MathDB
F 10

Source:

May 25, 2007
irrational numberrational numbers

Problem Statement

The set S S is a finite subset of [0,1] [0,1] with the following property: for all s∈S s\in S, there exist a,b∈S∪{0,1} a,b\in S\cup\{0,1\} with a,b≠s a, b\neq s such that s \equal{}\frac{a\plus{}b}{2}. Prove that all the numbers in S S are rational.
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