MathDB
Problem 1 IMC 2004 Macedonia

Source:

July 25, 2004
IMCcollege contests

Problem Statement

Let SS be an infinite set of real numbers such that ∣x1+x2+⋯+xn∣≤1|x_1+x_2+\cdots + x_n | \leq 1 for all finite subsets {x1,x2,…,xn}⊂S\{x_1,x_2,\ldots,x_n\} \subset S. Show that SS is countable.
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