If $x$ is a rational number, then $1/x$ is a rational number Why is this statement false?
If $x$ is a rational number, i.e. $\frac{p}{q}$, then shouldn't it be obvious that $\frac{q}{p}$ is also a rational number, by definition of rational numbers?

$x = 0$ is a rational number but $\dfrac{1}{x} = \dfrac{1}{0}$ isn't defined. 
