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Brainteaser about one set being a subset of another

Let be a set of cardinality . You uniformly and independently choose two subsets . What is the probability that ? Let’s solve this by counting the total possible number of pairs , and the number of pairs which satisfy … Continue reading

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[Soln] Carleman’s inequality

Prove Carleman’s inequality: for any sequence of positive real numbers , we have where is Euler’s number. (Credits: I learnt of this inequality from J. Michael Steele’s The Cauchy-Schwarz Master Class.)

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[Hints] Carleman’s inequality

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Carleman’s inequality

Prove Carleman’s inequality: for any sequence of positive real numbers , we have where is Euler’s number. (Credits: I learnt of this inequality from J. Michael Steele’s The Cauchy-Schwarz Master Class.)

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Statistical odds and ends

Between school and family duties, I’ve been finding it hard to find any time to indulge in olympiad math blogging 😦 At the same time, I’ve missed the feeling of typing up stuff that I find interesting and sharing it … Continue reading

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