Problem #PRU-109493

Problems Methods Algebraic methods Iterations Mathematical induction Mathematical induction (other) Processes and operations Calculus Real numbers Rational and irrational numbers Set theory and logic Theory of algotithms Theory of algorithms (other)
 14–16  4.0

Problem

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?