Why Does Zero Factorial Equal One

A zero factorial is a mathematical expression for the number of ways to arrange a data set with no values in it, which equals one. In general, the factorial  of a number is a short hand way to write a multiplication expression wherein the number is multiplied by each number less than it but greater than zero. 4! 24, for example, is the same as writing 4 x 3 x 2 x 1 24, wherein one uses an exclamation mark to the right of the factorial number (four) to express the same equation. It is pretty clear from these examples how to calculate the factorial of any whole number greater than or equal to one, but why is the value of zero factorial one despite the mathematical rule that anything multiplied by zero is equal to zero?   The definition of the factorial states that 0! 1. This typically confuses people the first time that they see this equation, but we will see in the below examples why this makes sense when you look at the definition, permutations of, and formulas for the zero factorial. The Definition of a Zero Factorial The first reason for why zero factorial is equal to one is because this is what it the definition says it should be, which is a mathematically correct explanation if not a somewhat unsatisfying one. Still, one must remember that the definition of a factorial is the product of all integers equal to or less in value to the original number—in other words, it a factorial is the number of combinations possible with numbers less than or equal to that number. Because zero has no lower numbers but is still in and of itself a number, there is still but one possible combination of how that data set can be arranged: it cannot. This still counts as one way of arranging it, so by definition, a zero factorial is equal to one, just as 1! is equal to one because there is only a single possible arrangement of this data set. For a better understanding of how this makes sense mathematically, its important to note that factorials like these are used to determine possible orders of information in a sequence, also known as permutations, which can be useful in understanding that even though there are no values in an empty or zero set, there is still one way that set is arranged.   Permutations and Factorials A permutation is a specific, unique order of elements in a set. For example, there are six permutations of the set {1, 2, 3}, which contains three elements, since we may write these elements in the following six ways: 1, 2, 31, 3, 22, 3, 12, 1, 33, 2, 13, 1, 2 We could also state this fact through the equation 3! 6, which is a factorial representation of the full set of permutations. In a similar way, there are 4! 24 permutations of a set with four elements and 5! 120 permutations of a set with five elements. So an alternate way to think about the factorial is to let n be a natural number and say that n! is the number of permutations for a set with n elements. With this way of thinking about the factorial, let’s look at a couple more examples. A set with two elements has two permutations: {a, b} can be arranged as a, b or as b, a. This corresponds to 2! 2. A set with one element has a single permutation, as the element 1 in the set {1} can only be ordered in one way. This brings us to zero factorial. The set with zero elements is called the empty set. To find the value of zero factorial we ask, â€Å"How many ways can we order a set with no elements?† Here we need to stretch our thinking a little bit. Even though there is nothing to put in an order, there is one way to do this. Thus we have that 0! 1. Formulas and Other Validations Another reason for the definition of 0! 1 has to do with the formulas that we use for permutations and combinations. This does not explain why zero factorial is one, but it does show why setting 0! 1 is a good idea. A combination is a grouping of elements of a set without regard for order. For example, consider the set {1, 2, 3}, wherein there is one combination consisting of all three elements. No matter what order we arrange these elements, we end up with the same combination. We use the formula for combinations, with the combination of three elements taken three at a time and see that 1 C (3, 3) 3!/(3! 0!) and if we treat 0! as an unknown quantity and solve algebraically, we see that 3! 0! 3! and so 0! 1. There are other reasons why the definition of 0! 1 is correct, but the reasons above are the most straightforward. The overall idea in mathematics is when new ideas and definitions are constructed, they remain consistent with other mathematics, and this is exactly what we see in the definition of zero factorial is equal to one.

Parallels In Power And Othering In 1984 And Imbeciles.

