Devoid of life Essays

Devoid of life Essays Devoid of life Paper Devoid of life Paper Roughly 126-127 thousand cubic kilometres is contained in lakes, rivers and streams (Clarke 1993: 8; Marshak and Prothero 2001: 479). Water inter-reacts with the three other spheres and can erode rock using onshore wave action or flood movement, transporting material as with moraines or lahars (Gomez et al. 2002: 217-222), warm or cool the atmosphere, and is essential to life. The hydrological cycle The hydrological cycle is the movement of water from reservoir to reservoir Passing through both nonliving and living entities (Marshak and Prothero 2001: 713). The hydrological cycle is significant because: Water is present in the atmosphere in only miniscule amounts, but it plays an important role in the aquatic environment by providing the precipitation to replenish the groundwater and surface water reservoirs (Kemp 2004: 57). Fig. 5: The Water Cycle (Wikipedia contributors 2006b) The hydrological cycle is complex, with many possible paths, Figure 5 illustrates this showing various mechanisms for moving water between bodies, such as evaporation from the ocean, run-off into the ocean, transpiration into the atmosphere, subsurface flow and infiltration. Global environmental change Global environmental change is the transformation or modification of both physical and biological components of the Earth system through time (Marshak and Prothero 2001: 708). It is an ever-present and complex process (Kemp 2004: 465), it is not a human creation. It has taken 3. 8 billion years for the global environment to change enough to support life on land. Global environmental change is a long-term process, although short term events may be noted in ones lifetime (Kemp 1994: 181), such as when wells in Canterbury that have never been dry before are drying up, or rivers running dry (Kent 2006: A17; Rodgers 2006: A17). Over time the polar ice caps and tropical rain forest have expanded and contracted (Marshak and Prothero 2001: 694), and the flora and fauna of the planet has changed accordingly (Kemp 2004: 76). There have been numerous human impacts on global environmental change through the ages including firestick farming, which saw the deforestation of large tracts as humans came into contact with pristine habitats (Flannery 2002: 222-223). Since the beginning of the industrial era, circa 1800, large volumes of sink materials have been released into the atmosphere and hydrosphere as by-products of mechanisation and urbanisation, as illustrated in Figure 6, exacerbated by the population growth which they have enabled (Kemp 2004: 125-128). Fig 6. The Present Carbon Cycle, showing the annual 5. 5 gigatons of fossil fuel emissions (UNEP 1996b) Industrially produced aerosols have caused global dimming (Sturman and Tapper 2006: 474) and in many regions acid rain from sulphur dioxide and photochemical smog from nitrogen oxides or volatile organic compounds (Kemp 2004: 321). Currently the anthropogenic impacts of most concern are global warming and ozone depletion. Global warming Carbon dioxide in the atmosphere, along with water vapour, methane, and twenty other gases are responsible for the greenhouse effect which is the term given to the capture of outgoing terrestrial radiation, and the subsequent retention of heat by the atmosphere, as illustrated in Figure 7. (Kemp 1994: 16). Fig. 7: The Greenhouse Effect (UNEP 1996a) The level of carbon dioxide in the atmosphere is increasing, as illustrated in Figure 8, as result of burning fossil fuels and tropical deforestation (Sturman and Tapper 2006: 20). Fig. 8: The increasing global atmospheric concentrations of CO2 (UNEP 1999) This has disrupted the equilibrium of the carbon cycle (Kemp 1994: 145) and global means surfaces temperatures have risen 0. 6 +/-0. 2 ? C during the twentieth century (Sturman and Tapper 2006: 462-463), although significant temperature fluctuations have occurred in the past ten thousand years: Before the human impact on the climatic environment was globally significant, and were caused by natural variability in the earth/atmosphere system. In contrast, modern global warming appears to have been initiated by human activities that have caused what at first sight seem to be relatively minor changes in the composition of the atmosphere. (Kemp 2004: 374). The effects of global warming in the ocean and atmosphere are evidenced in more intense tropical storm activity (which is generated by the intense heat gathered from the ocean), melting of the polar caps and glaciers, (with a significant rise in sea level and associated decrease in salinity), and increased water scarcity, as in Africa (where 80 per cent of dry land now suffers from desertification (Smith 2001: 300) and water allocation is becoming more contested. (Sichingabula and Sikazwe 1999: 297)). One of the problems in predicting global warming is the limited data available (Sturman and Tapper 2006: 430). The ozone hole As mentioned earlier ozone keeps out ultraviolet radiation, and is necessary for life. The ozone hole is a naturally occurring feature in the stratosphere over Antarctica which coincides with the Southern spring. As a result of the production of chlorofluorocarbons (CFCs) by human industrial processes, ozone is being destroyed at an accelerated rate, and the ozone hole has grown, as illustrated in Figure 9. Once scientists were aware of the existence of the ozone hole CFC production was curtailed, although there has not been sufficient time to observe if this is of benefit (Kemp 2004: 366-374). In this essay the Earths biogeochemical cycle has been assessed as a closed system that exists with finite resources. The parts of the biogeochemical cycle have been identified as the atmosphere, lithosphere, hydrosphere and biosphere; with these all these four parts inter-reacting, and the elements within them circulating in an ongoing, dynamic series of complex exchanges. Natural processes identified inside the biogeochemical cycle include vulcanism, the ozone cycle, the production of oxygen by biospheric organism, and the necessity of maintaining the water cycle due to the critical importance of fresh drinkable water, which is relatively scarce, for terrestrial life. Global environmental change is the ongoing transformation over time of the worlds land surfaces; water, both in form and availability; the atmosphere, in terms of its chemical makeup, temperature fluctuations and climate change; and the responding flora and fauna adaptations. Changes in the biogeochemical cycle directly affect global environmental change, as illustrated in the increase in atmospheric carbon dioxide levels and subsequent warming, and ozone depletion. In the last two hundred year there has been a massive increase in the human impact on the global environment as a result of industrialisation and deforestation, disrupting the biogeochemical cycles, and on the basis of current trends human impact upon the process needs to be brought into check. It would seem that unless humans can become more bio-friendly global environmental change will accelerate. There will not be a biogeochemical cycle equilibrium conducive to habitation: there will not be sustainable growth for everyone, food for everyone and water for everyone as the biosphere could be devoid of life.

