Agnew's theorem
Agnew's theorem, proposed by American mathematician Ralph Palmer Agnew, characterizes reorderings of terms of infinite series that preserve convergence for all series. == Statement == We call a permutation p : N → N {\displaystyle p:\mathbb {N} \to \mathbb {N} } an Agnew permutation if there exists K ∈ N {\displaystyle K\in \mathbb {N} } such that any interval that starts with 1 is mapped by p to a union of at most K intervals, i.e., ∃ K ∈ N : ∀ n ∈ N # [ ] ( p ( [ 1 , n ] ) ) ≤ K {\textstyle \exists K\in \mathbb {N} \,:\;\forall n\in \mathbb {N} \;\;\#_{[\,]}(p([1,\,n]))\leq K\,} , where # [ ] {\displaystyle \#_{[\,]}} counts the number of intervals.