Betrayed by my best friend Essay Example

Betrayed by my best friend Essay As a child growing up friends are everything. Your best friend is the one you share all your secrets with and trust them not to tell anyone. They are the one who knows everything about you and stands by your side through everything. For some, best friends may change frequently, but that wasnt the case of Michelle and l. That was the type of friend Michelle was. We had been friends since the first grade and shared everything. We never kept secrets from one another and more importantly, we never shared those secrets with anyone else. Well at least I didnt. One fall I learned many important lessons in life. We will write a custom essay sample on Betrayed by my best friend specifically for you for only $16.38 $13.9/page Order now We will write a custom essay sample on Betrayed by my best friend specifically for you FOR ONLY $16.38 $13.9/page Hire Writer We will write a custom essay sample on Betrayed by my best friend specifically for you FOR ONLY $16.38 $13.9/page Hire Writer The most important one was not to trust people. Sounds cynical I know, but I dont know any other way to put it. I was 12 years old and trust had never been an issue for me, but that year brought on many changes. On a beautiful Saturday afternoon my whole outlook on life changed. On a day that seemed like so many before, my brother-in-law raped me. Dealing with that was more than I knew how to handle. The betrayal of the one person I thought I could trust only added to the pain. A few weeks passed before I could even bring myself to tell Michelle. He had made me feel like it was my fault, that I had done something to deserve it. He has also convinced me that if my sister found out it would cause her to lose the baby she was carrying. At that time I really didnt know any better so I believed him. Finally I realized I had to tell someone and of course Michelle was who I turned to. I explained what happened, how it made me feel, how it made me view things. Never in my life did I think she would tell anyone. Once again I was wrong, within three days it seemed the whole school knew. To make matters worse Michelle told people that it had been my fault. That it wasnt rape at all, that I had agreed to it. Even worse she told them I was pregnant by him. I couldnt understand how she could do something like that to me. Here I was trying to cope with what had been done to me physically and she betrayed me in a way that I couldnt even begin to understand. Granted, in time the talk moved on to something else as it always does in schools, and they all realized that I wasnt pregnant. Still, the damage to me was already done. I learned the hard way the need to be careful who you trust. It is something that was remained with me to this day. After being betrayed by my best friend, it became nearly impossible to trust anyone. Betrayed by my best friend By eschewing 123

A Report On The Novel 1984, By George Orwell Essays - Free Essays

A Report On The Novel 1984, By George Orwell Essays - Free Essays A Report on the novel 1984, by George Orwell The Importance of 1984 1984 was a very important book. First, it helped show where communism was headed, and helped create repulsion towards Communism. Before this book (and Animal Farm) a lot of people thought Communism was a good thing. The major mainstream generally neutral about it, but this book really opened up and showed what a bad idea it was, because it showed where communism was headed, not a place where everyone was equal, but a place that was once that and evolved into a horrible totalitarian government that could never be toppled. Second, I'm not sure whether this book could last for years for generations to enjoy. Although I hope it remains a favorite, it was really ment as a political novel of the 20th century. It could still last though, if people don't forget about the 20th century, or something similar to communism appears in the future. (and even if that doesn't happen, it will probably still be liked because it's just a good book) Also, it would be ironic if something sim! ilar to "newspeak" comes about, English is forgotten and this book would be unreadible. Third, I think this shows an interesting portrait of human life. It's true, the upper class always tries to stay upper, the middle class tries to join the upper class, and the lower class wants everyone to be equal. Forth, I think this book would go very good in a series. I don't mean exactly sequels, but