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Problems > High School Math > 2008

A Set of Rational Numbers

Let S be a set of rational numbers with the following properties:

1) 1/2 is an element of S

2) If x is an element of S, then both 1/(x+1) is an element of S and x/(x+1) is an element of S

Prove that S contains all rational numbers in the interval 0

 

Source: unknown

 



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