解题方法
1 . 对集合
,定义其特征函数
,考虑集合
和正实数
,定义
为
和式函数.设
,则
为闭区间列;如果集合
对任意
,有
,则称
是无交集合列,设集合
.
(1)证明:L和式函数的值域为有限集合;
(2)设
为闭区间列,
是定义在
上的函数.已知存在唯一的正整数
,各项不同的非零实数
,和无交集合列
使得
,并且
,称
为
和式函数
的典范形式.设
为
的典范数.
(i)设
,证明:
;
(ii)给定正整数
,任取正实数
和闭区间列
,判断
的典范数
最大值的存在性.如果存在,给出最大值;如果不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1304eb00ab95d664dc84385f602a8f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81f69939291758b5eaa19146f76709e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee6c8ae5004f2ffe7f8392b4d3c39b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/238908949859936af0e109ef684599b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81f69939291758b5eaa19146f76709e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81f69939291758b5eaa19146f76709e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937c09d82c480e4d67f8a48d3f66c5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a02da5d46478a54d279755a295d548f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1b56da93ba7a2dec958070eb2666240.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05386869739fb11a190c637ba8a93174.png)
(1)证明:L和式函数的值域为有限集合;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81f69939291758b5eaa19146f76709e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20b4010030e10725398b64d4dcc09429.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0fa51de98f090eda3e3f60a26475db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecfcda4333678bafacc4c676c2836977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee06844034f61cab7d421d55179ee367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/359a16305129aeea0953efd9100f4b9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7b4e32041b54703ade8e8c2cee01f13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed82555c7d6fc6b449fbdb1f68fef1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20b4010030e10725398b64d4dcc09429.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20b4010030e10725398b64d4dcc09429.png)
(i)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1462612f3654548c39489985987cb67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7870c36161f465fc992534b5fc3777f3.png)
(ii)给定正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81f69939291758b5eaa19146f76709e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20b4010030e10725398b64d4dcc09429.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2 . 给定素数
,定义集合
.对于
,
,定义
如下:当
时
;当
时
.对于
的一个子集
,定义
.若集合
满足
且对任意
有
则称集合
为好集合.求最大正整数
,使得可以找到
个互不相同的好集合
,
,
,
,满足
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20dd7cdef44777d41d74d699ffdd746d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf98a71fd95ad5e8fc967e6657f24a20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fe1e80f50c9dd61376740023ed35344.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e596ab8948a8ea4a590268681ae2b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0c46d1a90bc64c45cd13974eefb0dbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d9db389d4841fc977f20f7d33520270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c37313b684f4ea9714c3f6df0053c603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0fb864828d5a10dd99566d29eda3b86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec588a1061937a72a456e2fa57d78cfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5097380cbd3805cc9598de5b166549cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44073b5701bb43060b3248a8145c67b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c633305229937a241ed6b6a4c3b032d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0dbb44d7459e2c69c046775664c21d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed928e013218b7e12883775aa0d0a71e.png)
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2023-12-14更新
|
383次组卷
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3卷引用:专题1 集合新定义题(九省联考第19题模式)讲
名校
3 . 设集合S,T,S,T中至少有2个元素,且S,T满足:①对于任意的
,若
,则
;②对于任意的
,若
,则
.若S有3个元素,则T可能有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c36aecba41f6f5ff0d46a29dccaaf01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a11a069688e4c797fcf527eab15afa82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d015f20727d06fcd4fde4ed4de4e7c56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/566d386cbedb1c8750f4837633c2af64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a5abe56c019ac914e1fcde1865a747.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e6a1c6d6c4b75d2162e6d0ff5419a31.png)
A.2个元素 | B.3个元素 | C.4个元素 | D.5个元素 |
您最近一年使用:0次
4 . 已知集合
.
