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Subsequences of Xn

  • #1

Homework Statement


What are all of the subsequences of {xn}?


Homework Equations


{xn}={1, 1+1/2, 2, 1-1/2, 1, 1+1/3, 3, 1-1/3, 1, 1+1/4, 4, 1-1/4, 1, ...}


The Attempt at a Solution


So far I have:
{1}, {1+1/n}, {1-1/n} and {n} but I can't find any more... I am pretty sure there are though

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
14,916
19
Well, there is

{1+1/2, 2, 1-1/2, 1, 1+1/3, 3, 1-1/3, 1, 1+1/4, 4, 1-1/4, 1, ...}

and

{1, 2, 1-1/2, 1, 1+1/3, 3, 1-1/3, 1, 1+1/4, 4, 1-1/4, 1, ...}



I doubt there's a reasonable way to describe "the set of all subsequences of xn" in any way other than that description.
 
  • #3
sorry, I miswrote the question, it was "what are the subsequences of {xn}", I think it refers to subsequences that you can define like I did previously using n
 

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