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} $

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- Aug 21st 2009, 09:12 AMflower3real analysis
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} $ - Aug 21st 2009, 09:25 AMPlato
- Aug 21st 2009, 12:36 PMflower3
Is there a rational number between these two numbers http://www.mathhelpforum.com/math-he...1e076689-1.gif sure!!!

- Aug 21st 2009, 01:26 PMPlato