# real analysis

• August 21st 2009, 09:12 AM
flower3
real analysis
prove that for each $x \in \mathbb{ R} \mbox { and each} \ n \in \mathbb{ N }$
$\mbox { there is rational number} \\$ $\mbox {rn such that } \ \mid r n$ $- x \mid< \frac{1}{n}$
• August 21st 2009, 09:25 AM
Plato
Quote:

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 $\frac{x}
{n} - \frac{1}
{{n^2 }}\;\& \,\frac{x}
{n} + \frac{1}
{{n^2 }}?$
• August 21st 2009, 12:36 PM
flower3
Is there a rational number between these two numbers http://www.mathhelpforum.com/math-he...1e076689-1.gif sure!!!
• August 21st 2009, 01:26 PM
Plato
Quote:

Originally Posted by flower3
Is there a rational number between these two numbers http://www.mathhelpforum.com/math-he...1e076689-1.gif sure!!!

Well call it $r$.
Then you are done if you multiply by $n$ and write the interval in absolute value form.