How to Treat Postpositive Adjectives

How to Treat Postpositive Adjectives How to Treat Postpositive Adjectives How to Treat Postpositive Adjectives By Mark Nichol Nearly a thousand years ago, the Norman Conquest had a profound effect not only on the English nation but also on the English language. One of the manifestations of this event is the survival of the postpositive adjective. In many languages, including French, a modifying word follows the word it modifies, such as in the phrase ressource naturelle (â€Å"natural resources†). Because of Norman French’s influence on law, politics, and other matters sovereign, we still sometimes use this form in the mongrel melange that is the English language. Thus â€Å"attorney general† (as well as â€Å"secretary general† and â€Å"postmaster general†), which refers not to a military rank but to the office holder’s generic scope of responsibility. Thus court-martial, which literally pertains to a court of a martial, or warlike, nature but practically applies to a military court in wartime or peacetime. Thus â€Å"heir apparent† and knight-errant, artifacts of feudal system. (Note that compound form is inconsistent: Open compounds prevail, but some hyphenated forms persist. When in doubt, look the term up. If certain, look the term up anyway.) This form reaches even into the quotidian vocabulary of business, with â€Å"accounts payable† and â€Å"accounts receivable,† as well as â€Å"notary public,† and in terms that apply to government but have entered general use, such as â€Å"body politic.† There’s even a pair of ordinary words that sometimes take postpositive adjectives in some contexts; I used one earlier in this post, in the phrase â€Å"matters sovereign.† Another is things, as in â€Å"things unsaid.† And how are such terms pluralized? Generally as shown in the first two examples in the paragraph above the noun, not the adjective, logically takes the plural form: for example, â€Å"attorneys general† (but attorney-generals in British English), courts-martial, and â€Å"notaries public.† The same is true of mother-in-law and like terms, the plural form of which is rendered mothers-in-law, and similar constructions such as â€Å"editor in chief† (sometimes hyphenated, though that style is outmoded), right-of-way, and sergeant-at-arms (pluralized as â€Å"editors in chief,† rights-of-way, and sergeants-at-arms, respectively). Want to improve your English in five minutes a day? Get a subscription and start receiving our writing tips and exercises daily! Keep learning! Browse the Grammar category, check our popular posts, or choose a related post below:Does "Mr" Take a Period?Writing Styles (with Examples)

Developing Career Prospects Assignment Example | Topics and Well Written Essays - 1500 words

