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Numbers of integers

-1

1

$begingroup$

Let $C_2>1$ be a fixed constant. Is it true that there exists $Jinmathbb{N}$ such that for any couple of integers $(j, j'),$
begin{align}
|j - j'|
geq J Rightarrow left[2^jC_2^{-1}
,;2^jC_2right] cap left[2^{j'}C_2^{-1}
,;2^{j'}C_2right]= emptyset;.
end{align}
If so, how can I prove it? Thanks in advance

real-analysis functional-analysis functions

share|cite|improve this question

edited Mar 24 at 12:18

Bernard

124k742117

asked Mar 24 at 12:08

AymenAymen

224

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Can us take $J=lfloorfrac{log(C_2^2)}{log(2)} rfloor +1$? Thanks
  $endgroup$
  – Aymen
  Mar 24 at 12:46
  

  
  
  
  

add a comment | 

-1

1

$begingroup$

Let $C_2>1$ be a fixed constant. Is it true that there exists $Jinmathbb{N}$ such that for any couple of integers $(j, j'),$
begin{align}
|j - j'|
geq J Rightarrow left[2^jC_2^{-1}
,;2^jC_2right] cap left[2^{j'}C_2^{-1}
,;2^{j'}C_2right]= emptyset;.
end{align}
If so, how can I prove it? Thanks in advance

real-analysis functional-analysis functions

share|cite|improve this question

edited Mar 24 at 12:18

Bernard

124k742117

asked Mar 24 at 12:08

AymenAymen

224

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Can us take $J=lfloorfrac{log(C_2^2)}{log(2)} rfloor +1$? Thanks
  $endgroup$
  – Aymen
  Mar 24 at 12:46
  

  
  
  
  

add a comment | 

$begingroup$

Let $C_2>1$ be a fixed constant. Is it true that there exists $Jinmathbb{N}$ such that for any couple of integers $(j, j'),$
begin{align}
|j - j'|
geq J Rightarrow left[2^jC_2^{-1}
,;2^jC_2right] cap left[2^{j'}C_2^{-1}
,;2^{j'}C_2right]= emptyset;.
end{align}
If so, how can I prove it? Thanks in advance

real-analysis functional-analysis functions

share|cite|improve this question

edited Mar 24 at 12:18

Bernard

124k742117

asked Mar 24 at 12:08

AymenAymen

224

$endgroup$

share|cite|improve this question

edited Mar 24 at 12:18

Bernard

124k742117

asked Mar 24 at 12:08

AymenAymen

224

share|cite|improve this question

edited Mar 24 at 12:18

Bernard

124k742117

asked Mar 24 at 12:08

AymenAymen

224

edited Mar 24 at 12:18

Bernard

124k742117

edited Mar 24 at 12:18

Bernard

124k742117

asked Mar 24 at 12:08

AymenAymen

224

asked Mar 24 at 12:08

AymenAymen

224