The Imagery of Hamlet essays

The Imagery of Hamlet essays Shakespeares Hamlet uses imagery as a means to portray ideas that varies away from the normal representation of a thought. Shakespeare uses imagery as a vivid or figurative language to represent objects, actions, or ideas. Imagery permits the reader to reveal the authors intentions instead of hearing their descriptions. Learning the ideas makes this type of doubtfulness more powerful rather than being shown to the reader. The intensity of imagery used throughout the play is unmistakable.(Imagery) Three important functions are used to show the performance of imagery in Hamlet. First, the main characters of the play are individualized. Second, major themes are announced and elaborated. Finally, it places images in the audiences mind by establishing the atmosphere of the play and it keeps the basic mood of the tragedy. The clarity in which Shakespeare uses imagery helps to define these functions, emphasizing what is really important to humanity.(Imagery of Hamlet) A clear reoccurring pattern in the plays imagery is evident by the poisoned sword and cup. Hamlets father being poisoned is a major symbol of the moral condition of Denmark. Just as Claudius poured the leporous distilment into his sleeping brothers ear, which spread all throughout his body and destroyed the healthy living being, Claudius morally poisons Gertrude with the witchcraft of his wit and with traitorous gifts. In order to please his evil master, Polonius yields the kings moral poison and will even give up his daughter Ophelia to Hamlet. As a result of moral poison, the morally unstable Laertes loses his life because he is unable to resist Claudius moral poison. The symbols of the poisoned sword and cup represent the evil plot developed by the treacherous, which specifically spell out the end product of their development.(Mack 2) Unmistakably Claudius and Laertes developed their...

How to Print an Array in PHP Using Print_r()

How to Print an Array in PHP Using Print_r() An array in PHP computer programming contains a group of similar objects that are the same type and size. The array can contain integers, characters, or anything else with a defined data type. The print_r PHP function is used to return an array in a human readable form. It is written as: print_r($your_array) In this example, an array is defined and printed. The tag pre indicates the following code is preformatted text. This tag causes the text to be displayed in a fixed-width font. It preserves line breaks and spaces, making it easier for the human observer to read. pre?php $Names array (a Angela, b Bradley, c array (Cade, Caleb)); print_r ($Names); ? /pre When the code is run, the results looks like this: Array([a] Angela[b] Bradley[c] Array([0] Cade[1] Caleb)) Variations of Print_r You can store the result of print_r in a variable with a second parameter to print_r. This technique prevents any output from the function. Augment the function of print_r with var_dump and var_export to show protected and private properties of the objects, including type and value. The difference of the two is that var_export returns valid PHP code, whereas var_dump does not. Uses for PHP PHP is a server-side language used to add enhanced features  to a website developed in HTML, such as surveys, shopping carts, login boxes, and CAPTCHA codes. You can use it to build an online community, integrate Facebook with your website, and generate PDF files. With PHPs file-handling functions, you can create photo galleries and you can use the GD library included with PHP to generate thumbnail images, add watermarks, and resize and crop images. If you host banner ads on your website, PHP rotates them at random.  The same feature can be used to rotate quotations. It is easy to set up page redirects using PHP and if you are wondering how often your visitors check out your website, use PHP to set up a counter.

