02-StudentNotes

02-StudentNotes - Math 135: Lecture 2: What is a Proof?...

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Unformatted text preview: Math 135: Lecture 2: What is a Proof? What Makes a Mathematician a Mathematician? Its not numbers. Accountants use numbers. Its not quantities. Engineers use quantities. Its not patterns. Scientists use patterns. Its . Definition 2.1. A proof is a convincing argument communicated in the language of mathe- matics. Definition 2.2. A statement is a sentence which is either true or false. Example 2.3. 1. 2 + 2 = 4. 2. 2 + 2 = 5. 3. x 2- 1 = 0 has two distinct real roots. 4. There exists an angle such that sin( ) > 1 . 5. 4 ABC is congruent to 4 PQR . 6. x > . 7. If a,b and c are integers, and a divides b , and b divides c , then a divides c . Exercise 2.4. Which of the following sentences are statements? For each statement, determine whether it is true, false or conditional. 1. { 1 , 3 , 5 , 7 , 9 } 2. sin 2 + cos 2 3. sin 2 + cos 2 = 1 4. Therefore, x = / 2 ....
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This note was uploaded on 10/27/2011 for the course MATH 135 taught by Professor Andrewchilds during the Fall '08 term at Waterloo.

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02-StudentNotes - Math 135: Lecture 2: What is a Proof?...

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