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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What Is the Largest Jellyfish

Question: What Is the Largest Jellyfish? What is the largest jellyfish, and where is it found? And most importantly, is it dangerous to humans? Find out below. Answer: The largest jellyfish is the lions mane jellyfish (Cyanea capillata). Although most are much smaller, the bell of a lions mane jellyfish can be over 8 feet across. As huge as their bell is in diameter, thats not even the biggest part of the lions mane jellyfish. Their long, slender tentacles can reach over 100 feet, and they have many of them - the lions mane jellyfish has eight groups of tentacles, and there are 70-150 tentacles in each group. The tentacles hang down underneath the jellyfishs bell, along with its much-folded lips and gonads. All these structures together in a mass resemble a lions mane. Interestingly, the lions mane jellyfish changes in color as it ages. They start out pink and yellow, and then once the bell grows to 5 inches, the jellyfish is reddish to reddish brown. As the bell grows over 18 inches, the jellyfish deepens in color. Where Are Lions Mane Jellyfish Found? Lions mane jellyfish have a relatively wide distribution - they are found in both the Atlantic and the Pacific Oceans, but in cooler water that is less than 68 degrees F. What Do Lions Mane Jellyfish Eat? Lions mane jellyfish eat plankton, fish, crustaceans and other jellyfish. They have an interesting feeding strategy in which they rise into the water column, then spread out their tentacles in a wide net and descend, trapping prey as they fall into the water column. This page shows a beautiful image of a lions mane jellyfish with its tentacles spread out. Are Lions Mane Jellyfish Dangerous? Lions mane jellyfish stings are rarely fatal, but their stings can be painful, although the pain is generally temporary and causes redness in the area. According to this site, more severe reactions can include muscle cramps, breathing difficulty and skin burning and blistering. What If I Get Stung? First, rinse the area with sea water (not fresh water, which can cause more severe stinging), and neutralize the sting using vinegar. Scrape off any remaining stingers using something stiff like a credit card, or by making a paste using sea water and talcum powder or baking soda, and letting it dry. Covering the area with shaving cream or meat tenderizer and letting it dry before scraping it off may also help reduce the sensation and remove stingers. How to Avoid a Lions Mane Jellyfish Sting Lions mane jellyfish may be large, with a mass of long tentacles, so always give them a wide berth. And remember, the stingers may still work even after the jellyfish has died, so dont assume its safe to touch a jellyfish, even if its dead on a beach.

