lecture01_basics

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Speaking Mathematically Mariusz Bajger COMP2781/8781 School of Computer Science, Engineering and Mathematics February 25, 2011 1 / 12 Reading and Exercises Reading Epp, Chapter 1 Exercises Sec. 1 (all), Sec. 2 (all), Sec.3 (all) Good learning strategy: BE ACTIVE! I Regularly revise lectures I Solve the suggested exercises I Be critical when reading textbook/lectures I Ask your colleagues, ask the lecturer, don’t be shy! I It is OK to ask for help any time 2 / 12 Mathematical Statements Notation R : the set of real numbers Z : the set of integers Z + : the set of positive integers (greater than zero) Q : the set of rational numbers I Is there a number ± such that 2 · ± 4 = ± 2 ? I For every integer n : ( n + 1) 2 = n 2 + 2 n + 1 I Are there two numbers with the property that the sum of their squares equals the square of their sums? I Are there two numbers a and b such that a 2 + b 2 = ( a + b ) 2 ? or even better I Do there exist a , b R such that a 2 + b 2 = ( a + b ) 2 I For any two real numbers a and b : a 2 + b 2 = ( a + b ) 2 3 / 12 Universal, Existential and Conditional I universal statement says that a property is true for all elements e.g. For all n Z : n 2 0 I existential statement

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