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#### Iterations , Mathematical induction (other) , Processes and operations , Rational and irrational numbers , Theory of algorithms (other)

With a non-zero number, the following operations are allowed: $x \rightarrow \frac{1+x}{x}, x \rightarrow \frac{1-x}{x}$. Is it true that from every non-zero rational number one can obtain each rational number with the help of a finite number of such operations?

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