Child Development And Childhood Development - 1564 Words

Child Development 2 to 5 Years By creating a decent understanding of parenting strategies and childhood development, this will help parents understand and comprehend exactly what to expect and how to provide what their child needs during each developmental stage of their life. All parents can benefit, also those who work with children can benefit greatly by increasing their knowledge, awareness and understanding of overall childhood development. The stage of child development I have chosen to discuss is 2 to 5 years old. This developmental stage is often referred to as the â€Å"preschool years† where children learn a great deal. The reason I chose this stage is because I believe it is very broad and quite a bit goes on during this stage in a child’s life. When a child begins to take the first steps on their very own, they are free to explore and roam around their own little world; this opens up a brand new phase of development. During the preschool years, children are able to take huge leaps in lang uage development, discover independent nature, self/emotional regulation and rapid physical and intellectual development. As preschoolers enter and exit the â€Å"terrible twos,† their language skills change radically. Parents, caregivers and other family members play a strong role and influence on a child’s development of language and pre-literacy skills. The number of words a child can say during this stage increases not only highly but also very quickly. When children reach 2 years ofShow MoreRelatedChildhood Development And Child Development Essay2174 Words   |  9 PagesMy topic is Early Childhood Development and this is the finding to know if attending pre-school or head start would help the child’s development and have the child more prepared for kindergarten. This topic is based on the social learning theory and how each family teaches their child differently. I have chosen to do my topic on Early Childhood Development because of my practicum being a developmental center (Inspire), also because I have a passion in working with families and children. This appealsRead MoreChild Development And Childhood Development1877 Words   |  8 PagesIntroduction Childhood development encompasses the cognitive, physical, social, moral and emotional changes from birth until the end of adolescence (White, Hayes Livesey, 2013). Throughout childhood, environment and genetics promote or discourage growth and development. This essay will analyse the cognitive, physical, social, moral and emotional domains in relativity to my own development from the prenatal stage until adolescence. Psychological and environmental theories are used to develop theRead MoreEarly Childhood And Child Development928 Words   |  4 PagesChildren that are well nurtured can live well and be sociable. Early childhood is the most rapid period of development in a human life. A child creates their own sense of identity. Indeed, it is important for a child to have a sense of identity. Although individual children develop at their pace, all children progress through an identifiable sequence of physical, cognitive, and emotional growth and change. The early child development approach is based on that children respond best when caregivers useRead MoreChildhood Development : Child And Adolescent Psychology1265 Words   |  6 PagesChild and Adolescent Psychology Early Childhood Development Unit 9 Assignment Kenneth Peter Smith PS220 December 18, 2014 Professor Linda Smith So what goes on during Early Childhood - ages 3 to 6. Development is very crucial in every aspect of childhood but why is it important during early childhood? What goes on during this time frame in a child’s life that’s going to dictate every aspect of the child’s life for now and evermore? Is this stage of a child’s development even importantRead MoreEarly Childhood Development : Child Welfare1640 Words   |  7 Pages Early Childhood Development Rossy Sical SWK 346 Child Welfare Professor Carew February 3, 2015 Early Childhood Development Early childhood development is a fundamental key to a full and productive life. This stage of development is not only important because of its rapid development but also because it is the foundation of children’s future cognitive, behavioral and emotional well-being. Children during this stage require love and physical and verbal stimulationRead MoreChildhood Development And The Whole Child Concept Essay1365 Words   |  6 Pagesearly childhood development and the Whole Child concept. Early childhood development is the study of children’s growing and development from eight years old to pre-birth. Explain why it is important to understand early childhood development. It is important to understand early childhood development because it helps to understand the children better. In order for the teachers to meet the children’s needs, they have to know how and what they need to do. Learning early childhood development is alsoRead MoreChild Development And Early Childhood Education Essay1193 Words   |  5 Pageshe location chosen to do the twelve hours of service learning participation was the Early Childhood Learning Center. Interviews to the agency occurred on November 8th and 9th. The Early Childhood Learning Center (ECLC) is a child development and early childhood education center. ECLC was established the fall of 1970 to provide Early Childhood Education Majors an opportunity to familiarize themselves with children and their characteristics. ECLC is a great facility that not only helps children butRead MoreEarly Childhood Development: Breastfeeding and Child Milestones632 Words   |  3 Pagesmost nutritional option. The CDC (center for dieses control) released a statement saying, â€Å"Breast milk is widely acknowledged as the most complete form of nutrition for infants, with a range of benefits for infants health, growth, immunity and development (Nrdc.org, 2005).† When an infant is born they are rapidly exposed to a multitude of new diseases and infections. Infant formulas are only able to mimic a very small amount of the nutritional components found in breast milk. One of the best thingsRead MoreThe Impact Of Early Childhood Education On Child Development1298 Words   |  6 PagesImpact of Early Childhood Education on Child Development Over the past century, the role of education has greatly increased in areas all over Canada. It has grown in not just in the number of students attending, but also in the ways it has been offered. Before the 1960’s, the education of children consisted solely of parenting done at home (Molnar, 2002, p. 2). Over time, due to the growing importance of education, schools have slowly begun to target younger and younger generations. As a resultRead MoreChildhood Development : An Reliable And Affordable Child Care Essay2067 Words   |  9 Pagesmany families in America struggle to find reliable and affordable child care? The problem is epidemic; households spend close to $30 billion a year due to this child care problem. The government should step in and offer more support to these families by developing a government sponsored day care system that would be staffed by professionals trained in early childhood development. This would help solve the reliable and affordable child care p roblem because the fees would be based on a family’s income