(1)写出所有满足条件
的集合B;
(2)满足条件
的集合C有多少个?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ea38cda97cb3f536f42260b99ac52e8.png)
(1)写出所有满足条件
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdbbe46a98a8fdebfc46fcbc45dc88e8.png)
(2)满足条件
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07241606934d6c75cf04455979d0e1b0.png)
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2020-02-07更新
|
510次组卷
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6卷引用:1.3集合的基本运算【第一练】
(已下线)1.3集合的基本运算【第一练】人教B版(2019) 必修第一册 逆袭之路 第一章 1.1 集合 1.1.3 集合的基本运算(已下线)【新教材精创】1.1.3+集合的基本运算+教学设计(1)-人教B版高中数学必修第一册(已下线)第一章 集合与常用逻辑用语 1.1 集合 1.1.3 集合的基本运算湖南省郴州市桂阳县展辉学校2020-2021学年高一上学期第一次段考数学试题人教B版(2019)必修第一册课本习题1.1.3 集合的基本运算
名校
5 . 设
、
、
是两个两两不相等的正整数.若
,则
的最小值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b8429214f1f47081172e867a215f18c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dd4067a19eeb07474557fe7b2508880.png)
A.2007 | B.1949 | C.1297 | D.1000 |
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2018-12-27更新
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400次组卷
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4卷引用:第09讲 函数的基本性质(7大考点)-2022-2023学年高一数学考试满分全攻略(人教A版2019必修第一册)
(已下线)第09讲 函数的基本性质(7大考点)-2022-2023学年高一数学考试满分全攻略(人教A版2019必修第一册)数学奥林匹克高中训练题_101上海市南洋模范中学2022-2023学年高一上学期开学考试数学试题北京市第八十中学2023-2024学年高一上学期(10月月考)阶段测评数学试题
6 . 已知集合
,则.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6773d153e5cd13a3e972de2702ed99f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2018-12-21更新
|
730次组卷
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8卷引用:专题01 集合与常用逻辑用语-2020年新高考新题型多项选择题专项训练
(已下线)专题01 集合与常用逻辑用语-2020年新高考新题型多项选择题专项训练(已下线)专题1.1 集合-备战2021年高考数学精选考点专项突破题集(新高考地区)(已下线)专题01 集合-2022年高考数学一轮复习小题多维练(新高考版)2018全国中学生数理化创新能力大赛(预赛)高三数学试题人教A版(2019) 必修第一册 章末检测卷(一) 集合与常用逻辑用语(已下线)第1章+集合单元测试(基础卷)-2020-2021学年高一数学十分钟同步课堂专练(苏教版2019必修第一册)第1章 集合 单元综合测试卷(已下线)第1章 集合 综合测试-【暑假自学课】(苏教版2019必修第一册)
名校
7 . 对于函数
,若
,则称
为
的“不动点”;若
,则称
为
的“稳定点”.函数
的“不动点”和“稳定点”的集合分别记为
和
,即
,
.
(1)求证:
;
(2)若
,且
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e44284cb19805a584880a686ac3df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/801d492de7ae12be2bf576f25c4f1ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d30bf91f31613ce80bba22a49862db03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73339743a70345917d3a3e648b30525c.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ad78dc8b8aed907b4fe9640c997454.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bfac30eb449e17bbee48dd07c7ab385.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79d02e5de0c92487382f4b98376e9740.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2018-12-15更新
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1386次组卷
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7卷引用:专题1.1—集合—2022届高三数学一轮复习精讲精练
(已下线)专题1.1—集合—2022届高三数学一轮复习精讲精练(已下线)第1章集合与常用逻辑用语专练1 集合-2022届高三数学一轮复习(已下线)模块二 大招16 不动点与稳定点湖南省长沙市长郡中学2020-2021学年高一上学期适应性调查考试数学试题湖南省长沙市长郡中学2021-2022学年高一上学期第一次适应性调查数学试题2004年湖南省高中数学竞赛试题江西省景德镇一中2020-2021学年高一(2班)上学期期末考试数学试题