LECTURE NOTES ON MATHEMATICAL INDUCTION PETE L. CLARK Contents 1. Introduction 2. The (Pedagogically) First Induction Proof 3. The (Historically) First(?) Induction Proof 4. Closed Form Identities 5. More on Power Sums 6. Inequalities 7. Extending binary properties to n-ary properties 8. Miscellany 9. The Principle of Strong/Complete Induction 10. Solving Homogeneous Linear Recurrences 11. The Well-Ordering Principle 12. Upward-Downward Induction 13. The Fundamental Theorem of Arithmetic
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possesses their own unique powers and practices checks and balances with the other two. However‚ whereas the US governmental branch are completely reliant and subservient to each other and the constitution‚ the Belize government must answer to the Prime Minister‚ and finally‚ the Queen. On the other hand‚ both Belize and the US boast an official constitution by which they must adhere to. Government at the lower lever functions similarly. The US is a government based on federalism‚ meaning that governmental
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FRY Image 1 Support for flood-affected Queenslanders at the Gabba Support for flood-affected Queenslanders at the Gabba This photograph has been extracted from an article on the news website: “The Australian”. Taken in January 2011‚ it shows Prime Minister Julia Gillard at the Gabba Sporting ground in Queensland at their first major sporting event since the floods of December 2010. This Image is intended to promote Julia Gillard’s image as a caring and community minded Australian. The reason
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CONSTITUTIONAL LAW ASSIGNMENT MADE BY: MANSUMYER SINGH B.A.LL.B (2010-15) SEC: A; ROLL NO: 09 A3211110009 DEBATE BETWEEN PARLIAMENTARY AND PRESIDENTIAL FORMS OF GOVERNMENT TABLE OF CONTENTS Introduction...............................................................................................................2 The parliamentary system..........................................................................................2 The Westminster model................................
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Presidential vs. Parliamentary Presidential and parliamentary government systems are two main forms of democratic political systems and executive-legislative relations. Both hold advantages‚ disadvantages and similarities. With fluctuating stability‚ both systems of government have had their share of prosperity‚ with the ability to maintain. In the presidential government system a president is elected into office by qualified citizens. Those same citizens are also obligated to elect a legislature
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9. 10. 11. 12. Find the LCM and HCF of 6 and 20 by the prime factorization method. Find the HCF of 96 and 404 by the prime factorization method. Hence‚ find their LCM. Find the HCF and LCM of 6‚ 72 and 120‚ using the prime factorization method. Find the value of y if the HCF of 210 and 55 is expressible in the form 210 x 5 + 55y Prove that no number of the type 4K + 2 can be a perfect square. Express each number as a product of its prime factors:(i) 140 (ii) 156 (iii) 3825 (iv) 5005 (v) 7429 Find
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Each system has its own dynamic and ever-changing functionality‚ creating advantages and disadvantages for each system.1 It is important to note that in a Parliamentary system‚ the Head of Government and Head of State are not the same person. The Prime Minister is the Head of Government‚ and is given this position when he or she has confidence of the house.2 This is conducted by having a general election‚ in which after‚ the Head of State‚ the Governor General‚ asks a Member of Parliament if he or
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important than the executive. Contrary to presidential systems‚ in parliamentary systems power is concentrated. There is no real head of state.Peole are nominated for the figure. Indeed‚ it is whether a monarch or a weak president. Power belongs to the Prime minister. Voters
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monarchy; this means that the powers of the monarchy in Canada are limited by the Constitution. Our monarch is now Elizabeth II‚ who is also the Queen of the United Kingdom. As our Queen does not live in Canada‚ she appoints‚ under the advice of our Prime Minister‚ a Governor General to represent her authority in Canada. There is a great debate among Canadians‚ on if they really need a constitutional monarchy. The fact is Canada does need a monarch. Firstly‚ power corrupts people. The monarch lends
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general obligations regarding government undertakings‚ parliamentary officials should share duties with the members. This implies that the cabinet‚ with the prime minister‚ is together in charge of the considerable number of activities of the legislature‚ and the head administrator‚ subsequently‚ is just first among equals. Truth be told‚ prime ministers in numerous nations have obtained more power than this. The principle components of a parliamentary system‚ along these lines‚ are: a straightforwardly
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