Let $x$ be irrational and let $r$ be a non-zero rational number. Prove by contradiction that \(r

Question

Let $x$ be irrational and let $r$ be a non-zero rational number. Prove by contradiction that $rx$ is irrational.

Accepted Answer

For irrational $x$ and non-zero rational $r$, the number $rx$ is irrational.

Rational Multiples of Irrational Numbers