名校
1 . 已知集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99dd46e001c117104353b2e41867994e.png)
,
,
,对任意
,定义
.若存在正整数
,使得对任意![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ff430dfb9275eed8c6e0cbe671a2798.png)
,都有
,则称集合
具有性质
.如集合
、
都具有性质
.记
是集合
中的最大值.
(1)判断集合
和集合
是否具有性质
(直接写出结论);
(2)若集合
具有性质
,求证:
和
;
(3)若集合
具有性质
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99dd46e001c117104353b2e41867994e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14ef42f964d02549eec898b0d3f0588e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d20e326e8f60f19e64e32c584ccfc40c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a703c80c9a9624b08ada02523257b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ff430dfb9275eed8c6e0cbe671a2798.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66ff43ffdcc8b03787a1faa6509d79c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ff430dfb9275eed8c6e0cbe671a2798.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db67bc808e5b3a6ba3f7691a50d20957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20362ac95ee78ef94caeb0579bb40bfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1baf30f84a1797c8e345c624e6cab1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36cd2052417ccb1650cc533f62273aab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e10cda3e056f1db8777f3c322165bb05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/287adcb739a4890d108dd974358345fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b87cd94fef6e528d0913bb1b7b53de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1be13762bee8c87a904b93379c76ac8b.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb6d9e9e68d8fa416188fe9c5efafae0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2309c5526d918b1e6d456a999ab88c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/287adcb739a4890d108dd974358345fa.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57e296d9adecd44ddd36ec145dcf9dc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67f80a1f6a8c236559e2fa55feb9ee1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923eed4cf08e8bef3e7a61ce3ba48d62.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f3b97c217370c2b3d22e6738006cc2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5d5ade4406641db15a62630f06e4201.png)
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2022-12-26更新
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