Combinatorics · Infinite sets · Well ordering · Lattice points · Partial orders · Extremal principle
An infinite set \(S\) of pairs of positive integers is given. Prove that \(S\) contains two different pairs \((a,b)\) and \((x,y)\) for which
\[ a \leq x \quad \text{and} \quad b \leq y . \]
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Serbian Regional Competition (Okruzno takmicenje) 1995, high school grade I, problem 2. The 1995 regional paper was not split into categories. Organized by the Mathematical Society of Serbia (DMS).