the "world of 1984", a series of books that shows Big Brother's rise to power, and who he really is, stories about Eastasia and Eurasia, what's going on in the Inner Party, a visit to the place where the telescreens are monitored, et cerera (by the way, I think there might be a sequel, I'm not sure. I saw a book that's supposed to be similar, only it's in the year 2000 and written by a different author, and it was written in the last two years) Well, I hoped I proved why 1984 is my favorite book, I guess. Summary of 1984 This story takes place in London, Airstrip One, formally called England, before it joined with North America, South America and some small European countries to form Oceania, which is based on the Ingsoc (English Socialism) political structure, which consists of Big Brother, the Inner Party, the Outer Party, and the proles. Big Brother is the mysterious elite totalitarian leader, whom the Outer Party adores. Only his voice is heard on the telescreen (a two direction broadcasting television, used for constantly pumping propaganda into people while monitoring them simultaneously), and a picture of him is posted on the walls. No one knows where he resides, and no one knows what his real name is. Then there's the elite, the Inner Party. They're upper class, and their main focus is to keep the middle class (the Outer Party) and the lower class (the proles) in line, and prevent them from getting to their status or starting revolutions or something. They get the Outer Party in line by getting them to love Big Brother, torturing them, and constantly pumping their heads with propaganda. They get the proles in line by keeping them ignorant, by giving them entertainment and such to keep them happy, and keep them ignorant about the suffering and injustice going on. If the proles wished so, they could easily overthrow the party. The book's main character is named Winston Smith, and he's from Airstrip One. He works at the Ministry of Truth, a place where propaganda is made, and media is changed and edited. Winston's job is editing old copies of The Times, which is the newspaper in London. Winston had been a thought criminal, which is someone who thought against Big Brother or the establishment, even very slightly. Winston bought a diary, and wrote "DOWN WITH BIG BROTHER" in it, as kind of a way to express himself and his rebelliousness on paper. Soon, Winston has an affair with a women named Julia. They rebel against Big Brother by loving each other, and having sex. Love and sex are against Big Brother because they divert love and energy away from him. Winston

School uniform Essay Example | Topics and Well Written Essays - 1500 words

School uniform - Essay Example Some students and organizations, which promote freethinking and freedom of expression, have strongly contest in requiring school uniforms. This paper asserts that public school students in the US should be compelled to wear school uniforms by pointing out the various advantages would bring in terms of financial implication, convenience, safety in school, students' sense of identity and belonging as well as their discipline and learning. It is clearly seen that school uniforms would help parents save money on their children's clothing expenses. The set of tailor-made uniforms would be used by students on school days so parents would not have to be burdened with always buying clothes for their kids. With this, students would not find a reason to impel their parents to buy clothes for school since they already have school uniforms. Aside from this, wearing of school uniforms would also facilitate the convenience of students in selecting day-to-day clothes. Normally, these students encounter difficulties in choosing what to wear in school. At times, this problem may cause them to be late for class as they can hardly decide on what to actually wear or how to mix-and-match their clothes to look good. With school uniforms, they can save time in going about the said dilemma every morning. Instantly, they have something to wear everyday without the worries if their peers or classmates would notice if they wear the same clothes at frequent intervals. Some argue that requiring school uniforms may be burdensome for low-income families since even school uniforms are acquired at a cost. But then this argument can be countered by the fact that school uniforms are still relatively more affordable that most clothes bought in malls, particularly the branded ones. Moreover, students whose parents