Assignment 2 Example | Topics and Well Written Essays - 500 words - 2

2 - Assignment Example In the current methodology of commissions for the front-line salesmen, the annual break-even point in dollar sales and in unit sales for Shop 48 is sales of 12,500 pair of shoes for gross sales of $375,000. Appendix 1 shows a graph from zero to seventeen thousand units sold in a given year, with both fixed and variable expenses taken into account. Based upon projected annual sales of 17,000 pairs of shoes, potential profit for Shop 48 would be $54,000 on annual sales of $510,000. Another question raised was what the profit or loss would be on 12,000 pairs yearly. After expenses, the store would realize a net loss of $6,000. In the next circumstance, the company is toying with the idea of offering the store manager of Shop 48 an incentive commission of $0.75 (seventy-five cents) per pair of shoes, leaving the salespersons’ commission intact. What would this added commission have on the break-even point in dollar sales and in unit sales? It is clearly shown that the break even point would indeed rise considerably. Technically there would be no â€Å"break even point†, for at 13,333 pairs the shop would be operating at a loss of $3.75 and one more pair (13,334) would give them a net profit of $7.50. Either way, sales would have to be roughly $400,000 per annum to achieve a profit, or an increase of $25,000 in gross sales annually. As an another option to the situation above, what if the store manager was given fifty cents commission on each pair of shoes sold beyond the break-even point? Their question on this was what the shops net operating income would be based upon 15,000 pairs of shoes sold annually. This would include the data as discussed for current operations in that 12,500 pair of shoes for gross sales of $375,000 is the BE point. With this, 15,000 pairs of shoes would give the store gross sales of $450,000 annually. With the added expense of the fifty cent commission on 2,500 pairs net profit would then be

Case study 2 Essay Example | Topics and Well Written Essays - 500 words - 2

Case study 2 - Essay Example This paper will describe the approach to care that is necessary to be given to Mr. P and the treatment plan. The paper will also describe the methods for providing both the patient and family members with education. In order to give the proper care needed for any sickness, the care provider should first seek the doctors’ guidance. Since Mr. P is suffering from heart failure, it would be necessary that a follow up is made to ensure that he uses the prescribed drug as required without missing a single prescription. The care will also involve ensuring that Mr. P visits the hospital at the right time. It is also essential that care should involve provision of moral support. In this case, he should be provided with all assistance needed, especially with activities that he cannot do due to his condition (Maron, 2008). The treatment plan of cardiomyopathy and heart failure is to cope with the disease symptoms and signs. It also involves ensuring that the condition is not left to worsen and risks and complications are minimized. The recommended treatments for Mr. P regarding his health status include the use of angiotensin-converting enzyme (ACE) inhibitors. This enzyme assists in boosting heart pumping aptitude. The enzymes include lisinopril, enalapril, captopril, and ramipril. In case he is not able to take ACE, he should be given angiostensin recerpter blockers such as valsartan and losartan. This should be taken in accordance with doctor’s prescriptions. Cardiomyopathy can also be treated using Digoxin (lanoxin) drug. This drug helps in increasing the strength of the patient’s heart muscle contraction. The drug is also said to slow down rate of heartbeat. It minimizes symptoms of heart failure thereby improving the patient’s ability to live with the disease (Maron, 2008). Since Mr. P has some traces of blood fluid in his lungs, it would be necessary that he be given Diuretics water pills that make the patient urinate

