A Surreal Land :: Mathematics Papers

A Surreal Land "To infinity and beyond!" These were the inspired words of Buzz Lightyear in the Disney movie Toy Story. Granted, one would not expect to find much mathematical content in an animated film directed toward children, but these words raise an interesting issue that mathematicians and the general public struggled with for many years. Can one go beyond infinity? How can such a concept be possible or even imaginable? These questions led to the development of many new theories and even a new system of numbers. Disney's Buzz Lightyear A study of infinity must begin with an introduction to set theory. A set is merely a collection of objects. Georg Cantor was the sole creator of set theory; he published an article in 1874 that marks the beginning of set theory and has come to change the course of mathematics. Cantor's theory was met with a great deal of opposition due to its assertion of infinite numbers. The famous mathematician Leopold Kronecker was especially opposed to Cantor's revolutionary new way of looking at numbers. Kronecker believed only in constructive mathematics, those objects that can be constructed from a finite set of natural numbers. Despite this opposition from influential thinkers, set theory laid the foundation for twentieth century mathematics. Although there were some flaws in Cantor's theory, sets became an essential part of new mathematics and therefore set theory was adapted to eliminate its original paradoxes [2]. Georg Cantor Cantor's set theory incorporated infinity in the form of infinite cardinal numbers. Cardinal numbers are those which measure the number of objects in a set, as opposed to ordinal numbers, which are numbers with a fixed predecessor and successor. If two sets have equal cardinality, then they contain an equal number of objects. One way to determine this is through "one-to-one correspondence." Two sets are said to be in one-to-one correspondence if each object, or element, of the first set can be paired with exactly one element of the second set, and vice versa [1]. Cantor compared the cardinality of the set of all positive even integers to the set of all positive integers and found them to be equal. Thus the infinite cardinal number of these two sets is the same and is defined to be aleph-naught. This is the first transfinite number. The set of rational numbers also has a cardinality of aleph-naught, and thus is the same size as the set of integers.

Reaction Paper on Hello Garci Tape Wiretapping Issue

The electoral fraud issue on last 2004 election has proven an obvious breach in the national security. The tape evidence presented by Samuel Ong, former National Bureau of Investigation (NBI) deputy director for intelligence, contained a conversation between the former President Arroyo and Commissioner Virgilio Garcillano. Having analyzed the content of the said conversation, proven and admitted by the former president that the voice was hers, somehow confirmed the point of manipulation of the count in favor of the administration , perpetrated by the COMELEC However, even with the evidences, with the public apology made by the former president herself, and with the possible outcomes known, still no final course of action was taken to resolve GMA’s legitimacy or so to prevent electoral fraud. This is only due to the fact that the ‘original tape’ has not been authenticated by the anonymous wiretapper. If I may put my two cents in, our election system is just so full of dirty tricks. No one gets caught or punished also because of the flaws in the Philippine law and electoral rules. The fraudulent electoral system has been the way of the cheaters to win, and with their get away schemes comes the delayed progress of the country. Most are often suspicious of the winners and it is not a surprise that people generally doubt their leaders. If the leader is successful of curtailing the truth, what more can people expect of its underlings? Along with this, it is only imperative that electoral reforms be pushed through the senate or the country will continue to suffer from recurrence of such scandals and crisis. After the sprung of the aforementioned issue, wiretapping became a major contributor on certain issues from the government. Some of which are those that involve Chair Benjamin Abalos and Jose de Venecia III in connection with the $329-million National Broadband Network (NBN) contract, and Cheche Lazaro’s wiretapping case filed by the GSIS. The latter however in opinion of the many, was only one of the attempts by government agencies to silence the media through harassment and intimidation. None of the aforementioned issues that involve wiretapping has been resolved. It is just poignant that people find no justice in the wrongdoings of those in high power. Seemingly, in most cases our own system constricts punishments of those guilty personnel, only allowing recurrence of such events. If only our country IS or WILL be able to make a change for the greater good, those types of cases will not be dismissed without fair justice.

