shift is changing Maori representation in films, a shift called the â€Å"Maori Renaissance† (Keown 2008, p.197). Lee Tamahori’s Once Were Warriors bel ongs to this shift, as it portrays the implications of one of the historical events in the Maoris’ lives, their migration from rural, coastal ancestral lands to Pakeha-dominated urban areas and the effects of this migration to their ethnic identity-making process and identities (Keown 2008, p.197). For this essay, I explore how the film reflects indigenous expression and decolonisation themes. My research question is: How does Once Were Warriors reflect the ideas of the ‘indigenous self-expression’ (Murray and Conrich 2008), ‘our own image’