Performance distance Essay Example for Free

Performance distance Essay In â€Å" Embedded Learning Strategy Instruction: Story-Structure Pedagogy in Heterogenous Secondary Literature Classes†, Michael Faggela-Luby, Jean Schumaker, and Donald Deshler examine the problem of uneven learning structures among literature students. Their previous research found that a majority of secondary education level students were reading below the reading comprehension level appropriate for their age level. This was attributed to the inability of teachers to find a structure of teaching reading comprehension and story structure in a method that would both allow LD students to comprehend narrative story structures while still challenging higher level learning students. They present a number of relevant studies done over the years that have presented different story structure learning models to different focus groups of students to examine the results. However, these results are largely inconclusive because some studies failed to produce graphs that explained their results and others did not separate LD students from other students, therefore failing to examine the experimental structures in terms of these two distinguishable groups. Their research attempted to find a reading comprehension structure that could be applied to all levels of students and be used as a universal tool towards learning comprehension and story structure for students of all learning aptitudes and levels. They conducted a research experiment using 79 students to examine the effectiveness of the embedded-story structure. Some students were limited readers, while some were strong readers. Students taught in their regular classrooms with regular materials and were randomly assigned to one of two groups. One group would use the embedded story structure (ESS) while the other would use the comprehensive skills instruction (CSI) method. A graph and statistical data was included to present the statistics of these two groups in terms of age, gender, and test scores. Another figure displayed the categories of self questioning, story structure analysis and summary writing that were utilized in ESS. The CSI group used the categories of vocabulary strategy, question-answer relationships, and semantic summary mapping. More tables listed the statistical information for which students received which test form. Results of all tests administered revealed data that proved learning improvement and comprehension advancement in students using the ESS method. These increases in comprehension were in the non-LD students on both lower and higher reading strengths. The conclusion seems to be that ESS benefits readers on any reading level, but does not necessarily provide marked improvement for LD students. The results of the research seem positive, and it seems that the ESS method could represent a solution to the problem of uneven learning comprehension in students at different reading levels. But one of the limitations pointed out by the researchers is that in the experiment, the teacher was also the researcher. I found this interesting because it helped to ensure study viability, but does not guarantee that improvement results would be the same with other teachers, which makes it questionable as to its practical application in the classroom. A possible solution to this, and a way to help ensure that ESS is being taught similarly at learning institutions everywhere, would be to implement an educational forum to instruct teachers how to properly utilize ESS in the classroom. This could also give teachers suggestions for implementing the method with LD students in an effort to give them the same benefit. Further research could be done into streamlining ESS to better benefit LD students and instructing teachers accordingly. The article, â€Å"Ensuring Content-Area Learning by Secondary Students with Learning Disabilities†, Donald D. Deshler, Jean B. Schumaker, B. Keith Lenz, Janice A. Bulgren, Michael F. Hock, Jim Knight and Barbara J, Ehren research the problem of preparing learning disabled students to handle heavier course loads and learning expectations at the secondary and high school level. They provide background statistics finding a large number of LD students that experience self-esteem issues at these school levels or drop out. A graph included shows the performance distance between LD students and the general population students they are often put in classes with and illustrates how the two groups acquire knowledge differently. The researchers examine dual elements of a study done at the University of Kansas Research Center on Learning. The purpose of the article was to examine the study done at KU-CRL and determine whether its dual-intervention approach was beneficial to LD students and could be implemented in classrooms at all levels. The researchers at KU-CRL found that there needed to be two levels of intervention to help LD students. The first, according to the authors, needed to be done by the teachers and involved implementing teaching strategies that were accessible to students on all learning backgrounds. The second focused more on the students themselves and teaching them learning and studying methods that helped them understand and comprehend material. There are five levels of intervention teachers can use to impact learning levels of students. They vary according to the methods of intervention used by the teacher and the direct impact on the student, ranging from implementing overall learning routines to providing the student with individual strategy structures designed for them. The authors cite studies in which these strategies of embedding learning have worked with limited results. They also point out that the method of delivery for the strategies is important to their effect. A model explains the inclusion strategy for use. Overall, the authors find all of the studies done on the KU-CRL research finds that general learning strategies can be beneficial to LD students to help them with learning comprehension, and that once these are implemented in the classroom that many LD students are able to utilize these strategies outside the classroom too. It recognizes that placing LD students in general classroom settings doesn’t mean that they will be able to learn successfully according to general strategies. I found this article interesting for its examination of the learning needs of the LD student at both the individual and institution-wide level. The authors stress that individual attention and tutoring are still vital when implementing these blanket learning strategies, and I think that’s important to remember. My recommendation if these intervention level learning strategies were to be implemented would be to simultaneously implement a tutoring program for LD students that find themselves requiring a different level of intervention or a different strategy than what is being implemented in the classroom. This would assist teachers attempting to implement the intervention model but still finding that some LD students aren’t receptive. This tutoring could also encourage LD students to keep learning new methods for knowledge comprehension. The authors also emphasized proper training and ongoing support for teachers implementing this learning strategy in the classroom and I think that’s important as well. Teachers learning a new approach for helping LD students in their classroom should have the benefit of accessing new research and findings into the most effective methods of teaching to bridge the gap between normally developed learners and LD students.

