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CORE 1 proof More free powerpoints at http://www.worldofteaching.comhttp://www.worldofteaching.com

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What is Mathematical Proof? The process of starting with an assumption, or a statement which is given, and, by using logical argument, arriving at a conclusion

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Mathematical Proof Prove that … or Given …, prove … or Prove …, given … Form a logical argument Start with what is given or standard results Deduce each step from previous Standard results can be used at any stage

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MATHEMATICAL STATEMENTS ΔABC is isosceles sinθ = ¾ The gradient of y=mx+c is m

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Use to express the relationship between statements implies does not imply is implied by implies and is implied by Implication Signs

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Example: Prove that ΔABC is isosceles AB = AC B = _C AB = AC ΔABC is isosceles A B C

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Example: Link the statements a = 0 and ab = 0 using implication signs. a = 0ab = 0 ab = 0a = 0 (b could be 0) ab = 0Either a = 0 or b = 0

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Example:

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Example: Prove that sum of an even number and an odd number is always odd.

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Let 2n be any even number, where n is an integer. 2m + 1 be any odd number, where m is an integer. 2n + 2m + 1 = 2(n+m) + 1 n+m is an integer 2(n+m) is even 2(n+m) + 1 is odd 2(n+m) + 1 = 2n + 2m + 1 the sum of an even number and an odd number is always odd.

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MTH253 Calculus III Chapter 11, Part I (sections 11.1 – 11.6) Sequences Series Convergence Tests.

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