Exploring the Subsequences of {xn}: A Comprehensive Guide

[scooterboot1]

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

 

[Hurkyl]

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.

 

[scooterboot1]

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