could not afford trendy clothing or designer wear would be saved from embarrassment, especially at the adolescent stage where looking good is an important factor for social acceptance. Safety of Students With the advent of gang-related clothing such as loose-fitting clothing style, public school officials have related these trends with the aggravation of school violence. This is because baggy clothing style characterized by oversized shirts and pants may be one of the ways by which students or gang members bring in weapons and drugs to school concealed in their clothes. Moreover, gang members, who may dress in the same way as regular students, easily gain access in public schools by mixing with the school crowd. These increase the incidence of violence in public schools and make both parents and students be troubled about safety. To address the rising incidence of school violence, public school officials have considered implementing the policy on school uniforms so that public school students would become more easily identified and screened. School security officials may disallow entry of those who are not in school uniform. As such non-students and outsiders would be able to access the school premises and adversely influence students by distributing deadly weapons or illegal drugs. Such would also help prevent school violence. This does not mean though that this would be the only security measure undertaken by school officials. In

Walmart Undergoing Change Case Study Example | Topics and Well Written Essays - 750 words

Walmart Undergoing Change - Case Study Example It is expected that this change will greatly improve the performance and the competitive advantage of the company in the business environment. The needs of employees are often met by the leadership of a company or organization. The needs of employees within Wal-Mart’s different functional areas will therefore be met under a unified team of leaders. There are diverse needs among employees such as effective compensation, benefits, good working environment and suitable working hours. These needs would be affected by the new leadership structure. For example the needs of employees within the Logistics function are likely to be different from those within the Real Estate function. In order for these change to be effective, it is therefore necessary for the company leadership to effectively communicate with employees and understand their needs so that an effective plan for meeting them would be implemented (Vakola & Nikolaou, 2009). Since the organizational change at Wal-Mart is aimed at improving the service delivery to the customers, it is evident that the company is likely to recruit new employees to ensure that this objective is achieved effectively. The management of organizational change includes meeting the training needs of new employees (Tsoukas & Chia, 2008). This means that the new leadership team within Wal-Mart will be responsible for developing a training program in which the skills and knowledge of new employees on the job will be effectively attained. In the selection of new employees, the company must adhere to the recruitment policies within its policy notebook. This means that the required level of education, experience, skills or knowledge for the various functional areas of the company must be exhibited by the new employees. The recruitment process must also ensure that the new employees will add more value to the company through promoting its productivity and making it more competitive in its market. Since the systems and

Employee Privacy Rights in the Workplace Essay

Employee Privacy Rights in the Workplace - Essay Example The employees, caught in the middle, depend on references to find gainful employment, but may jeopardize their eligibility if a reference portrays them in a negative light. The wider community (consumers, families, friends and acquaintances of employers and employees) may be equally affected when full disclosure does, and does not, occur. It is contended in this paper that it is vital that standardized national laws should be developed to protect past and future employers, the employees themselves, as well as the communities they work within. Firstly, the growing trend of litigation against former employers will be presented. Secondly, the laws across the states will be outlined in regards to former employer's disclosure of ex-employee information. Thirdly, reasons to standardize the laws will be provided. Finally, a conclusion shall synthesize