Suppose you have an infinite tower of subsets of the integers: such that for any , there exists such that . Can I determine whether or not ?

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- April 23rd 2014, 12:22 PMSlipEternalLimit set question
Suppose you have an infinite tower of subsets of the integers: such that for any , there exists such that . Can I determine whether or not ?

- April 24th 2014, 03:51 AMSlipEternalRe: Limit set question
I figured out the answer is no. For example, if , then this satisfies the claim that for any , there exists with . However, , so it would not contain any non-positive integers.