The Great Gatsby - Narrators Role in Establishing Theme Essay

The evolving character of an interactive narrator can help discern key themes in a novel. F. Scott Fitzgerald's social examination of life in America's Jazz Age relies heavily on Nick Carraway, the narrator, acting as a 'Trojan horse' for Fitzgerald to smuggle his own ideologies into The Great Gatsby. Fitzgerald endorses realist class relations as power relations over the romantic and archaic 'Jeffersonian dream of simple agrarian value'. He also favours the view that the American upper class's 'carpe diem' approach to life placed capitalist society in a moral downwards spiral, instead of conforming to mainstream ideas of the Age such as 'money can buy happiness'. Nick?s statement that people are only ?pursued? (generally the upper classes, being chased due to their lifestyle) or ?pursuing? (chasing the lifestyle of the pursued). These mutually exclusive states mean that Nick believes all the characters with which he interacts can be stratified into one of these two groups, seemingly based on class. The narrator also claims that people can also be ?busy and?tired?. Again, these two vaguer classes cannot exist together. At first examination it may seem that this ?black and white? observation of the members of Gatsby?s America is shortsighted. However at that stage on the novel Nick is entitled to make such a judgement. Immediately after Nick?s thought entered his ?heady? mind, he had just learnt the purpose of ?purposeless splendour? from Jordan: that Gatsby had moved to West Egg to be close to Daisy. This ?pursuing? of Daisy, the ?five years? of busy waiting, is certainly a revelation to the reader, and to Nick. Nick also says that he had forgotten about ?Daisy and Gatsby?, though it still must have played on his subcons... ...towards her old family (?Do they miss me), these all serve to promote Fitzgerald?s endorsed theme of the corruption of the traditional values of the West, and how the ?Money can buy happiness? myth sends society into a downwards spiral. The way that Nick Carraway, as an interactive narrator, relates to different characters (and what they stand for) in the novel conveys the extent to which Fitzgerald endorses or challenges that character?s ideologies. Nick tarnishes all characters with a cynical, stratifying brush in order to smuggle in the main ideologies of the text by creating a pastiche of these themes. Nick?s black-and-white thought of the ?pursuing, the pursued, the busy and the tired? serves to reinforce the contrast of what is endorsed and challenged through the book, via the medium of the narrator?s interaction with different creations of the author.