Parallels in Power and Othering in 1984 and Imbeciles Like many I was aware of the eugenics movement in the United States in the 1920’s. However, after reading the story of Carrie Buck and learning more about the nature of the procedurals involved in these sterilizations I have a new found understanding of the roles Power and Othering played in the unlawful tests conducted on Carrie buck and many members of her family. The way in which those elite of the 1920’s mimics the party and the thought police in George Orwell’s 1984, is incredibly interesting to ponder. There are even instances of power and othering having the exact effects among nations today as well. The similarities between these major themes that we have continuously†¦show more content†¦Due to the popularity of the Eugenics movement among the social hierarchy there was ample opportunity for those employed the legal system to get involved such as lawyers and judges. This was such the case in Albemarle County, Virginia with Judge Oliver Wendell Holmes and Dr. John Hendren Bell working very closely together to protect the true intentions of the movement and to keep anyone the deemed â€Å"feeble-minded†, to be sterilized. Their relationship also allowed for the legal cover up and of these events and they also produced falsified documents to further protect the sterilizing program â€Å" Holmes agreed, telling Pollock the discussion make him inclined to believe â€Å"it would be possible to breed a race.† In the five years since his Illinois Law Review article, his phrasing had become more biological: he had gone from wanting to â€Å"build† a race to wanting to â€Å"breed† one† (Cohen, 2016:241-42). Once again, we can see the exploitation of power by those who possess it can lead to severely negative effects for the lesser classes. There is another great parallel example of such the abuse of power by the Party in 1984, with they have the ability to strip a person’s name from ever y record that exists which mean the Party has the power to remove a person’s entire existence. If that is not a clear and blazon example of absolute power over people than what else is? We also see examples this ability to use corrupt political

What do you understand by the term ‘hegemony’ Free Essays

Introduction This essay will consider the meaning of the term ‘hegemony’. It will weave personal interpretation with the academic literature, concentrating on Gramsci’s theory of cultural hegemony. Hegemony arguably originated with the Ancient Greek conception of political and military dominance (hegemonia means ‘leadership’ and ‘rule’) (Chernow and Vallasi 1994: 1215). We will write a custom essay sample on What do you understand by the term ‘hegemony’? or any similar topic only for you Order Now According to the traditional conception of hegemony the ‘ruler’ (hegemon) imposes its will upon subordinate states through the exercise or threat of military power, which is then translated into political dominance (Antoniades 2008). In the modern world, this kind of hegemony has largely disappeared. The mechanisms of control now operate in civil society in more subtle forms, such as politics, ideology, and the media. This essay will discuss some interpretation of hegemony and how they relate to contemporary capitalist society. Some scholars and political commentators, such as the former French Minister of Foreign Affairs Hubert Vedrine, believe that the United States is currently a global hegemon due to its widespread influence in countries such as Iraq and Afghanistan. However, as realist scholars such as Mearsheimer and Nye point out, the United States has never established a system of governance in these regions (Nye 1993). This political and military hegemony has largely disappeared. In its place one might say that there is a kind of ‘cultural hegemony’. This concept was theorised in the early 19th century by the Marxist philosopher Antonio Gramsci, who argued that the capitalist state was divided into two spheres, the ‘political society’, which rules through the use of force, and the ‘civil society’, which rules through popular consent. The latter is the public realm in which people, groups, trade unions and political parties interact. In this sphere, the ruling elite reproduce their ideology in popular culture and thus ‘manufacture consent’ for the bourgeois domination of the proletariat (Simon 1990). Domination is not imposed by force, but rather is adopted unwittingly and under the pretense of ordinary cultural development (Simon 1990; Bullock and Trombley 1999). This theory was adapted from Marx’s analysis of the socio-economic class syste m (another example of a hegemonic theory), and in a sense is part of a larger set of theories hypothesising that culture, ethics, and norms arise through what Bernard Mandeville called ‘the artifice of politicians’, although Gramsci placed greater emphasis on intellectuals. Indeed, it might be fitting to suggest that scholars such as Anderson and Hobsbawm, who spoke of ‘imagined communities’ and ‘invented traditions’, respectively, are also working within an intellectual framework of cultural hegemony. However, it is important to note that these theories do not describe an exploitative, alienating relationship in the same way as cultural hegemony does. Both Gramsci’s theory of cultural hegemony and the modernist theories of nation are accurate in their analysis. Whether in the form of informal social and moral traditions transmitted from parent to child, or more structured systems conveyed through instruments such religion and law, culture is a means for the elite to control and manipulate the masses. As modernist anthropologists argue, patriotism is a particularly potent hegemonic force. Created in its present form in the 18th century by the state, today it provides justification for the foreign conflicts of the bourgeoisie. George Bush’s rhetoric related to the Iraq War (2003 – 2011) employed subjective concepts of the ‘enemy’, as well as identity terms such as ‘them’ and ‘us’, linguistic and cultural constructs designed to win over the American population. Contemporary democracy is one of the clearest forms of cultural and political hegemony. It is an idealised political type, inculcated in the civil domain since the enlightenment, and now ‘perfected’ through universal suffrage. In Britain, politicians are almost exclusively from the middle class (usually educated at Oxford or Cambridge). Western liberal democracy is presented by the bourgeois state, operating in the civil realm, as the only viable political system. Thus the entire population willing participates in a game in which the middle class is demonstrably dominant. Cultural hegemony can be seen with more clarity by looking at contemporary capitalist media. In many cases, the International News Agencies, such as Thomson Reuters, the Associated Press, and Agence France-Presse, control the information consumed by the public from start to finish. For example, in the coverage of the Egyptian Revolution, they commissioned the citizen-journalists who captured the news and then edited the copy that was distributed to clients, all of whom operated under contracts (Macgregor 2013). As Macgregor (2013: 35) argues, the coverage of ‘any major incident in the world originates as often than not in the words, photos, audio, and raw film footage coming from three main international agencies’. The American ‘televangelist’ movement, which is broadcast on channels such as the Trinity Broadcasting Network and The God Channel (featuring popular sensations like Joel Osteen), have been effective in propagating the religious ideals of a select few to a wider population. In this way, the state can feed the population the kind of information that supports its own cultural agenda. The best examples of this, of course, come from the pages of history, as in when the Nazi regime launched a calculated propaganda campaign through posters, the development of the ‘Hitler Youth’, and other devices to convince the people of Germany to support the persecution of the Jews. It can be argued that in postmodern society, which is somewhat apathetic and cynical with regard to bourgeois cultural grade narratives, hegemony is less dominant. However, even here hegemonic capitalist consumerism has taken hold. The products produced by firms such as Google, Apple, and Nike provide the cultural pabulum for the people, who are controlled to an extent by corporations. The meaning of the term hegemony is really a matter of interpretation. Cultural hegemony of the Gramscian type can clearly be seen in contemporary society. Some of it manifestations are centuries old, such as patriotism and religion, while others, such as consumerism, are relatively (but not entirely) unique to modern capitalism. Ultimately, hegemony has a variety of meanings, perhaps even one for every set of social, political and cultural instruments of control. Reference list: Antoniades, A (2008) From ‘Theories of Hegemony’ to ‘Hegemony Analysis’ in International Relations Bullock, A. and Trombley, S. (1999) The New Fontana Dictionary of Modern Thought (3rd ed.) Chernow, B. A. and Vallasi, G. A. eds. (1994) The Columbia Encyclopedia (Fifth ed.). New York: Columbia University Press Simon, R. (1990) Gramsci’s Political Thought: An Introduction, London: Lawrence Wishart Ltd Macgregor, P. (2013) International News Agencies: Global eyes that never blink, chapter in Journalism: New Challenges (ed. Fowler-Watt, K. and Allan, S.) Centre for Journalism Communication Research, Bournemouth University: pp. 35-63 http://microsites.bournemouth.ac.uk/cjcr/files/2013/10/JNC-2013-Chapter-3-MacGregor.pdf [Retrieved 21/02/2014] Nye, J. S. (1993) Understanding International Conflicts: An introduction to Theory and History. New York: HarperCollins How to cite What do you understand by the term ‘hegemony’?, Essay examples