Personal Financial Planning Worksheet Essay

Based on your readings and discussions in class this week, answer the following multiple choice questions. 1. The process of creating a detailed plan to meet your financial needs and prepare for the future is called a. developing goals b. personal financial planning c. collecting financial information d. personal finance The answer would be (B) Personal financial planning. 2. Which of the following is not one of the five major steps of the financial planning process? a. Analyze your current finances. b. Establish and implement your plan. c. Collect and organize your financial information. d. Reevaluate and revise your plan as needed. The answer would be ( C) Collect and organize your financial information. 3. Which phase in life is commonly associated with focus on marriage, family, purchasing a home, and career development? a. Teenage years b. Between your 50s and 60s c)Late 20s through your 40s c. During retirement The answer would be (c) 4. Which of the following is a benefit of having a college degree that can affect your financial planning? a. The potential to make a higher salary b. Jobs with retirement plans and benefits c. The ability to receive promotions and wage increases d. All of the above The answer would be (D) All of the above 5. Which of the following elements of a comprehensive financial plan involves analyzing future needs, such as saving for retirement or college funding for dependents? a. Building wealth b. Securing basic needs c. Establishing a firm foundation d. Protecting wealth and dependents The answer would be (a) Building wealth Directions Respond to the following short-answer questions in 50-to 100-words: 6. People have different styles when it comes to handling their money. List the two things that affect your personal beliefs and opinions about financial planning. How well do you feel you manage your money? Can you spot areas for improvement in your money management style, and if so, where/how? I feel lthat I don’t manage my money as well as I should . I find myself waisting money on things I don’t need.I defiently need to improve on making a list when going to the grocery store.I always write a list but never stick to it .I end up spending more money than I budget for. 7. Which element of the comprehensive financial plan focuses on your housing  needs, setting aside money for emergencies, and establishing a career path? Consider your own finances. Do currectly own a vehicle and/or home? If yes, how well do you manage monthly home and auto expenses? How well do you save for unforeseen expenses? I manage my home and auto expenses pretty well . I place these things high priority. With having kids things are pretty tight . I have a small rainey day savings. I try to save for things like this as much as possible , because my car and home is two things I need. 8. The economy is unpredictable and can affect your personal financial planning. List one factor in economic conditions that may affect your financial future. How could you reduce the impact of that factor on your finances? One factor in economic conditions that may affect my financial future would be Job employment and security. In a tough economy its hard to maintain a job and job security. To reduce the impact of job employment I will save and do whats needed to maintain my job. That is honestly the best plan for me in this economy. 9. Which step in the five-step financial planning process requires you to organize your financial information, create personal financial statements, and evaluate your current financial position? Have you ever completed this step? If so, is it still applicable to your current financial situation? If not, do you plan to do this soon? Why or why not? 10. Step Five in the five-step financial planning process discusses the importance of regularly reevaluating and revising your plan because personal circumstances often change. List two life changes that may require you to update your financial plan. Have you recently experienced a change that requires you to reevaluate your financial plan? If so, what was it and how have you accommodated it? (Please share only what you are comfortable sharing)

Richard Nixon and the WaterGate Scandal Essay Example | Topics and Well Written Essays - 2500 words

Richard Nixon and the WaterGate Scandal - Essay Example The edifice of the Watergate scandal has been based on corruption, espionage and antidemocratic activities, ostensibly based on ensuring President Nixon, a second term in the Oval Room. However, certain facts like the Vietnam war, the release of Pentagon papers, and growing public resentment for his policies were serious impediments to this objective and had to be dealt with a firm, and if necessary, strong arm methods. This was ensured by use of the CIA and other governmental agents to discredit the President's political opponents, and seek to ensure his victory in the Presidential elections. He was able to achieve re-elections but he was constrained to pay the final price in terms of loss of his office and personal humiliation amidst a political scandal that rocked the entire country and shocked the world into mute speechlessness. At the time of instigating the Watergate scandal, President Nixon was not aware, or did not make himself to visualize that his political career would leave him a bitter and disillusioned man, devoid of moral principles and ethics that are the hallmarks of a strong and committed leader.This entire episode started when, while conducting security checking at the Watergate hotel, a security guard noticed a door prevented from closed by the use of tape. He removed the tape and continued with his check However, he was dismayed to find, that on his return, the door was reaped. He informed the police about the burglary. The police arrested five persons from the office of the Democratic National Congress, who had been illegally repairing wiretapping equipment and taking photographs of documents. Likewise, before the burglary in the Watergate Hotel on June 17, 1972, when a group of five burglars, who were members of a group of anti-Castro Cuban refugees called 'Plumbers', broke into the Democ ratic Party's National Committee offices, the term "Watergate" had no greater implication to the Americans and the entire world, rather than an office and a sumptuous apartment complex in Washington, D. C. As a result of the 'third-rate burglary', "it came to be associated with the greatest political scandal of that century and would change the lives of the many people involved" - principally the then President Richard M. Nixon and as for the present day political system, it imparts great meaning. (U.S. History.com, 2008). In the current American Background, the term Watergate has become a common phrase which denotes and expresses the fall of Richard Nixon, one of the most outstanding political figures of the 20th century America and the world. He had refused to hand over incriminating tapes illegally recording the conversation he had when he served in the White House. He refused to hand over the tapes even during the Supreme Court Proceedings. The Court had no other option but to impeach the President, but he preferred to resign rather than face impeachment. The former President of the USA was the only conspirator in the Watergate scandal who did not go to jail. "The lessons learned by these events are enormous. The story of Watergate is a complex and deep one full

