- #1
Doom of Doom
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- 0
How can I prove this?
Suppose X is a set of 16 distinct positive integers, X=\left\{{x_{1}, \cdots , x_{16}}\right\}.
Then, for every X, there exists some integer k\in\left\{{1, \cdots , 8}\right\} and disjoint subsets A,B\subset X
A=\left\{a_{1},\cdots\ ,a_{k}\right\} and B=\left\{b_{1},\cdots\ ,b_{k}\right\}
such that \left|\alpha - \beta\right|<.00025,
where \alpha= \frac{1}{a_{1}}+\cdots+\frac{1}{a_{k}} and \beta= \frac{1}{b_{1}}+\cdots+\frac{1}{b_{k}}.
I know that .00025 is pretty close to 2^-12.
Suppose X is a set of 16 distinct positive integers, X=\left\{{x_{1}, \cdots , x_{16}}\right\}.
Then, for every X, there exists some integer k\in\left\{{1, \cdots , 8}\right\} and disjoint subsets A,B\subset X
A=\left\{a_{1},\cdots\ ,a_{k}\right\} and B=\left\{b_{1},\cdots\ ,b_{k}\right\}
such that \left|\alpha - \beta\right|<.00025,
where \alpha= \frac{1}{a_{1}}+\cdots+\frac{1}{a_{k}} and \beta= \frac{1}{b_{1}}+\cdots+\frac{1}{b_{k}}.
I know that .00025 is pretty close to 2^-12.
