MATH135 Lecture Notes - Lecture 2: Angle

• School: University of Waterloo
• Department: Mathematics
• Course: MATH135
• Professor: Shane Bauman

Document Summary

Math 135 - lecture 2: introduction to proofs. Proposition a statement that needs to be proven true or demonstrated false by a valid argument. Lemma a proposition that is often not useful on its own, but is used to prove another theorem. Corollary a proposition that follows almost immediately without much work from another theorem. Axiom a statement that is assumed to be true without proof. Multiplying or dividing by a negative number when dealing with inequalities. 5x > 4 when dividing both sides of the inequality by -5, the new equation becomes: x < - . Note that the inequality sign is flipped. When using variables, it is not always obvious when division by 0 occurs. Ex. a = b a2 = ab a2 - b2 = ab - b2 (a + b)(a - b) = b(a - b) a + b = b.