Continental Drift Theory and Plate Tectonic Theory

In the early 20th century, German scientist Alfred Wegener published a book explaining his theory that the continental landmasses, far from being immovable, were drifting across the Earth. He called this movement continental drift. Wegener noticed that the coasts of western Africa and eastern South America looked like the edges of interlocking pieces of a jigsaw puzzle. He was not the first to notice this, but he was the first to formally present evidence suggesting that the two continents had once been connected. Wegener was convinced that the two continents were once part of an enormous, single landmass that had split apart. He knew that the two areas had many geological and biological similarities. For example, fossils of the ancient reptile mesosaurus are only found in southern Africa and South America. Mesosaurus, a freshwater reptile only one meter (3. 3 feet) long, could not have swum the Atlantic Ocean. The presence of mesosaurus suggests a single habitat with many lakes and rivers. Wegener believed that all the continents—not just Africa and South America—had once been joined in a single supercontinent. This huge ancient landmass is known as Pangaea, which means â€Å"all lands† in Greek. Pangaea existed about 240 million years ago. By about 200 million years ago, this supercontinent began breaking up. Over millions of years, Pangaea separated into pieces that moved away from one another. These pieces slowly assumed their present positions as the continents. PLATE TECTONIC THEORY Plate tectonics is the theory that the outer rigid layer of the earth (the lithosphere) is divided into a couple of dozen â€Å"plates† that move around across the earth's surface relative to each other, like slabs of ice on a lake. There are seven or eight major plates and many minor plates. Where plates meet, their relative motion determines the type of boundary: convergent, divergent, or transform. Earthquakes, activity, mountain-building, and oceanic trench formation occur along these plate boundaries. The lateral relative movement of the plates typically varies from zero to 100 mm annually. Tectonic plates are able to move because the Earth's lithosphere has a higher strength and lower density than the underlying asthenosphere. Plate movement is thought to be driven by a combination of the motion of the seafloor away from the spreading ridge and drag, downward suction, at the subduction zones. Another explanation lies in the different forces generated by the rotation of the globe and the tidal forces of the Sun and the Moon. The relative importance of each of these factors is unclear, and is still subject to debate. The geoscientific community accepted the theory after the concepts of seafloor were developed in the late 1950s and early 1960s. Fun Facts: * The highest mountain range above sea level, the Himalayas, was formed 55 million years ago when the Eurasian and Indo-Australian continental plates converged. Due to ongoing convergence, the Himalayas, including Mount Everest, continue to rise by approximately 2 centimeters (?1 inch) each year. * The Mid-Atlantic Ridge runs down the center of the Atlantic Ocean. Along its crest, the ridge has a deep rift valley that, on average, is similar to the depth and width of the Grand Canyon: 1 to 3 kilometers (0. 6 -1. 8 miles) deep and 6. 5 to 29 kilometers (4-18 miles) wide. * Scientists are able to calculate average rates of tectonic plate movement for a given time period. These rates of movement range widely. For example, the rate of spreading at the Mid-Atlantic Ridge near Iceland is relatively slow, about 2. 5 centimeters (1 inch) per year. This is similar to the rate at which fingernails grow. The fastest known rate of plate movement, 15 centimeters (6 inches) per year, occurs on the East Pacific Rise in the South Pacific. SEAFLOOR SPREADING Seafloor spreading is a process of plate tectonics. New oceanic crust is created as large slabs of the Earth's crust split apart from each other and magma wells up to fill the gap. The large slabs of rock that make up the Earth’s crust are called tectonic plates. As they slowly move away from each other beneath the ocean floor, hot magma from the Earth’s mantle bubbles to the surface. This magma is then cooled by seawater. The new rock forms a new part of the Earth’s crust. Seafloor spreading occurs along mid-ocean ridges—large mountain ranges rising from the ocean floor. New bodies of water and even continents can be created through seafloor spreading. The Red Sea, for example, was created through seafloor spreading, as the African plate and the Arabian plate tear away from each other. Today, the northern Sinai Peninsula connects the Middle East (Asia) with North Africa. Eventually, geologists predict, seafloor spreading will expand the Red Sea so that it will completely separate the two continents. . Seafloor spreading disproves an early part of the theory of continental drift. Continental drift was one of the first theories that the Earth's crust was dynamic and always in motion. Supporters of continental drift originally theorized that the continents moved (drifted) through unmoving oceans. Seafloor spreading proves that the ocean floor itself is the site of tectonic activity. Subduction is the opposite of seafloor spreading. Subduction happens where tectonic plates crash into each other instead of spreading apart. In subduction zones, the edge of the heavier plate subducts, or slides, beneath the lighter one. It then melts back into the Earth's mantle. Seafloor spreading creates new crust. Subduction destroys old crust. The two forces roughly balance each other, so the shape and diameter of the Earth remains constant.