Love in the Fault in Our Stars Essay Example

Love in the Fault in Our Stars Essay Augustus and Hazel have an epic love story. They bring out the best in each other. Augusts shows Hazel that there is more to life than staying at home at letting cancer consume you. Hazel brings the light back into Augustuss life. When Augustus had to stop playing basketball he felt that there was something missing, and thats when he met Hazel.It doesnt take long for these to friends to fall in love. Together they are unbeatable, and wont let anything bring them down. In the story Hazel and Augustus go through some hard times, in the story Hazel passed out from overexertion and was admitted into the hospital. Augustus had to battle with his Osteosarcoma returning. In each of these situations, the two lovers were sitting by each others side every step of the way. The novel The Fault in our Stars, written by John Green, is narrated by 17-year-old cancer patient Hazel Grace Lancaster who fell in love with a 17-year-old ex-basketball player and an amputee Augustus Waters. One of the main themes of the story is the different ideas about life, death and existence itself throughout the whole novel. The theme of life, death, transforming and existence is prevalent throughout the novel and embodied as fearing oblivion or being forgotten or one day all of us will die and mortality. Mortality, in the novel Augustus and Hazel thinks about life and death itself, both ideas are presented as Augustus fearing that no one will remember him after he dies and Hazel believes that she is a grenade and will harm those who are close to her and love her once she dies but there are still some pieces missing. Both Hazel and Augustus fears dying but for different reasons. In the novel Augustus states that he fears oblivion when talking to Hazel and Hazel states that she doesnt want to harm anyone because she is a grenade that will hurt people to her parents. Augustus may have a selfish reason not to die because he wants himself to be famous first bef We will write a custom essay sample on Love in the Fault in Our Stars specifically for you for only $16.38 $13.9/page Order now We will write a custom essay sample on Love in the Fault in Our Stars specifically for you FOR ONLY $16.38 $13.9/page Hire Writer We will write a custom essay sample on Love in the Fault in Our Stars specifically for you FOR ONLY $16.38 $13.9/page Hire Writer

