What is the mistake in following infinite nested radical?

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I have written $$\sqrt{2-\sqrt{2\overline{-\sqrt2}}}$$ for $$\sqrt{2-\sqrt{2-\sqrt{2-\sqrt{2-\sqrt{2-\sqrt{2-\sqrt{2...}}}}}}}$$

[Just care the overline above last $\overline{- \sqrt2}$]

I have taken second radical because it links to another operation. Someone math scholar says, that is not standard format of notation. Is there any standard format of notation for this?

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You can write it as a recurrence: $$f(n + 1) = \sqrt{2 - f(n)}; f(0) = \sqrt{2}$$ And then once you've established that, you can now write: $$\lim_{n\rightarrow\infty}f(n) = \sqrt{2 - \sqrt{2 - \sqrt{2 - \sqrt{2...}}}}$$ Which allows you to use $\lim_{n\rightarrow\infty}f(n)$ as a shorthand.