equality of fractional parts Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)Weyl Equidistribution Theorem and a LimitIs this Riemann-Integrable?On a certain limit.How do I estimate the error term when computing the number of integers which have the fractional part of their square roots in a given interval?Density of positive multiples of an irrational numberDual of the Banach space of $k$-times continuously differentiable functions.Fractional part of $1+frac12+dots+frac1n$ dense in $(0,1)$Dirichlet approximation theorem proofProve that $forall n, , exists N,x :lfloorx^Nrfloor =n , land ,lfloorx^N+1rfloor =n+1$Real number integer and fractional part separation
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equality of fractional parts
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)Weyl Equidistribution Theorem and a LimitIs this Riemann-Integrable?On a certain limit.How do I estimate the error term when computing the number of integers which have the fractional part of their square roots in a given interval?Density of positive multiples of an irrational numberDual of the Banach space of $k$-times continuously differentiable functions.Fractional part of $1+frac12+dots+frac1n$ dense in $(0,1)$Dirichlet approximation theorem proofProve that $forall n, , exists N,x :lfloorx^Nrfloor =n , land ,lfloorx^N+1rfloor =n+1$Real number integer and fractional part separation
$begingroup$
I am asking myself a question. Let $alpha > 1$ and $x$ denote the fractional part of $x$ which is $x - lfloor x rfloor$. Let $ u_n(x) =alpha^n x _n in mathbbN^*$ Given $x in [-infty,0[ cup ]1, +infty[$. Could we find $x' in [0,1]$ such that $ u_n(x) =alpha^n x _n in mathbbN^*$ and $ u_n(x') =alpha^n x' _n in mathbbN^*$ contain exactly same elements which mean if we take an element of $u_n(x)$ we can find it in $u_n(x')$.
Thanks in advance !
real-analysis equidistribution
asked Apr 2 at 9:28
bsmbsm
261
$endgroup$
add a comment |
$begingroup$
I am asking myself a question. Let $alpha > 1$ and $x$ denote the fractional part of $x$ which is $x - lfloor x rfloor$. Let $ u_n(x) =alpha^n x _n in mathbbN^*$ Given $x in [-infty,0[ cup ]1, +infty[$. Could we find $x' in [0,1]$ such that $ u_n(x) =alpha^n x _n in mathbbN^*$ and $ u_n(x') =alpha^n x' _n in mathbbN^*$ contain exactly same elements which mean if we take an element of $u_n(x)$ we can find it in $u_n(x')$.
Thanks in advance !
real-analysis equidistribution
asked Apr 2 at 9:28
bsmbsm
261
$endgroup$
$begingroup$
Do you mean that $u_n(x) = alpha^n x$?
$endgroup$
– Milten
Apr 2 at 9:50
$begingroup$
Yes for every $n in mathbbN^*$ @Milten
$endgroup$
– bsm
Apr 2 at 9:51
add a comment |
$begingroup$
I am asking myself a question. Let $alpha > 1$ and $x$ denote the fractional part of $x$ which is $x - lfloor x rfloor$. Let $ u_n(x) =alpha^n x _n in mathbbN^*$ Given $x in [-infty,0[ cup ]1, +infty[$. Could we find $x' in [0,1]$ such that $ u_n(x) =alpha^n x _n in mathbbN^*$ and $ u_n(x') =alpha^n x' _n in mathbbN^*$ contain exactly same elements which mean if we take an element of $u_n(x)$ we can find it in $u_n(x')$.
Thanks in advance !
real-analysis equidistribution
asked Apr 2 at 9:28
bsmbsm
261
$endgroup$
I am asking myself a question. Let $alpha > 1$ and $x$ denote the fractional part of $x$ which is $x - lfloor x rfloor$. Let $ u_n(x) =alpha^n x _n in mathbbN^*$ Given $x in [-infty,0[ cup ]1, +infty[$. Could we find $x' in [0,1]$ such that $ u_n(x) =alpha^n x _n in mathbbN^*$ and $ u_n(x') =alpha^n x' _n in mathbbN^*$ contain exactly same elements which mean if we take an element of $u_n(x)$ we can find it in $u_n(x')$.
Thanks in advance !
real-analysis equidistribution
real-analysis equidistribution
asked Apr 2 at 9:28
bsmbsm
261
asked Apr 2 at 9:28
bsmbsm
261
asked Apr 2 at 9:28
bsmbsm
261
asked Apr 2 at 9:28
bsmbsm
261
asked Apr 2 at 9:28
bsmbsm
261
261
$begingroup$
Do you mean that $u_n(x) = alpha^n x$?
$endgroup$
– Milten
Apr 2 at 9:50
$begingroup$
Yes for every $n in mathbbN^*$ @Milten
$endgroup$
– bsm
Apr 2 at 9:51
add a comment |
$begingroup$
Do you mean that $u_n(x) = alpha^n x$?
$endgroup$
– Milten
Apr 2 at 9:50
$begingroup$
Yes for every $n in mathbbN^*$ @Milten
$endgroup$
– bsm
Apr 2 at 9:51
$begingroup$
Do you mean that $u_n(x) = alpha^n x$?
$endgroup$
– Milten
Apr 2 at 9:50
$begingroup$
Do you mean that $u_n(x) = alpha^n x$?
$endgroup$
– Milten
Apr 2 at 9:50
$begingroup$
Yes for every $n in mathbbN^*$ @Milten
$endgroup$
– bsm
Apr 2 at 9:51
$begingroup$
Yes for every $n in mathbbN^*$ @Milten
$endgroup$
– bsm
Apr 2 at 9:51
add a comment |
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$begingroup$
Do you mean that $u_n(x) = alpha^n x$?
$endgroup$
– Milten
Apr 2 at 9:50
$begingroup$
Yes for every $n in mathbbN^*$ @Milten
$endgroup$
– bsm
Apr 2 at 9:51