Ford Motor Company Swot Analysis Free Essays

Ford Motor Company SWOT Analysis Strengths †¢Timely acquisition of capital makes Ford more financially sound than the other Big Three carmakers. †¢Product line is respected by industry experts and is qualitatively seen to be a step above many of its competitors. Recent surveys place Ford in a tie with Toyota for greatest customer satisfaction, a significant improvement from five years ago. We will write a custom essay sample on Ford Motor Company Swot Analysis or any similar topic only for you Order Now †¢Have a global market presence, with worldwide brand recognition and a particularly strong presence in Europe. †¢Is perceived to be a thoroughly â€Å"American† brand, which helps Ford among certain groups of consumers. U. S. market share, after years of decline, has stabilized in recent years. †¢The Ford F-series pickup remains the most respected commercial truck available; despite demand shifts, profitability on this line should remain high. †¢Ford has had great success, particularly when compared to its competitors, at renegotiating labor contracts with the UAW. Weaknesses †¢Poor Profitability: Ford still loses money on many automobile lines, particularly within the United States. †¢Importance of single components source (Visteon). The automotive market is highly competitive with large fixed costs. In addition, the market demands continual long term planning and research and development. †¢Very little market penetration within China and India. †¢Global excess capacity for the automobile industry is estimated to average 30. 5 million vehicles per year from 2009-2011. 9 †¢Ford is selling a durable good during the most severe economic downturn in recent history. Opportunities †¢Ford has recognized the importance of small, fuel efficient vehicles and is actively transitioning into this market. Of particular interest is Ford’s ‘EcoBoost’ technology, which the company claims will result in 20% greater fuel efficiency and 15% fewer CO2 emissions. †¢The ‘One Ford’ vision has the chance to generate significant margin increases for Ford’s smaller line of vehicles. Of particular importance is the Ford Fiesta, which was recently released in Europe and China and is slated for an early 2010 release in North America. The ‘One Ford’ vision appears to be a coherent strategy for Ford to adopt given its changed role within the industry. Ford is perceived to be the most stable ‘American’ car manufacturer because it has not been forced to take bailout money, leading to slight increases in market share. †¢GM and Chrysler flexibility is limited by government involvement in their debt situation, putting Ford as a competitive advantage. †¢In the event of a GM or Chrysler bankruptcy, Ford has placed itself in a pos ition to steal market share—at least in the short term. Threats †¢While not in need of a government bailout, poor financial results are straining Ford’s capital. Cash burn continues unabated, and estimates indicate Ford may be forced to seek government financing by early 2010 unless sales stabilize. †¢While Ford is readjusting production, truck sales are falling rapidly and Ford may not be able to shift production quickly enough to meet changing demand. †¢Bankruptcy of Visteon or other parts supplier could cause severe disruption of supply chain. †¢While Ford has too many dealers at this time, it should remain wary of too many closures. In addition, because Ford Credit provides financing for most dealers it must be careful to avoid holding the bag when dealerships close. How to cite Ford Motor Company Swot Analysis, Papers

Confidence. My college essay. free essay sample

If you were to ask a number of kids at my high school to describe me in one statement, I bet you most would sadly say lacking confidence. While having no one relatively close to my age in my immediate, as well as extended family, I formed a path for years to follow of feeling alone and constantly keeping things to myself. In school especially, I refrained from expressing my thoughts and put so much of my attention on the lives of other people. For the longest time, I really did not mind being the listener. Their stories were so interesting and full of excitement; I was always entertained. In the midst of purposely never being the center of attention, I created an addicting habit of being obsessed with appearances and acceptance from others. My obsession of trying to impress people looks wise has come with an unfortunate cost; literally. I dare you to name any kind of cosmetic or beauty product, Im more than certain Ive probably bought it. We will write a custom essay sample on Confidence. My college essay. or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page Ive gone to great lengths to astound my peers physically and let that hinder my confidence in what I say and do. Ive put all of my focus in presenting myself with outer beauty in an attempt to gain confidence and cover my fear of being rejected socially. During the summer going into my senior year, I started the great college search. Beginning this long process was so overwhelming at first with all the applications, qualifications, tours, and deciding what I wanted to do during the years to come. It really hit me that sooner rather than later, I was going to be taken out of my so called comfort zone and expelled into the real world. This none the less scared the living daylights out of me. While looking through the pamphlets of colleges I wanted to attend, I was not surprised to find that blondes most accepted or average number of friends were nowhere to be found. As cliche as it sounds, the light bulb finally went on. I realized that while being caught up in a world of trying to strike my peers appearance wise, I forgot to focus on what I know is more important and satisfy myself. Dont get me wrong, Ive always known that education truly is the key to success, but I would be lying if I told you it was always a top priority of mine. It was a bittersweet feeling when I discovered my class rank and GPA sitting in my guidance counselors office, because I know that they did not reflect my potential and were affected by my out of whack priorities. This was the eye opener for me and it was here where I decided for once in my life I wanted to satisfy me, myself, and I. Over the next couple of months I made an honest effort to focus less on other people and their opinions and focus on myself. When my homeroom teacher placed my report card on my desk upside down, I was nothing less than anxious to flip it over immediately. I knew how hard I had worked academically that quarter and was just hoping for the best. I scanned my eyes down the column of straight As and felt something that was so new to me; real self-assurance. I didnt care who was staring at me, or how dumb I mustve looked smiling from ear to ear at a piece of paper. For once I wasnt concerned about what people thought about me, because I was incredibly proud of myself. I of course still make a huge effort to present myself well on the surface, but I now have a new found confidence that will help me carry a good head on my shoulders into the real world, and is greater than a perfectly straight smile or bleach blonde hair could possibly ever give me.