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石家庄一模19题居然直接考贝蒂定理

  • 2026-03-26 19:16:35
石家庄一模19题居然直接考贝蒂定理

第(2)问(ii)

贝蒂(Beatty)定理：

设  是正无理数，满足 记集合，，则  是正整数集的一个划分.

证明：对正整数 ，

所以  中有  个元素小于 .

同理， 中有  个元素小于 .

所以  中共有

个元素小于 .

同理， 中共有  个元素小于 ，故  中恰有一个元素为 .

总结

也可以根据定义利用不等式证明

直接考定理不合适

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  1. CONNECT:[ UseTime:0.001116s ] mysql:host=127.0.0.1;port=3306;dbname=nowww460;charset=utf8mb4
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  14. SELECT * FROM `article` WHERE `id` < 488261 ORDER BY `id` DESC LIMIT 10,10 [ RunTime:0.009514s ]
  15. SELECT * FROM `article` WHERE `id` < 488261 ORDER BY `id` DESC LIMIT 20,10 [ RunTime:0.005746s ]
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