# 2014-11 Subsets of a countably infinite set

Prove or disprove that every uncountable collection of subsets of a countably infinite set must have two members whose intersection has at least 2014 elements.

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# Solution: 2014-10 Inequality with pi

Prove that, for any sequences of real numbers $$\{ a_n \}$$ and $$\{ b_n \}$$, we have
$\sum_{m=1}^{\infty} \sum_{n=1}^{\infty} \frac{a_m b_n}{m+n} \leq \pi \left( \sum_{m=1}^{\infty} a_m^2 \right)^{1/2} \left( \sum_{n=1}^{\infty} b_n^2 \right)^{1/2}$

The best solution was submitted by 장기정. Congratulations!

Alternative solutions were submitted by 김경석 (+3), 김동석 (+3), 박경호 (+3), 이규승 (+3), 이영민 (+3), 이종원 (+3), 정성진 (+3), 채석주 (+3), 황성호 (+3), Zhang Qiang (+3). Thank you for your participation.

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