Let
$x_1 = \sqrt2$ mod $1$
$x_2 = 2x_1$ mod $1$
$x_3 = 2x_2$ mod $1$
continue the process
How to prove the sequence {$x_n$} is uniformly distributed modulo 1
my friend tell me that the question can be solved by Calculus
but I still have no idea
Uniform Distribution Modulo 1
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sequences-and-series
uniform-distribution
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0You just asked this very same question an hour ago. – 2017-02-14
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0What does "uniformly distributed modulo 1" mean? – 2017-02-14
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0I did not describe the question clearly one hour ago. I delete previous one – 2017-02-14
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0Please don't delete and re-ask questions, edit to clarify instead. – 2017-02-14
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0The sequence {$x_n$} ,n=1,...N of real numbers is said to be uniformly distributed modulo 1 if for every pair a, b of real numbers with 0 < a < b < 1 we have $$\lim _{N\rightarrow \infty }\dfrac {C\left( \left[ a,b\right] ,N\right) } {N}=b-a$$ $C\left( \left[ a,b\right] ,N\right)$ is counting function – 2017-02-14
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0Thank you for your comment! – 2017-02-14
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0Are you aware of [Weyl's criterion](https://en.wikipedia.org/wiki/Equidistributed_sequence#Weyl.27s_criterion) for equidistribution? – 2017-02-14