Does there exist a subset \(A\) of \(\mathbb{R}^2\) such that \( \lvert A\cap L\rvert=2\) for every straight line \(L\)?
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Tag Archives: set
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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2011-16 Odd Sets with Even Intersection
Let A1, A2, A3, …, An be finite sets such that |Ai| is odd for all 1≤i≤n and |Ai∩Aj| is even for all 1≤i<j≤n. Prove that it is possible to pick one element ai in each set Ai so that a1, a2, …,an are distinct.
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2010-7 Cardinality
Let S be the set of non-zero real numbers x such that there is exactly one 0-1 sequence {an} satisfying \(\displaystyle \sum_{n=1}^\infty a_n x^{-n}=1\). Prove that there is a one-to-one function from the set of all real numbers to S.
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