Relationships in Charlotte Bronte’s Jane Eyre Essay

‘To what extent is Jane Eyre influenced by relationships in chapters 1-10 in the novel?’ Relationships are a key theme in Charlotte Bronte’s Jane Eyre. Throughout the novel we see the rise and fall of Jane, all most importantly due to relationships. This starts primarily with her lack of relationship with her parents, as she was orphaned when she was very young, she has no idea what it is like to love or to be loved and we see her strive to find out these feelings throughout the novel, until finally she achieves it, but the journey towards this is deeply important. In chapters one and two we see the basis of Jane’s view of relationships through her connection with the Reed’s. Firstly Mrs Reed does her upmost to make sure Jane is excluded from her and her ‘contented, happy, little children’ we as readers see this as a cruel act from Mrs Reed, she does not care that Jane is deeply unhappy because Jane is not one of her children, therefore she does not see it as her duty to care for her emotionally and thinks by punishing her and excluding her from the family that this will teach Jane to be a ‘contented child’ however we as readers see that this causes Jane to be deeply troubled within herself. This leads to Jane not only resenting Mrs Reed but also her children as they have been taught that Jane is a ‘dependant’ especially John who ultimately sees himself as above Jane in every aspect of life, he believes that Jane is just scavenging off them and this causes him to act in a horrific and bullying manor towards Jane. This causes Jane to act in a way she ordinarily would not, she even says herself that it causes ‘sensations for the time predominated over fear’ she feels so angry and let down that she finally stands up for herself. Therefore this influences Jane in a way that she feels like nobody will ever truly love her and she feels very much an outcast, this causes Jane to act in a way that even she herself expresses that she does not want to, she is cold and unloving and strives desperately to be appreciated but of course, this all happens in vain. We also see Jane to act very irrationally towards Mrs Reed, she deeply wants her to love her, yet w hen it comes down to it and she realises Mrs Reed never will she has an explosion of anger and tells Mrs Reed all the things that have been stewing up in her mind for so long; ‘I am glad you are no relation of mine. I will never call you aunt again as long as I live. I will never come to visit you when I am grown up; and if anyone asks me how I liked you, and how you treated me, I will say the very thought of you makes me sick. . . .† this we  see as Jane being bitter towards Mrs Reed which we learn in later chapters as a very uncharacteristic feature of Jane Eyre, she is usually forgiving. The relationship between Jane and the nursery maid; Bessie is an important one, in the first few chapters we see Bessie as being somewhat cruel and dismissive of Jane compared to the other Reed children, she does not feel a connection towards Jane as she is not as pretty or funny as the other children therefore Bessie does not see her appeal. However after the event in the red room we see a change with Bessie’s attitude towards Jane, she turns somewhat softer as we see her feel sorry for Jane and how hard Mrs Reed is on her. This is an extremely important turning point in the novel as we see Jane in the chapters leading up to this as very self involved and saddened as she has no one to love, yet as soon as Bessie softens to Jane and tells her that she can sympathise with the position she’s been put in she tells Jane ‘I don’t dislike you, Miss; I believe I am fonder of you than of all the others.’ This affects Jane greatly and we see a completely different little girl, she seems to talk which much more glee and excitement and even for her ‘life had its gleams of sunshine’. So we see how much relationships influence Jane and her attitudes in the novel, relationships affect Jane and how her personality is. In chapter five Jane meets Helen Burns, Helen is also an orphan and see’s the school as somewhat of a sanctuary even though she is constantly picked upon by the teacher. Helen is Jane’s first friend but more importantly she becomes Jane’s best friend and we see as the relationship grows that Helen deeply influences Jane, she teaches her to be less excitable and too see the best in others, a quality that Jane desperately needs after her experience with the Reed’s. She teaches Jane to be self sacrificing when she tells her ‘it is far better to endure patiently a smart which nobody feels but yourself, than to commit a hasty action whose evil consequences will extend to all connected with you’. Helen believes that you should suffer pain yourself than have others see and feel an action that you may regret when you have calmed down. Jane learns from this and this causes Jane to be a character who thinks beyond this life and onto the next with God. We see Jane finds this as a great comfort and now instead of looking onto God as something to be feared, she looks at him as somewhat of a comfort, especially after Helen dies of typhoid. Helen believes that after she dies she is going to be with her family and loved  ones and most importantly with God, therefore she does not fear death and although Jane is deeply distraught by the death of the only friend she’s ever had in the world, the fact that she will, if she lives correctly see her again is a great comfort. This shows the importance of friendship throughout the novel and how with Jane having the comfort of a friend she can be the person that she has always wanted to be, thanks to Helen Jane finds herself acting more appropriately and being able to handle her anger. Therefore this relationship has greatly affected Jane as she strives to be more like Helen. Relationships are of key importance to Bronte writing about Jane Eyre, it is how she expresses her feelings of how relationships have perhaps affected her and it shows how deeply the lack of love can affect someone. This novel is primarily about love, whether it being a lack of love or so much love that it turns into passion, Jane strives to feel this emotion and closeness with anyone who will allow her to be their friend. Therefore relationships are a key influence to Jane Eyre, they affect how she acts and how she feels and without them, as we learn in the first few chapters, life can be a very lonely existence.