the main points of the paper, and provide support for the adoption of a standardized national employment and labor policy in regards to termination disclosure. It is becoming more common for employees to ask their former employers for a written reason for their termination of employment, as well as a copy of their personnel record (Boisvert, 1999). It has been suggested that for previous employers, such a request is a cause for concern, as it is often a clear indication of discontent on behalf of the employee, and likely that the employee has consulted with a lawyer and is considering a lawsuit. As such, it is recommended to employers to assume they may be as risk of being sued, and to seek advice from their attorney immediately (Boisvert, 1999). When an employer terminates an employee they must be aware of the risk of being presented with a lawsuit, and have risk management policies in place to minimize such an event from occurring. The process of providing a reference for the employee will play a large part in determining if the employee can make a legal claim (Boisvert, 1999). For this reason, there has been an increasing tendency for e mployers not to provide comprehensive details of a former employees work practices. Many employers are heeding their lawyer's advice to tailor references to provide a neutral profile of the employee. In general, this involves confirming the employee's position, dates of employment and salary (Boisvert, 1999).There are numerous areas of potential liability for the former employer when providing a reference (Lovett & Potter, 2004). Most notably, is the risk of being sued for defamation or invasion of privacy. There is also the risk of liability for retaliation, such as when management takes revenge on an employee for a past non-compliance within the organization. Another liability risk is that of 'compelled self-publication' which occurs when an employee must repeat what they perceive to be false allegations as their reason from termination, so that the future employer does not hear it first from a previous employer (Lovett & Potter, 2004). In general, employers should implement polic y for the response to requests of a written reference, or for requests of information from future employers (Boisvert, 1999). It is recommended that such a policy prohibit employees from disseminating information about their co-workers, and that the policy direct all inquiries for information

Construction Of Real Numbers

Construction Of Real Numbers All mathematicians know (or think they know) all about the real numbers. However usually we just accept the real numbers as being there rather than considering precisely what they are. In this project I will attempts to answer that question. We shall begin with positive integers and then successively construct the rational and finally the real numbers. Also showing how real numbers satisfy the axiom of the upper bound, whilst rational numbers do not. This shows that all real numbers converge towards the Cauchys sequence. 1 Introduction What is real analysis; real analysis is a field in mathematics which is applied in many areas including number theory, probability theory. All mathematicians know (or think they know) all about the real numbers. However usually we just accept the real numbers as being there rather than considering precisely what they are. The aim of this study is to analyse number theory to show the difference between real numbers and rational numbers. Developments in calculus were mainly made in the seventeenth and eighteenth century. Examples from the literature can be given such as the proof that Ï€ cannot be rational by Lambert, 1971. During the development of calculus in the seventeenth century the entire set of real numbers were used without having them defined clearly. The first person to release a definition on real numbers was Georg Cantor in 1871. In 1874 Georg Cantor revealed that the set of all real numbers are uncountable infinite but the set of all algebraic numbers are countable infinite. As you can see, real analysis is a somewhat theoretical field that is closely related to mathematical concepts used in most branches of economics such as calculus and probability theory. The concept that I have talked about in my project are the real number system. 