Shift of Bernoulli, defined as x(n)=0.k(1)k(2)k(3)...k(m)... & x(n+1)=0.k(2)k(3)k(4

[Mattiatore]

Shift of Bernoulli, defined as x(n)=0.k(1)k(2)k(3)...k(m)... & x(n+1)=0.k(2)k(3)k(4

Considered the shift of bernoulli defined as the sequence x(0)=0.01234567891011121314151617181920 and x(n)=0.k(1)k(2)k(3)...k(m)... and x(n+1)=0.k(2)k(3)k(4)...k(m+1)... does it converge to something? Is it a monotonic sequence? Is it a regular sequence?
I think that it is not monotic and it does not converge to any real value neither diverge... therefore it is oscillating and it is not regular.

 

[Deleted member 4993]

Considered the shift of bernoulli defined as the sequence x(0)=0.01234567891011121314151617181920 and x(n)=0.k(1)k(2)k(3)...k(m)... and x(n+1)=0.k(2)k(3)k(4)...k(m+1)... does it converge to something? Is it a monotonic sequence? Is it a regular sequence?
I think that it is not monotic and it does not converge to any real value neither diverge... therefore it is oscillating and it is not regular.

What does your textbook/class-notes say?

What does Google say?

 

[Mattiatore]

My notebook doesn't give any information about it and i could not find anything useful on google because the one I wrote is just one of the possible Bernoulli's shift... There is also a part in which it asks if there is a subsequence which is converging to 1/2. I would answer yes because there will be values like 0,500... with every time increasingly more zeroes and if we create a subsequence with those it converges to 1/2. I think it may have a subsequence that converges to any positive integer value.