buy custom PowerCo essay

buy custom PowerCo essay PowerCo is the largest power generating company selling electricity throughout many states in the southeast region of the United States. The company also believes that the demand of the electricity would increase over the next 10-12 years. The current capabilities of the company are not enough to meet this estimated demand over the next decade. The management of PowerCo has decided that they need to build a new generator in order to meet the anticipated high demand appropriately. It is an estimate that the building of the new generator would be completed within two years and this generator would remain functional for the next ten years. A financial analysis has been done according to the projections with the help of the Treasury Department, which is given below. Q1. PV of the Expected Cost at 8% Year 1: PV= $25 * 0.926= $23.15 Year 2: PV= $28 * 0.857= $23.996 Total Cost= $23.15+ $23.996= $47.15million Q2. PV of after tax cash inflows with 8% interest rate Year 3: PV= $6 * 0.794= $4.764 Year 4: PV= $7 * 0.735= $5.145 Year 5: PV= $8 * 0.681= $5.448 Year 6: PV= $9 * 0.63= $5.67 Year 7:PV= $9 * 0.583= $5.247 Year 8: PV= $9 * 0.54= $4.86 Year 9: PV= $9 * 0.5= $4.5 Year 10: PV= $9 * 0.463= $4.167 Year 11: PV= $9 * 0.429= $3.861 Year 12: PV= $9 * 0.397= $3.573 Total PV of cash inflows= $47.24million Q3. Net Present Value is the difference between the PVs of outflows and inflows. NPV= $47.24 - $47.15= $0.09million; this is a positive net present value which states that the expected profits are greater than the expected costs. The cash outflows in the first two years are the project costs when being built and the cash inflows would be the profits generated from the project. This positive NPV shows that the investment would generate a profit in returns therefore, it can be and it should be made. If the case was a negative net present value, then the investment should have been avoided as it exhibits a potential loss. Q4. First and the main risk associated with the building of the facility is that there is no absolute calculation of the cash flows and costs; all the mentioned figures are expected. The anticipated cash flows is based on the sales and demand that is stretched over a period of ten years which can never be truly estimated at the moment. By the end oof the first two years, the company is opting for an optimistic outlook on the demand. The duration of the ten years seems to be on a very conservative side according to the department of treasury but, one thing not considered is the risk of changing rate of inflation which has the potential to vastly change the outcome of the expected cash flows after tax. Q5. Reviewing all the data calculated above, my recommendation is that the company should definitely carry on with the investment in this project. As the net present value is positive, the company is expecting a profit of $0.09million as calculated above. There is also a chance that the cash flows may continue longer than simply ten years. Although the company has taken a conservative side but there are many chance that the cash inflows may come for more than ten years which means that the NPV would be even greater. Lets assume even the cash inflow remains the same at $9 million but it come for 13 years the PV would be: Year 13: PV= $9 * 0.386= $3.312 Year 14: PV= $9 * 0.34= $3.06 Year 15: PV= $9 * 0.315= $2.84 If we calculate now, the NPV= $56.44 - $47.15= $9.29million; this shows that if the life of the project simply increases by 3 years, the NPV increases to $9.29 million. So, this investment should be made as it is in the best interest of the company. Buy custom PowerCo essay

