prove that for each $\displaystyle x \in \mathbb{ R} \mbox { and each} \ n \in \mathbb{ N }$
$\displaystyle \mbox { there is rational number} \\ $ $\displaystyle \mbox {rn such that } \ \mid r n $ $\displaystyle - x \mid< \frac{1}{n} $
prove that for each $\displaystyle x \in \mathbb{ R} \mbox { and each} \ n \in \mathbb{ N }$
$\displaystyle \mbox { there is rational number} \\ $ $\displaystyle \mbox {rn such that } \ \mid r n $ $\displaystyle - x \mid< \frac{1}{n} $
Is there a rational number between these two numbers $\displaystyle \frac{x}
{n} - \frac{1}
{{n^2 }}\;\& \,\frac{x}
{n} + \frac{1}
{{n^2 }}?$