3 The language of proof In Section 3 we examine the language used to express mathematical statements and proofs, and discuss various techniques for proving that a mathematical statement is true. These techniques include direct proof, proof by mathematical induction, proof by contradiction and proof by contraposition. We also illustrate the use of counter-examples to show that a statement is false. Click the link below to open Section 3 (17 pages, 374KB).
Sunflower DP068840 Osborne House, Isle of Wight. Upper Terrace. Sunflower.
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4.3.2 Network externalities and increasing returns to scale The reader should ask herself the following question: Would I subscribe to a telephone service knowing that nobody else subscribes to a telephone service? The answer should be: Of course not! What use will anyone have from having a telephone when there is no one to talk to? (Shy, 2001, p. 3) The uncertainty surrounding production in the introductory phase, which places such importance on
Institute for Migration and Ethnic Studies
The Institute for Migration and Ethnic Studies is an interdisciplinary centre founded in 1984 to conduct "research into all forms of migration, through the study of national minorities and various aspects of ethnicity" and "to stimulate the implementation of new policies and activities" to aid in the resolution of problems associated with the integration of national minorities. The Institute publishes the journal 'Migracijske i etnicke teme', (Migration and Ethnic Themes), with articles publishe
Ten Frame Flash Game (1-10)
This one-minute video uses music, frames, and dots to help students learn how to expand their recognition of numbers and their memory.
Measuring success 3 : the economic impact of six major sports events supported by the world class ev The reports findi
This report was published and made available on the Web by UK Sport in 2005. “UK Sport commissioned the Sport Industry Research Centre at Sheffield Hallam University to undertake economic impact studies at six major sports events supported by the National Lottery funded World Class Events Programme. At each event the standard UK Sport methodology was used to calculate the additional expenditure in the host economy which was directly attributable to an event being staged.”
BIM and Comprehensive Design Studio Education
Building Information Modeling (BIM) has the potential to fundamentally alter the way composition, scale and abstraction are addressed in today?s comprehensive design studio by displacing the primacy of abstract conventions of representation with a methodology based on systems thinking and virtual simulation. BIM viewed as provocateur of design education provides great potential for the critical analysis of how architectural design is taught. The design studio project reflects new ways of teachin
Keep on learning   There are more than 800 courses on OpenLearn for you to choose from on a range of subjects. Find out more 4.4 The guillotine The new system of departments introduced in 1790 removed the many differing and often overlapping jurisdictions of Old Regime France and replaced them with a uniform system of justice. Each department had its own criminal court, each district a civil court. All criminal cases were to be tried by jury, another revolutionary innovation. Enlightenment thinkers including Montesquieu and Voltaire had criticized the arbitrariness and brutality of penal practice in Old Regime France. Judicial tortur Thousands welcome return of Serb nationalist Balloon crash CVS01_01_032 Tales of balloon flight. A hand-coloured engraving of a balloon ditched in the sea. From the Cecil Victor Shadbolt collection of lantern slides dating from 1882-1892. The Women's Center at Kent State Acknowledgements The content acknowledged below is Proprietary (see terms and conditions) and is used under licence. Course image: Chris Goldberg in Flickr made available under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence. Grateful acknowledgement is ma Lok Sabha OrganWise Guys Shorts: Breakfast Starts Your Day Right The Non-Inflationary Great Leveraging Westward Expansion The week ahead: Back in power The restaurant industry : business cycles, strategic financial practices, economic indicators, and f "This study supports the view that the cyclical fluctuations of the growth of the restaurant industry can be projected by measuring and a Conclusion This free course provided an introduction to studying Science. It took you through a series of exercises designed to develop your approach to study and learning at a distance and helped to improve your confidence as an independent learner.
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Thousands rally in Serbia to welcome the return of nationalist leader Vojislav Seselj, who was temporarily released by the UN war crimes court to get cancer treatment. Yiming Woo reports.
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Kent State University’s Women’s Center exists to facilitate the advancement of and to enhance the quality of educational experience and professional life of women students, faculty and staff at all Kent State campuses.
Official website of the Lok Sabha (House of the People) which is one of the Indian Houses of Parliament. Lok Sabha is composed of representatives of the people directly elected by the adult population who are eligible to vote. The website gives details of members, parliamentary business and the work of committees. Parliamentary debates back to 2004 can be viewed in full text along with parliamentary questions. The site provides an outline of how laws are passed in the Indian Parliament.
Come learn about health and nutrition with the OrganWise Guys! In this short: Sir Rebrum talks with kids about the importance of starting their days off right with a good breakfast. (0:30)
Session on the Economics of Financial Crises and Business Cycles. Recorded 9 March 2012 at the Ludwig von Mises Institute in Auburn, Alabama. [19:22]
By the mid-nineteenth century, the American economy that had been based on local commerce and small-scale farming was maturing into a dynamic, wide-reaching capitalist marketplace. As the industrial revolution in the northeast altered the economy and intensified the process of urbanization, an agricultural empire began to emerge in the west, and westward expansion began. In this video you will learn about westward expansion and it's trials and tribulations. (Video is of high q
Muhammadu Buhari takes power in Nigeria, Rick Santorum is likely to announce his presidential candidacy and David Cameron discusses a European referendum
This PhD thesis on the restaurant industry by Jeong-Gil Choi was submitted to the Faculty of the Virginia Polytechnic Institute and State University in 1999. Continuing from previous studies, it developed business cycle models for the restaurant industry and examined financial practices of the high and low performing firms in the US between 1970 and 1998.