Biography of Physicist Albert Einstein

Biography of Physicist Albert Einstein Albert Einstein was a theoretical physicist and one of the geniuses of 20th Century physics. His work has helped along our understanding of the universe. He was born and lived much of his life in Germany, before emigrating to the United States in 1933. Growing a Genius When he was five years old, Einsteins father showed him a pocket compass. Young Einstein realized that something in empty space affected the needle. He said the experience was one of the most revelatory of his life.  About a year later, Alberts education began.   Although he was clever and built models and mechanical devices for fun, he was also considered a slow learner. Its possible he was dyslexic, or he may have simply been shy. He was good at mathematics, especially calculus. In 1894, the Einsteins moved to Italy, but Albert stayed in Munich. The following year, he failed an exam which determined whether he could study for a diploma in electrical engineering in Zurich. In 1896, he renounced his German citizenship, not becoming a citizen of any other country until 1901. Also in 1896 he entered the Swiss Federal Polytechnic School in Zurich and trained as a teacher in physics and mathematics. He received his degree in 1900. Einstein worked from 1902 to 1909 as a technical expert at the patent office. During that time, he and  Mileva Maric, a mathematician, had a daughter Lieserl, born in January  1902. (What eventually happened to Lieserl is not know. Its possible she died in infancy or was put up for adoption.) The couple wasnt married until 1903. On May 14, 1904, the couples first son, Hans Albert Einstein was born. During this part of his life, Einstein began writing about theoretical physics. He also earned a doctorate from the University of Zurich in 1905 for a thesis called  On a new determination of molecular dimensions. Developing a Theory of Relativity The first of Albert Einsteins three 1905 papers looked at a phenomenon discovered by Max Planck. Plancks discovery indicating that electromagnetic energy seemed to be emitted from radiating objects in discrete quantities. This energy was directly proportional to the frequency of the radiation. Einsteins paper used Plancks quantum hypothesis for a description of the electromagnetic radiation of light. Einsteins second 1905 paper laid the groundwork for what would eventually become the special theory of relativity. Using a reinterpretation of the classical principle of relativity, which said that the laws of physics had to have the same form in any frame of reference, Einstein proposed that the speed of light remained constant in all frames of reference, as required by Maxwells theory. Later that year, as an extension of his theory of relativity, Einstein showed how mass and energy were equivalent.    Einstein held several jobs from 1905 to 1911, while still developing his theories. In 1912, he began a new phase of research, with the help of mathematician Marcel Grossmann. He called his new work the general relativity theory, which he was able to publish in 1915. It deals with the specifics of space-time theory as well as something called the cosmological constant. In 1914 Einstein became a German citizen and was appointed Director of the Kaiser Wilhelm Physical Institute and Professor at the University of Berlin. The Einsteins divorced on February 14, 1919. Albert then married his cousin Elsa Loewenthal. He received the Nobel Prize in 1921 for his 1905 work on the photoelectric effect.   Fleeing World War II Einstein renounced his citizenship for political reasons and emigrated to the United States in 1935. He became Professor of Theoretical Physics at Princeton University, and a United States citizen in 1940, while retaining his Swiss citizenship. Albert Einstein retired in 1945. In 1952, the Israeli government offered him the post of second president, which he refused. On March 30, 1953, he released a revised unified field theory. Einstein died on April 18, 1955. He was cremated and his ashes were scattered at an undisclosed place. Edited by Carolyn Collins Petersen.

Summary Essay Example | Topics and Well Written Essays - 500 words - 160

Summary - Essay Example Looking in her eyes you couldn’t actually tell that she was a criminal as she wore an innocent, attentive face with soft eye and an intelligent mouth. When she is arraigned in court for stealing a car, she looks at the camera with curious laughter and no remorse or guilt (Zhang, 206). They were brought up in time of war and lost their fathers, husbands and boyfriends in cold blood. They then experience cold peace at the end of it all where they are involved in criminal and immoral acts such as black markets, narcotics, sexual promiscuity and hucksterism. The beat generation is compared to the other post war generation which dubbed itself the ‘lost’ generation. They laugh hysterically because nothing else meant anything to them, they seem to be lost in their own world. They migrated to Europe in the face of war, unsure of whether they were looking for the ‘orgiastic future’ or escaping from the ‘puritanical’ past. They were eventually caught in the face of romance and disillusionment until they became an illusion. This generation lacks the eloquent air of bereavement which was a characteristic of the lost generation’s symbolic actions. The repeated inventory of of shattered ideals and the continued laments about the moral currents which obsessed people of the lost generation do not concern young people today. They were brought up In the ruins and no longer notice them and they drink to come down or to get high. Only the most bitter among them would call their reality a night mare and prot est that they have indeed lost the future. The absence of personal and social values to them is not a revelation of shaking the ground beneath them but a problem demanding day to day solutions. The aspect of how to live seems to them more crucial than why they live. The eager faced girl picked up in the face of doping describes the sense of community she has found in marijuana which she does not get in the society. The