Developing Career Prospects - Assignment Example Additionally, through the Chapter on management process, roles, behavior and skills has made me to identify the skills that managers should have. These include personal, social, technical and political skills among others. Myers Briggs Type Indicator (MBTI) entails the process that people pass through as they perceive the world and make decision. The theory, which indicates the existence of two dichotomous pairs of cognitive functions, was of great assistance to me (Emmons, 1996). In terms of rational function, my thinking and feeling towards life challenges were positively enhanced. I felt that with determination and confidence I was able to handle any challenge that comes on my way. On its part, irrational function aroused my sensation and intuition towards my duties. As a student or an employee, one should be able to identify areas that they are effective as well as areas that they are weak. In this way, one is able to identify the areas that they need assistance. My competence in the area of business was based on the skills that I gained in the course of my school work as well as the assistance I received from the instructors. Through the skills, I was able to receive a positive outcome that included strong positive relationship with my customers (Schneider and Alderfer, 1973). However, my inability to balance intuition with rational judgment was a negative perception that affected my outcome. I address this by thinking strategically and go beyond the obvious, gathers complex data, to get to the heart of the issues One’s values are important since they are source of motivation and they greatly make one to be identified by the values. My main value is working hard. I like to achieve my goals through working hard, remaining confident and be focused at my goals (Ibarra, 2003). Additionally, I value learning how to master new tasks by adopting high self efficacy. In this way, I am in a position to educate others on various issues thus our

Junk food is killing America Essay Example | Topics and Well Written Essays - 250 words

Junk food is killing America - Essay Example nderstand how exactly the food has been made, but more importantly, a person should consider making personal food from clear ingredients other than consuming anonymous junk products. Most junk food contains an excessive amount of sugar that lacks no nutrients other than a large amount of energy. The above causes demoralizing effect and increases the rate of metabolic reaction beyond the required amount of calories. Excursive calories thus increase chances for Triglycerides and the indigestible amount of cholesterol that accumulates around the liver and the abdomen, which in turn create avenues to chronic diseases that claim numerous life’s for American citizens. Besides, junk foods are often processed from a centralized processing plant that is susceptible to spreading of germs and bacteria. Health practitioners in the United States argue that majority of citizens in the United States often fall sick after contracting pathogens associated with junk food outlets such as ground beef of, which 15% do not survive. Therefore, it is recommended that that fresh food from gardens, salad restaurants and positive eating habit is critical to improved performance and a positive, healthy impact in the future (Smith

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

Love and Basketball: An Overview

Here’s the run-down. Love & Basketball is deceivingly simple in its structure. The movie is divided into the quarters of a basketball game and tells the story of a boy and a girl. Meeting at about the age 11, the film traces their lives as they run parallel and run apart from childhood, to high school, to college, and just after. Monica and Quincy each have their hopes and their dreams. They both want to play basketball on a professional level. For Quincy, it is easier and expected since he is the son of a professional player. It is harder for Monica, both being a woman and as a daughter whose mother cannot understand why she does not want to grow up to be a pretty stay at home wife. Through the whole film the constant between the two is their love for each other and for the game of basketball. The movie is full of honest moments, laughs, tears and some awesome basketball scenes. There are a lot of positives to this movie. This movie shows that no matter what race, gender, or where you came from you can be a successful athlete. Monica is a black female basketball player with an attitude of a male who makes it to the pros. Going into her senior year of high school, Monica was afraid she wasn’t getting any looks by colleges and at the games she was getting looked at she was riding the bench because of her attitude, but the movie showed that it is important to have a strong support system at home. Her parents recognized it and put her in her place! A good athlete has to be all around good. They have to be focused in the classroom and respectable on and off the court! The movie showed how important a healthy home life is needed in more ways than just at Monica’s home. Quincy’s father was a professional athlete that was cheating on his mother. This unhealthy home life affected Quincy and his athletics. Quincy didn’t finish college because of it and entered the draft. After he entered the draft he hurt his knee; consequently he thought his basketball career was over. That was also another positive aspect of the movie, showing the importance of education! If Quincy had finished college and received a college degree he would have had something to fall back on. The main plot line of the movie is very positive in and of itself! A story based on two individuals whom are childhood sweethearts trying to balance following their dreams while trying to keep their love alive is ultimately the hardest thing to do in the eyes of a student athlete of any age! Watching this movie gives you hope that it can actually happen. I know people who try to live this life. Truth be told, it can only happen in a fairy tale though! I don’t believe it. A little girl finds herself in a new neighborhood and having to make new friends. She stumbles upon some boys playing basketball. Being the tomboy she is, she assumes they will let her play. She ends up in a fight with one boy, Quincy. She goes home only to hear her mom go on and on about how she needs to be more girly and quit trying to be one of the boys. Monica has heard this bit her whole life. The young boy is fascinated by Monica; he has probably never had a girl ever stand up to him in that way. He asks her to be his girlfriend and they share their first kiss together. Throughout the years they maintain their strong friendship, living so close together they comfort each other during family problems. They live window to window. They get to high school and Quincy is, of course, quite the ladies’ man; being the best basketball player in the state, they tend to have that effect. Monica plays too, but in high school her anger problems are out of control on the court. Little did they know their romantic lives were about to cross paths again at their very last hooray of high school; senior prom. Quincy of course took one of his random hoes to the prom; whereas Monica just to please her mom. She went with a college guy who her sister set her up with.