2 Definitions Natural numbers Natural numbers are the fundamental numbers which we use to count. We can add and multiply two natural numbers and the result would be another natural number, these operations obey various rules. (Stirling, p.2, 1997) Rational numbers Rational numbers consists of all numbers of the form a/b where a and b are integers and that b ≠  0, rational numbers are usually called fractions. The use of rational numbers permits us to solve equations. For example; a + b = c, ad = e, for a where b, c, d, e are all rational numbers and a ≠  0. Operations of subtraction and division (with non zero divisor) are possible with all rational numbers. (Stirling, p.2, 1997) Real numbers Real numbers can also be called irrational numbers as they are not rational numbers like pi, square root of 2, e (the base of natural log). Real numbers can be given by an infinite number of decimals; real numbers are used to measure continuous quantities. There are two basic properties that are involved with real numbers ordered fields and least upper bounds. Ordered fields say that real numbers comprises a field with addition, multiplication and division by non zero number. For the least upper bound if a non empty set of real numbers has an upper bound then it is called least upper bound. Sequences A Sequence is a set of numbers arranged in a particular order so that we know which number is first, second, third etc and that at any positive natural number at n; we know that the number will be in nth place. If a sequence has a function, a, then we can denote the nth term by an. A sequence is commonly denoted by a1, a2, a3, a4†¦ this entire sequences can be written as or (an). You can use any letter to denote the sequence like x, y, z etc. so giving (xn), (yn), (zn) as sequences We can also make subsequence from sequences, so if we say that (bn) is a subsequence of (an) if for each n∈ à ¢Ã¢â‚¬Å¾Ã¢â‚¬ ¢ we get; bn = ax for some x ∈ à ¢Ã¢â‚¬Å¾Ã¢â‚¬ ¢ and bn+1 = by for some y ∈ à ¢Ã¢â‚¬Å¾Ã¢â‚¬ ¢ and x > y. We can alternatively imagine a subsequence of a sequence being a sequence that has had terms missing from the original sequence for example we can say that a2, a4 is a subsequence if a1, a2, a3, a4. A sequence is increasing if an+1 ≠¥ an ∀ n ∈ à ¢Ã¢â‚¬Å¾Ã¢â‚¬ ¢. Correspondingly, a sequence is decreasing if an+1 ≠¤ an ∀ n ∈ à ¢Ã¢â‚¬Å¾Ã¢â‚¬ ¢. If the sequence is either increasing or decreasing it is called a monotone sequence. There are several different types of sequences such as Cauchy sequence, convergent sequence, monotonic sequence, Fibonacci sequence, look and see sequence. I will be talking about only 2 of the sequences Cauchy and Convergent sequences. Convergent sequences A sequence (an) of real number is called a convergent sequences if an tends to a finite limit as n→∞. If we say that (an) has a limit a∈ F if given any ÃŽ µ > 0, ÃŽ µ ∈ F, k∈ à ¢Ã¢â‚¬Å¾Ã¢â‚¬ ¢ | an a | < ÃŽ µ n ≠¥ k If an has a limit a, then we can write it as liman = a or (an) → a. Cauchy Sequence A Cauchy sequence is a sequence in which numbers become closer to each other as the sequence progresses. If we say that (an) is a Cauchy sequence if given any ÃŽ µ > 0, ÃŽ µ ∈ F, k∈ à ¢Ã¢â‚¬Å¾Ã¢â‚¬ ¢ | an am | < ÃŽ µ n,m ≠¥ k. Gary Sng Chee Hien, (2001). Bounded sets, Upper Bounds, Least Upper Bounds A set is called bounded if there is a certain sense of finite size. A set R of real numbers is called bounded of there is a real number Q such that Q ≠¥ r for all r in R. the number M is called the upper bound of R. A set is bounded if it has both upper and lower bounds. This is extendable to subsets of any partially ordered set. A subset Q of a partially ordered set R is called bounded above. If there is an element of Q ≠¥ r for all r in R, the element Q is called an upper bound of R 3 Real number system Natural Numbers Natural numbers (à ¢Ã¢â‚¬Å¾Ã¢â‚¬ ¢) can be denoted by 1,2,3†¦ we can define them by their properties in order of relation. So if we consider a set S, if the relation is less than or equal to on S For every x, y ∈ S x ≠¤ y and/or y ≠¤ x If x ≠¤ y and y ≠¤ x then x = y If x ≠¤ y and y ≠¤ z then x ≠¤ z If all 3 properties are met we can call S an ordered set. (Giles, p.1, 1972) Real numbers Axioms for real numbers can be spilt in to 3 groups; algebraic, order and completeness. Algebraic Axioms For all x, y ∈ à ¢Ã¢â‚¬Å¾Ã‚ , x + y ∈ à ¢Ã¢â‚¬Å¾Ã‚  and xy ∈ à ¢Ã¢â‚¬Å¾Ã‚ . For all x, y, z ∈ à ¢Ã¢â‚¬Å¾Ã‚ , (x + y) + z = x (y + z). For all x, y ∈ à ¢Ã¢â‚¬Å¾Ã‚ , x + y = y + x. There is a number 0 ∈ à ¢Ã¢â‚¬Å¾Ã‚  such that x + 0 = x = 0 + x for all x ∈ à ¢Ã¢â‚¬Å¾Ã‚ . For each x ∈ à ¢Ã¢â‚¬Å¾Ã‚ , there exists a corresponding number (-x) ∈ à ¢Ã¢â‚¬Å¾Ã‚  such that x + (-x) = 0 = (-x) + x For