# Math Help - real analysis

1. ## real analysis

prove that for each $x \in \mathbb{ R} \mbox { and each} \ n \in \mathbb{ N }$
$\mbox { there is rational number} \\$ $\mbox {rn such that } \ \mid r n$ $- x \mid< \frac{1}{n}$

2. Originally Posted by flower3
prove that for each $x \in \mathbb{ R} \mbox { and each} \ n \in \mathbb{ N }$
$\mbox { there is rational number} \\$ $\mbox {rn such that } \ \mid r n$ $- x \mid< \frac{1}{n}$
Is there a rational number between these two numbers $\frac{x}
{n} - \frac{1}
{{n^2 }}\;\& \,\frac{x}
{n} + \frac{1}
{{n^2 }}?$

3. Is there a rational number between these two numbers sure!!!

4. Originally Posted by flower3
Is there a rational number between these two numbers sure!!!
Well call it $r$.
Then you are done if you multiply by $n$ and write the interval in absolute value form.