Microeconomic Essay Example | Topics and Well Written Essays - 500 words

Microeconomic - Essay Example Policymakers intervene in the market by establishing market controls. When the government think that the prevailing market price if unfair to buyers and sellers, they enact price controls which involves setting a price ceiling or a price floor. This paper will look at how price ceiling affect market outcomes specifically focusing on the case of rent controls in the short and long run. A price ceiling is "a legal maximum on the price at which a good can be sold" Supply Demand and Government Policies 4). It should be noted that setting a price ceiling can bring two different outcomes in the economy. The price ceiling becomes not binding if it is set above the equilibrium price. The price ceiling is only binding if it is lower than the equilibrium price. However, this situation brings about shortages because quantity demanded is greater than quantity supplied. It should be noted that a binding price ceiling also leads to non-price rationing in the forms of long lines, black markets, and seller discrimination. The primary goal of rent control policy is to make housing more affordable to the less fortunate. Thus, the government enacts rent control which establishes the price ceiling that tenants can charge their landlords. However, as will be illustrated below, one economist says that rent control is "the best way to destroy a city other than bombing" (Mankiw 84). In the short run, both the demand and supply for housing is inelastic.

The capital structure decision and the cost of capital Research Paper

The capital structure decision and the cost of capital - Research Paper Example Thus a lesser D/E ratio would be recommended for a typical company. Therefore, D/E ratio = aggregate liabilities/ shareholders’ equity A very high D/E ratio would translate to the fact that the company has been applying debt in its growth to a high extent. The resultant impact is a scenario of very volatile earnings by the company due to the marginal interest expense. If a company applied a lot of debt financing to finance additional business operations, this would result to more generation of revenues and if the revenues outdo the costs, then the shareholders would be left better of since they would earn more dividends. But it is essential to note that this is if, and only if, the earnings surpass the cost of debt. D/E ratios may also vary depending upon the industry the company is operating. For instance, a company that is highly capital intensive would have a higher D/E ratio than those who operate computer software operations. (Gibson, 2008 p260) MATTEL Mattel is a premier company for toys. It designs, manufactures as well as markets toys. The Company’s believes that PLAY is vital for the development of Children besides other benefits. These include the development of imagination and creativity, good healthy interaction and the construction of strong learning foundation among others. Most of Mattel’s business is done online. ... They say their business is global and thus, internationalized and have subsidiaries besides the parent company which is registered in the US. (mattel.com, 2011) Mattel’s gross sales are formed up as follows: 30% in Latin America, 52% in Europe, 11% in Asia Pacific and 7% in others areas. They manufacture toy products themselves as well as outsourcing from other companies. Their main manufacturing facilities are set up in Indonesia, China, Malaysia, Thailand and Mexico. Their business is also seasonal where they experience peaks during the traditionally set holiday seasons. In fact the biggest sale revenues are experienced in the 3rd and 4th quarters of their fiscal year. The risks facing Mattel are only based on non-satisfaction of clients since its business depends almost entirely on Toy business. Shifts in demand would, therefore, impact adversely on their business. Seasonality as mentioned earlier is also another risk as well as inaccurate anticipation of the trends and cul ture. Though no market beta is given on this website, it is stated in their 2010 financial reports that the business is highly dependent on market behavior, where it faces to a large extent both foreign and local market rates of interest variances that form up market financial risk. (files.shareholder.com, 2011) Mattel Company had a market beta of 1.0 as reported by smartmoney.com website as of 2011. (smartmoney.com, 2011) Due to the high levels of financial risks that Mattel as a company faces and its doing business world wide, usage of debt as a source of capital would have a very huge impact on the capitalization of the company. Therefore, the recommendation is

Criminal investigation Essay Example | Topics and Well Written Essays - 1250 words - 1

Criminal investigation - Essay Example uthouse having hay or grain therein; any barrack, rick or stack of hay, grain, or bark; any public building, church or meeting-house, college, school or library. (Arson, lectlaw, n.d). Chapter 806.01 of the Florida Statutes, considers a person guilty of arson if that person wilfully and unlawfully or while in the commission of a felony by fire or explosion damages or causes to be damaged any structure, or structure in which people are usually present for example – jails, prisons, hospitals, department stores, offices, churches, educational institutions, during the time when these are occupied as also, the damaging by these means of any structure which this person knows is occupied. Such a person is deemed to be guilty of arson in the first degree. This constitutes a felony of the first degree, punishable as per the provisions of sections 775.082, 775.083 or 775.084. These Statutes further, state that a person who commits an act of arson which results in physical harm to any other person, irrespective of intent to cause such harm, is considered to be guilty of misdemeanour of the first degree. This is punishable under sections 775.082 and 775.083. (The 2005 Florida Statutes n.d). According to this definition intent is not an important criterion in deciding whether a person is guilty of arson or not. In the case under consideration the accused agreed that he had applied a flame to the canvas litters. He stated that he did this to determine whether the canvas litters were fire proof or not. Though he had no intention of causing harm to anyone or any property he wilfully started the fire. As per the Statutes he is guilty of arson. As a consequence of this fire one person died due to asphyxiation while others were injured. In view of the above, John Notthink is guilty of arson of the first degree and is punishable under sections 775.082, 775.083 and 775.084 for first degree arson, which is a felony of the first degree. To prove an arson charge it is sufficient if it