MathDB

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}

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