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$\begin{aligned} S_{1}&=&\sqrt{n+\sqrt{n-\sqrt{n+\sqrt{n-\cdots}}}} \\ S_{2}&=&\sqrt{n-\sqrt{n+\sqrt{n-\sqrt{n+\cdots}}}} \end{aligned}$

When both infinitely nested radicals are defined, what is $S_1 -S_2$?

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