Dayo Ogundipe edited begin_itemize_item_textbf_sqrt__.tex  over 8 years ago

Commit id: b25a16e01c9f6fe36130623b4d823792b9bb7a18

deletions | additions      

       

\\ The product of two integers will always be an integer. The product of a integer and an irrational is not an integer. Since n is an integer and $\sqrt{2}$ is irrational, $n\sqrt{2}$ is not an integer.   \\ Both statements are false.  \item \textbf{Obtain a contradiction by taking n to be the smallest positive integer for which (2) is true, and so conclude that $\sqrt{2}$ is not a rational number.}  Smallest positive integer is when n = 1. Then $1\sqrt{2}$ = $\sqrt{2}$   \item \textbf{Convert the above into a structured proof that $\sqrt{2}$ is not a rational number.}  \item \textbf{Show that $\log _2(3)$ is not a rational number.}  \\