Business Axe Commercial Research Essays - 1132 Words

Introduction with Background Information Company Axe is one of the 400 brands which is belonged to Unilever Company. The portfolio of this multinational company focuses on health and wellbeing mainly, including food, beverages, cleaning agents and personal care products. Many world-leading brands including Axe, Lipton, Knorr, Dove, Hellmann’s and Omo are some of these brands (unilever.com). Market Axe Brand, which was named Lynx in Europe, was first launched in France in 1983 as a teenage boys’ grooming category (theguardian.com). For its first 19 years since 1983, AXE brand has developed its market merely in Europe. Later on, in 2002, AXE was introduced to another big market-- the U.S and increased its target customers†¦show more content†¦However, according to most of the commercials they did before, their advertisements are well known for sexual humor and exaggerated scenarios and exaggerated scenarios that play into male fantasies. Significant changes about the campaign has changed in the year of 2014. The way how the company promoted the Axe Peace fragrance line gave a new idea to the public with its content and meaning behind. The new global campaign and commercial advertisement is related to peace. The concept behind the advertisement and its marketing campaign was developed with the Peace fragrance because Axe often visits college campuses an d they finds peace and harmony are the topics and themes that are supported by students (time.com). Thus, it aims to generate the awareness of the peace message, as well as encouraging people to take simple but meaningful actions that will have a positive impact on the future of their world. Also, partnered with international non-profit organization, Peace One Day, Axe brand set a Peace Day on 21st September, 2013 (unilever.com). $250,000 from Axe brand was donated to the organization and is promoting it in its advertisements and on Facebook page (businessinsider.com). Besides these, the promotional campaign also includes a Kiss-For-Peace Twitter hashtag. Users can submit photos of themselves kissing to Axe, and the best photos are being broadcast on electronicShow MoreRelatedEthical Policies Vs. Corporate Social Responsibilities1238 Words   |  5 Pagesand senses make use of right or off-base. Presently apply this as business definition, the ultimate goal of the company is t o make profits and there can be either positive or negative Impact by the company on operation of business. Simply business ethics is the behavior of the business in accordance with the society or community [1]. Unilever Company Code of Practice Paul Polman (CEO) of Unilever Company reported that its business earned reputation based on integrity and interests in accordanceRead MoreNew Product Entry Strategies1678 Words   |  7 Pagestruly profitable business growth in an otherwise depressing economic environment. 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Unilever owns over 400 brands, amongst the largest selling of which are Aviance, Axe/Lynx, Ben Jerrys, Dove, Flora/Becel, Heartbrand, Hellmanns, Knorr, Lipton, Lux/Radox, Omo/Surf, Rexona/Sure, Sunsilk, Toni Guy, TRESemmà ©Read MoreEssay on Pre-campaign Analysis: Old Spice Brand Image1560 Words   |  7 PagesPre-campaign Analysis Research Research is a crucial step in determining the problem or issue faced by the organisation (Gregory, 2000). Old Spice conducted their research and found that the brand’s image was fading away along with their sales at the start of 2010 (Rowe, n.d.). The image that the public had in mind was that Old Spice’s products were something their â€Å"grandfathers† would buy and use (Effie Awards, 2011). Sales had dropped due to the increased number of competitors for bodyRead MoreThe Ethical Dilemma of Sexual Appeal in Advertising Essay2621 Words   |  11 Pagesadvertisement that carries a â€Å"sexy† message in it than one that does not. 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Economic Factors 5 3.3. Social Factors 7 3.4. Technological Factors 7 3.5. Environmental Factors 8 3.6. Legal Factors†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦8Read MoreSexism And Its Effects On The Media3229 Words   |  13 Pageshamburgers or sandwiches in a very weird, uncomfortable and seductive way. For the 2015 Superbowl, Carl’s Jr. but out an advertisement that was said to be the most sexist ad of the Superbowl. The 30-second commercial, titled â€Å"Au Naturel† was promoting their All Natural burger. The premise of the commercial was a naked lady, model Charlotte McKinney, walking through a famer’s market eating a Carl’s Jr. burger. 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