For all $n \in {\mathbb Z^+}$ we define $$I_n=\{\frac{0}{n},\frac{1}{n},\frac{2}{n},\dotsm,\frac{n-1}{n},\frac{n}{n},\frac{n+1}{n},\dotsm\}$$infinite cluster. For whichever $x$ and $y$ real number, we say $\mid{x-y}\mid$ is between distance of the $x$ and $y$. a) For all $n$'s we find a number in $I_n$ such that, the between distance of the this number and $\sqrt 2$ is less than $\frac{1}{2n}$ b) We find a $n$ such that, between distance of the a number in $I_n$ and $\sqrt 2$ is less than $\frac{1}{2011n}$