Jamaica essays

Jamaica essays The country of Jamaica has an ideal location. Located just south of Cuba, it is the third largest island in the Caribbean Sea with 10,990 km ². Although the capital is Kingston, there are many other important centers of trade and business. The official language is English and the major religion is Protestantism. Transportation in Jamaica connects the entire country and movement thought out the island is very easy. There is a coastal highway traveling the whole coast. Air Jamaica and cruise ships make traveling to and from the island very easy. But despite all of the joys, there are very serious human-environmental interactions present. Mining on the island causes serve pollution and soil erosion. Most of the natural rainforest is destroyed. But the many beautiful beaches seem to make all of the worries disappear. The history of Jamaica starts at about 1000 AD when a Tiano tribe called the Arawaks crossed the Caribbean Sea in canoes to settle on the island. The Arawaks lived in simple villages, relying on fishing and hunting for substance. They lived there peacefully for 500 years until Columbus landed at Discovery Bay in 1494. The contact with the Spanish was very traumatic to the Arawaks. Within 70 to 100 years of first contact, the entire Arawaks population was eliminated, leaving only a few artifacts behind. With the natural inhabitants gone, the Spanish had unlimited control over the island. Since the island had no rich abundant gold sources, it meant little to the Spanish Crown. Instead, Jamaica was used as a base in which to launch attacks on the rest of the Americas. The population of Jamaica, even its capital Santiago de la Vega (now Spanish Town) never grew very large and was easy to capture. The British, after failed to capture Hispaniola, needed a solid base in the Caribbean. So in 1655, Admirals Penn and Venables attacked the sparsely defended island of Jamaica. Having little importance to the...

Common Examples of Uncountable Sets

Common Examples of Uncountable Sets Not all infinite sets are the same. One way to distinguish between these sets is by asking if the set is countably infinite or not. In this way, we say that infinite sets are either countable or uncountable. We will consider several examples of infinite sets and determine which of these are uncountable.​ Countably Infinite We begin by ruling out several examples of infinite sets. Many of the infinite sets that we would immediately think of are found to be countably infinite. This means that they can be put into a one-to-one correspondence with the natural numbers. The natural numbers, integers, and rational numbers are all countably infinite. Any union or intersection of countably infinite sets is also countable. The Cartesian product of any number of countable sets is countable. Any subset of a countable set is also countable. Uncountable The most common way that uncountable sets are introduced is in considering the interval (0, 1) of real numbers. From this fact, and the one-to-one function f( x ) bx a. it is a straightforward corollary to show that any interval (a, b) of real numbers is uncountably infinite. The entire set of real numbers is also uncountable. One way to show this is to use the one-to-one tangent function f ( x ) tan x. The domain of this function is the interval (-π/2, π/2), an uncountable set, and the range is the set of all real numbers. Other Uncountable Sets The operations of basic set theory can be used to produce more examples of uncountably infinite sets: If A is a subset of B and A is uncountable, then so is B. This provides a more straightforward proof that the entire set of real numbers is uncountable.If A is uncountable and B is any set, then the union A U B is also uncountable.If A is uncountable and B is any set, then the Cartesian product A x B is also uncountable.If A is infinite (even countably infinite) then the power set of A is uncountable. Two other examples, which are related to one another are somewhat surprising. Not every subset of the real numbers is uncountably infinite (indeed, the rational numbers form a countable subset of the reals that is also dense). Certain subsets are uncountably infinite. One of these uncountably infinite subsets involves certain types of decimal expansions. If we choose two numerals and form every possible decimal expansion with only these two digits, then the resulting infinite set is uncountable. Another set is more complicated to construct and is also uncountable. Start with the closed interval [0,1]. Remove the middle third of this set, resulting in [0, 1/3] U [2/3, 1]. Now remove the middle third of each of the remaining pieces of the set. So (1/9, 2/9) and (7/9, 8/9) is removed. We continue in this fashion. The set of points that remain after all of these intervals are removed is not an interval, however, it is uncountably infinite. This set is called the Cantor Set. There are infinitely many uncountable sets, but the above examples are some of the most commonly encountered sets.