all x, y, z ∈ à ¢Ã¢â‚¬Å¾Ã‚ , (x y) z = x (y z). For all x, y ∈ à ¢Ã¢â‚¬Å¾Ã‚  x y = y x. There is number 1 ∈ à ¢Ã¢â‚¬Å¾Ã‚  such that x x 1 = x = 1 x x, for all x ∈ à ¢Ã¢â‚¬Å¾Ã‚  For each x ∈ à ¢Ã¢â‚¬Å¾Ã‚  such that x ≠  0, there is a corresponding number (x-1) ∈ à ¢Ã¢â‚¬Å¾Ã‚  such that x (x-1) = 1 = (x-1) x A10. For all x, y, z ∈ à ¢Ã¢â‚¬Å¾Ã‚ , x (y + z) = x y + x z (Hart, p.11, 2001) Order Axioms Any pair x, y of real numbers satisfies precisely one of the following relations: (a) x < y; (b) x = y; (c) y < x. If x < y and y < z then x < z. If x < y then x + z < y +z. If x < y and z > 0 then x z < y z (Hart, p.12, 2001) Completeness Axiom If a non-empty set A has an upper bound, it has a least upper bound The thing which distinguishes à ¢Ã¢â‚¬Å¾Ã‚  from is the Completeness Axiom. An upper bound of a non-empty subset A of R is an element b ∈R with b a for all a ∈A. An element M ∈ R is a least upper bound or supremum of A if M is an upper bound of A and if b is an upper bound of A then b M. That is, if M is a least upper bound of A then (b ∈ R)(x ∈ A)(b x) b M A lower bound of a non-empty subset A of R is an element d ∈ R with d a for all a ∈A. An element m ∈ R is a greatest lower bound or infimum of A if m is a lower bound of A and if d is an upper bound of A then m d. If all 3 axioms are satisfied it is called a complete ordered field. John oConnor (2002) axioms of real numbers Rational numbers Axioms for Rational numbers The axiom of rational numbers operate with +, x and the relation ≠¤, they can be defined on corresponding to what we know on N. For on +(add) has the following properties. For every x,y ∈ , there is a unique element x + y ∈ For every x,y ∈ , x + y = y + x For every x,y,z ∈ , (x + y) + z = x + (y + z) There exists a unique element 0 ∈ such that x + 0 = x for all x ∈ To every x ∈ there exists a unique element (-x) ∈ such that x + (-x) = 0 For on x(multiplication) has the following properties. To every x,y ∈ , there is a unique element x x y ∈ For every x,y ∈ , x x y = y x x For every x,y,z ∈ , (x x y) x z = x x (y x z) There exists a unique element 1 ∈ such that x x 1 = x for all x ∈ To every x ∈ , x ≠  0 there exists a unique element ∈ such that x x = 1 For both add and multiplication properties there is a closer, commutative, associative, identity and inverse on + and x, both properties can be related by. For every x,y,z ∈ , x x (y + z) = (x x y) + (x x z) For with an order relation of ≠¤, the relation property is a. we can claim that < b. if not then since < a and > b we would have > b a. John OConnor (2002) axioms of real numbers Theorem: The limit of a sequence, if it exists, is unique. Proof Let x and x†² be 2 different limits. We may assume without loss of generality, that x < x†². In particular, take ÃŽ µ = (x†² x)/2 > 0. Since xn→ x, k1 s.t | xn x | < n ≠¥ k1 Since xn→ x k2 s.t | xn x†²| < ÃŽ µ n ≠¥ k2 Take k = max{k1, k2}. Then n ≠¥ k, | xn x | < ÃŽ µ, | xn x†²| < ÃŽ µ | x†² x | = | x†² xn + xn x | ≠¤ | x†² xn | + | xn x | < ÃŽ µ + ÃŽ µ = x†² x, a contradiction! Hence, the limit must be unique. Also all rational number sequences have a limit in real numbers. Gary Sng Chee Hien, (2001). Theorem: Any convergent sequence is bounded. Proof Suppose the sequence (an) ®a. take = 1. Then choose N so that whatever n > N we have an within 1 of a. apart from the finite set {a1, a2, a3†¦aN} all the terms of the sequence will be bounded by a + 1 and a 1. Showing that an upper bound for the sequence is max{a1, a2, a3†¦aN, a +1}. Using the same method you could alternatively find the lower bound Theorem: Every Cauchy Sequence is bounded. Proof Let (xn) be a Cauchy sequence. Then for | xn xm | < 1 n, m ≠¥ k. Hence, for n ≠¥ k, we have | xn | = | xn xk + xk | ≠¤ | xn xk | + | xk | < 1 + | xk | Let M = max{ | x1 |, | x2 |, , | xk-1|, 1 + | xk | } and it is clear that | xn | ≠¤ M n, i.e. (xn) is bounded. Gary Sng Chee Hien, (2001). Theorem: If (xnx, then any subsequence of (xn) also converges to x. Proof Let (yn) be any subsequence of (xn). Given any > 0, s.t | xn x | < n ≠¥ N. But yn = xi for some so we may claim | yn x | < also. Hence, ( Gary Sng Chee Hien, (2001). Theorem: If (xn) is Cauchy, then any subsequence of (xn) is also Cauchy. Proof Let (yn) be any subsequence of (xn). Given any s.t | xn xm | . But yn = xi for so we may claim | yn ym | Hence (yn) x Gary Sng Chee Hien, (2001). Theorem Any convergent sequence is a Cauchy sequence. Proof If (an) a then given > 0 choose N so that if n > N we have |an- a| < . Then if m, n > N we have |am- an| = |(am- a) (am- a)| |am- a| + |am- a| < 2. We use completeness Axiom to prove Suppose X ∈ à ¢Ã¢â‚¬Å¾Ã‚ , X2 = 2. Let (an) be a sequence of rational numbers converging to an irrational 12 = 1 1.52 = 2.25 1.42 = 1.96 1.412 = 1.9881 1.41421356237302 = 1.999999999999731161391129 Since (an) is a convergent sequence in à ¢Ã¢â‚¬Å¾Ã‚  it is a Cauchy sequence in à ¢Ã¢â‚¬Å¾Ã‚  and hence also a Cauchy sequence in . But it has no limit in. An irrational number like 2 has a decimal expansion which does not repeat: 2 =1.4142135623730 John OConnor (2002) Cauchy Sequences. Theorem Prove that is irrational, prove that ≠¤ à ¢Ã¢â‚¬Å¾Ã‚  Proof We will get 2 as the least upper bound of the set A = {q Q | q2 < 2}. We know that a is bounded above and so its least upper bound b does not exists. Suppose x ∈ , x2 0 be given. Then k1, k2 s.t | xn xm | < ÃŽ µ/(2Y) n, m ≠¥ k1 | yn ym | < ÃŽ µ/(2X) n, m ≠¥ k2 Take k = max(k1, k2). Then | xn xm | < ÃŽ µ/(2Y) | yn ym | < ÃŽ µ/(2X) n, m ≠¥ k Hence, | xn yn xm ym | = | (xn yn xm yn) + (xm yn xm ym) | ≠¤ | xn yn xm yn | + | xm yn xm ym | = | yn | | xn xm | + | xm | | yn ym | ≠¤ Y | xn xm | + X | yn ym | < Y(ÃŽ µ/(2Y)) + X(ÃŽ µ/(2X)) n, m ≠¥ k = Hence, (xn yn) is also Cauchy. 5 Conclusion Real numbers are infinite number of decimals used to measure continuous quantities. On the other hand, rational numbers are defined to be fractions formed from real numbers. Axioms of each number system are examined to determine the difference between real numbers and rational numbers. Conclusion of the analysis of axioms resulted to be both real numbers and rational numbers contain the same properties. The properties being addition, multiplication and there exist a relationship of zero and one. The four fundamental results are obtained from this study. First concept is that the property of real number system being unique and following the complete ordered field. Second is that if any real number satisfies the axioms then it is upper bound, whilst rational numbers are not upper bound. The third being that all Cauchy sequences are converges towards the real numbers. Finally found out that all real numbers are equivalence classes of the Cauchy sequence. Appendices List of symbols à ¢Ã¢â‚¬Å¾Ã¢â‚¬ ¢ = Natural number à ¢Ã¢â‚¬Å¾Ã‚  = Real number = Rational number ∈ = is an element of = There exists = For all s.t. = Such that

Lyric Analysis

Kayla Keeney English 131 Ms. Jones 20 Feb. 2013 â€Å"Not Ready To Make Nice† Rhetorical Analysis â€Å"Not Ready To Make Nice,† a song released in 2006 by the Dixie Chicks is a controversial song written after Natalie Maines commented that she was â€Å"ashamed the president of the United States is from Texas† (Tyrangie), in between songs at a concert in Britain in 2003. The comment resulted in The Dixie Chicks being dropped from playlists at many radio stations across the south (Tyrangie). This song is about how Maines is not willing to forgive all of the negative remarks and actions made towards the band, some which include death threats.One rhetorical tool used by the Dixie Chicks is pathos. The first verse, â€Å"Forgive sounds good/ Forget I’m not sure I could/ They say time heals everything/but I’m still waiting,†opens the song showing forgiveness, anger and sadness (Dixie Chicks). They are letting it be known that they would like to f orgive all of the people that have hurt Natalie, and the rest of the band, due to her comment, but some of the actions taken towards them were so extreme that they are not sure that they could ever forget them.The next verse includes the lines â€Å"I’m through with doubt/There’s nothing left for me to figure out/ I’ve paid a price and I’ll keep paying† (Dixie Chicks). When this, and the lines â€Å"It turned my whole world around and I kind of like it† are sung, Maines is making it clear that she does not have any regret about her comment towards President Bush and she is done doubting herself because of it. She is letting it be known that she may have had to pay a price of the Dixie Chicks music no longer being on the radio, but she is no longer going to doubt herself or regret her comment because she is entitled to freedom of speech.This brings a bitter sweet emotion into play, because she realizes many other people probably feel the same way; she just voiced her opinion publicly and is not ashamed of it. Pathos is used in that verse when she is talking about the price they will keep paying. Music is their career and it got taken away by one band member’s comment. That