MATH 1P66 Lecture Notes - Lecture 9: Year 2000 Problem

• School: Brock University
• Department: Mathematics and Statistics
• Course: MATH 1P66
• Professor: Basil Nanayakkara

Document Summary

A proof is a valid argument that establishes the truth of a mathematical statement. Start with the hypothesis p and use the definitions, axioms and previously proven theorems to arrive at q. Questions: show that the sum of two odd integers is even. Rough work x = 2k+1 y = 2l+1 x+y=(2k+1)+(2l+1) = 2(k+l+1) even definition (even number can be shown as 2 x and integer) We want to show that x+y is even. Since x is odd, there is an integer k such that x = 2k+1. Similarly, there is an integer l such that y = 2l+1. Thus x+y=2k+2l+2 = 2(k+l+1), which says that x+y is even: the square of an even number is an even number n is even n^2 is even. Rough work n is even therefore n = 2k n^2 is even therefore: n^2=(2k)(2k) Let n be even, then n=2k for some integer k. this leads to n^2=4k^2.