All Politics is Local Essay Example | Topics and Well Written Essays - 1750 words

All Politics is Local - Essay Example Moreover, games both online and offline and smart phones are getting attention of learners. (Wagner et al.3) Laptops, videotapes, flash drives, cell phones, cell phones, networks, printers, tablets, computers, scanners, class management software programs, interactive whiteboards, internet technology and gaming consoles have one way or the other affected today’s schools. They have created a division in education system globally. In some way, technology use has serve schools well; modern technology has equalized educational opportunities and is playing an important role in all stakeholders who include parents, students, administrators, teachers, and school communities. For instance, Modern technology has removed geographical and generational barriers from learners; it has also lowered the cost of operational and instructional delivery of modes. This has also facilitated student-center education by allowing student to be more actively involved in technology-driven studying proces s and improve the quality of education aiming at individuals and it has made easier for remedial classes among individual students. Technology has been revolving in order to make studying process more efficient at a manageable cost. This has made legislators, policymakers, governors to have a tough time each year while trying to make attractive choices when it comes to educational improvement options. They have to know whether to use technology to invest in teacher training, class size reduction, or textbooks and tests. First, let us focus how technology has eliminated geographical and other barriers; internet connection has enabled everyone to get any online programs from any place in the globe it has brought impact in educational system. Any location someone is even it is overseas, one can access online program easily. Actually, the isolation or the geographical distance does not matter as it once did. The unseen web has, made a sense of togetherness possible to the whole world, b ecause the virtual classrooms have taken away geographical and time separation across the world. The classes are now archive, whereby someone can hold more jobs a day and later view or listen to class work later. In addition, modern institutions offer massive open online courses for free in order to reach on students from anywhere free so that they can cut the cost o education. Secondly, modern technology has reduced the cost of instructional operation; the overall operational cost of running a school has reduced by far with the use of modern technology. We know that running a brick and mortar school is costly than running an online school. No money I needed to invest in building infrastructure such as dormitories, library, classrooms, and other needed facilities such as parking lots. We do not need all this facilities in online programs, for instances, we can have ebray or cbrary created from consortium of schools from online school. Cybrary will make students who are registered to get resources of this consolidated library. Modern technology enables students and schools to leave behind a very small copy of carbon footprints as stunts do not go anywhere thus saving gas and making their cars to last because there is no wear and tear. The money saved from gas, for instances, can be used to upgrade the laptops o purchasing a quicker internet service provider. The initial cost of putting an online I very cheap compared to starting a traditional school. There is no need of many material things in starting

Principles and Practice of Psychosocial Rehabilitation (mental Essay

Principles and Practice of Psychosocial Rehabilitation (mental nursing) - Essay Example It is reported that the rehabilitation unit helped Mr. Brayan to develop living skills such as cognition, using laundry, cooking food etc. Psychosocial Rehabilitation is the process in which the psychiatric patients are trained systematically to bring back them to the active participation in the society. â€Å"Psychiatric rehabilitation aims to improve the functioning and quality of life of individuals with psychiatricdisabilities due to serious mental illnesses†. (Rudnick 2003, p.1). â€Å"The strategies adopted for the management of schizophrenia may differ from one country to other country and may influence motivational readiness for change. For this purpose, rehabilitation approaches like vocational training, employment guidance, cognitive behavioural therapy, and psychosocial methods were included. In addition, issues surrounding gender differences, scarcity of resources, conventional medicine, and importance on family role were also need to be considered for the rehabilitation of patients.† (Review of Literature, p. 2.). The recovery is the objective of the psychosocial rehabilitation. In this case study the Psychosocial Rehabilitation of a patient suffering from Schizophrenia in Shellharbour Hospital Mental Health Rehabilitation Unit is done. The aim of the rehabilitation is to enhance the quality of life of the patient named Brayne, who is a 45 years old male with chronic Paranoid Schizophrenia. Brayne lives alone. His functioning at home was very poor. He was not able to manage his finance and his condition make him vulnerable to the extend of exploitation by other. These conditions often leave him without sufficient money towards the end of each fortnight for basic necessities such as food and transport. He came to rehabilitation in need of help in Shellharbour Hospital to learn many skills like how to use kitchen for cooking, how to use the laundry etc. The case study further explains about the rehabilitation program that is carried out in the Mental