MATH135 Lecture Notes - Set-Builder Notation, New Zealand, Mathematical Induction

• School: University of Waterloo
• Department: Mathematics
• Course: MATH135
• Professor: Ross Willard

Document Summary

Office hours: tuesdays 9:00am-10:00am , fridays 1:00pm-2:00pm, in mc 5058. Tutorials: tuesdays 4:30pm-7:20pm (drop-in to biology 1 room 271) Proofs: x x x x x x x . 1) x x x x (1 (1 x x . Avoid starting with thing trying to be proved (assuming the thing is true) 2x x 0 x 2. Check the converse: x 2 x 2 x 0 x 2 x 0 x 2 and if. 2x x2 and x 2 x 0 x2. 2x + 1 0 x2 is true. 2x + 1 + 2x 0 + 2x. + 1 2x x + 2. , which was to be proved. x + 2. 1 x (double right arrow) is considered an acceptable replacement for therefore, hence, then, thus. A proposition is a true statement, proved with a valid argument. A theorem is an important or significant proposition. A lemma is a helper proposition used in the proof of a theorem.