verse brings heartbreak to not only the song, but the band members who are so passionate about their music and career choice, along with the listeners that loved the Dixie Chicks music. Joy and peace is brought into the song when â€Å"I made my bed and I sleep like a baby. With no regrets†¦ † is said.Natalie is saying she is content with what she said and all the trouble she got herself and her band into. She has no regrets. â€Å"It’s a sad, sad story when a mother will teach her daughter that she ought to hate a perfect stranger, and how in the world can the words that I said send somebody so over the edge that they’d write me a letter sayin’ that I better shut up and sing or my life will be over† (Dix ie Chicks), brings a confused emotion. In the song when this verse is sung, it sounds like Natalie is going on a rant about how sad our world is today, and an angry tone of voice is used to really show her anger about the situation.She sounds scared, sad, and mad all at the same time. She is confused at society. All of the pathos used already throughout the song, bittersweet, heart break, joy, peace, and confused, is revisited again in the chorus, which states â€Å"I’m not ready to make nice/ I’m not ready to back down/ I’m still mad as hell and I don’t have time to go round and round and round/ It’s too late to make it right/ I probably wouldn’t if I could/ ‘cause I’m mad as hell can’t bring myself to do what it is you think I should† (Dixie Chicks).Ethos is also a rhetorical tool the Dixie Chicks used throughout the song. The Dixie Chicks have credibility writing and singing this song, because it goes a long wit h a life event of theirs. If another singer or band would have published â€Å"Not Ready To Make Nice,† it would not have had as much meaning or emotion, and it would not have been expressed as it was by Maines, unless they had a similar experience. After Maines was asked if she was sorry about her London comments, she said no and responded with â€Å"Sorry about what? Sorry about what?Sorry about not wanting to go to war? And not wanting people to die? â€Å"(Schorn) Many people felt the same way as Natalie Maines did, but did not voice their opinion in such a way as she did. She has every right to do so though. It is common for people to not like the idea of going to war. Americans have the right of freedom of speech, in other words, â€Å"the right to express any opinions without censorship or restraint. † Natalie Maines should be able to voice her opinion as she pleases, due to the first amendment, which brings logos into play.Maines Logos in â€Å"Not Ready To Make Nice† includes the comment itself, that was made and freedom of speech. Since the first amendment exists the Dixie Chicks should not have been punished like they were. Knowledge about the comment, and some background about the Dixie Chicks lives afterwards, is needed to make sense of the song and the meaning behind it. After finding out about the death threats made towards the band, and the banning of their songs on the radio, there is more of an understanding as to why there is so much pathos throughout.It is logical to think that the Dixie Chicks wrote this song as feedback towards country music listeners and southerners, to voice how they feel about the actions done towards them; it is their way of expressing their feelings publically a couple of years later. Through pathos, ethos, and logos, the Dixie Chicks are able to speak out publically to let the world know how Maines’ comment has affected them. Though Maines states she does not regret what she said, she m akes it clear that her life has changed forever, along with the Emily and Martie’s, the other band members.This song is a way for Maines to stand behind her comment and to stand up to President Bush. Behind the words is passion. The Dixie Chicks are passionate about the meaning they are trying to get across to listeners. They want listeners to feel what this song means to them and they want us to feel their emotions that they have poured into writing this song. â€Å"Not Ready To Make Nice† is a way for them to show courage, by telling the world they are at peace with what was said back in 2003. Works CitedChicks, Dixie. â€Å"Not Ready To Make Nice. † Cowboy Lyrics. cowboylyrics. com. Web. 19 Mar 2013. . â€Å"freedom of speech. † Dictionary. com Unabridged. Random House, Inc. 19 Mar. 2013. . Schorn, Daniel . â€Å"Dixie Chicks: Not Ready to Make Nice. † http://www. cbsnews. com/8301-18560_162-1611424. html. CBS, 11 February 2009.