MATA02H3 Lecture Notes - Lecture 2: Least Common Multiple, Law And Justice, Irrational Number

• School: UTSC
• Department: Mathematics
• Course: MATA02H3
• Professor: Sophie Chrysostomou

Document Summary

Therefore p 2 q is a rational number p are integers and p2 q2 and p 2. 2q 2 = p2 p is even, must be even. 2q 2 = p2 p 2 is even, therefore must be even. If is also odd x 2 p p p is in lowest terms, meaning they"re not divisible by the same integer other than 1 or -1 q p 2. Is an even integer, therefore must be an even number since it is a multiple of 2 k= 2 k p is an integer) Are even, so they are divisible by 2 q and. Thus, it contradicts the statement that q. Therefore our assumption is wrong, and and are not divisible by the same integer other than 1 or -1 p is in lowest terms . This is an argument that shows the validity of the statement.