解题方法
1 . 设集合
,集合
,且
,则
的值可以是_______ .(写出满足条件的一个答案即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6ca16667d3b84428df451053607fa68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96318f5bb461ab80f33cdcf98546a67f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd9d50619b779c1056602f46b2a95e90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
2 . 已知集合
,若
,则实数
的值可以是________ .(写出一个满足条件的值即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b91660ec08789bb27e383ed92b6caa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04ceb1f338fa60976229d7ec6531b626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
3 . 已知集合
,
.设集合A同时满足下列三个条件:
①
;②若
,则
;③若
,则
.
(1)当
时,一个满足条件的集合A是__________ ;(写出一个即可)
(2)当
时,满足条件的集合A的个数为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7101a3eee1a6054a94a13c1285713bf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45020afb5156159ad42add5537797ee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827e0933211772799f65eccd2fbce592.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cde2827722685b8a71f9aae2dc4d7484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fc1108d22143e834bd69eeb9fd8775a.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe08722cf9300fe188dbbb71989c06c9.png)
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4 . 已知集合
,
,设集合
同时满足下列三个条件:①
;②若
,则
;③若
,则
.
(
)当
时,一个满足条件的集合
是__________ .(写出一个即可).
(
)当
时,满足条件的集合
的个数为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c2dd2c7f4bf194e5cf83eb8e01f491f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45020afb5156159ad42add5537797ee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827e0933211772799f65eccd2fbce592.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cde2827722685b8a71f9aae2dc4d7484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fc1108d22143e834bd69eeb9fd8775a.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764eff906937f9b1fb58e5abfb2eb8a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
2017-10-31更新
|
1183次组卷
|
5卷引用:专题01 条件开放型【讲】【北京版】1
名校
解题方法
5 . 已知
是定义在R上的奇函数,其中
,且
.
(1)求a,b的值;
(2)判断
在
上的单调性(判断即可,不必证明);
(3)设
,若对任意的
,总存在
,使得
成立,求非负实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b06295745406e6bf8f5af9a74fbf2807.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/360ff131c51a4ef6745538c18cec92c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9da4fdfdddc259dcef9fdd4b826b64.png)
(1)求a,b的值;
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cda591d3909af06eabf6b37c65bfe571.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfb8b52b9f71d8cc6e86c7d9a8a47a16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71f985718530cae9003dd401c044ef3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a49684ba67f71171321586f1a77ad4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e63bbadc6250f7139836ede33205550.png)
您最近一年使用:0次
名校
6 . 对称变换在对称数学中具有重要的研究意义.若一个平面图形K在m(旋转变换或反射变换)的作用下仍然与原图形重合,就称K具有对称性,并记m为K的一个对称变换.例如,正三角形R在
(绕中心O作120°的旋转)的作用下仍然与R重合(如图1图2所示),所以
是R的一个对称变换,考虑到变换前后R的三个顶点间的对应关系,记
;又如,R在
(关于对称轴
所在直线的反射)的作用下仍然与R重合(如图1图3所示),所以
也是R的一个对称变换,类似地,记
.记正三角形R的所有对称变换构成集合S.一个非空集合G对于给定的代数运算.来说作成一个群,假如同时满足:
I.
,
;
II.
,
;
Ⅲ.
,
,
;
Ⅳ.
,
,
.
对于一个群G,称Ⅲ中的e为群G的单位元,称Ⅳ中的
为a在群G中的逆元.一个群G的一个非空子集H叫做G的一个子群,假如H对于G的代数运算
来说作成一个群.
(2)同一个对称变换的符号语言表达形式不唯一,如
.对于集合S中的元素,定义一种新运算*,规则如下:
,
.
①证明集合S对于给定的代数运算*来说作成一个群;
②已知H是群G的一个子群,e,
分别是G,H的单位元,
,
,
分别是a在群G,群H中的逆元.猜想e,
之间的关系以及
,
之间的关系,并给出证明;
③写出群S的所有子群.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77ab1256702aef4e9f1a5eb6c12ecc96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77ab1256702aef4e9f1a5eb6c12ecc96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f8278c090ec35994a2300a2f6e03cd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2858005b9ae89ae080d83dcc13cf8e81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b9a0da1382342078b9b0bc326a0b58e.png)
I.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8362f15e544684164f38ff9ad7c38ac7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68f73696ca1660407be38423825ac579.png)
II.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/509a09a7391de2cc86e5e44ccccc981b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47512437070ec582249e3fe8a9422516.png)
Ⅲ.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27321be7cc5aec6555c61775f6638cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebf00e8864c86c3ce8118ea76bf69773.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a34726666c0499373270f6ca37136f.png)
Ⅳ.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebf00e8864c86c3ce8118ea76bf69773.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e78818e18abc456ae7a86110636386ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b2db6609d50b3b58c4c98ee07396606.png)
对于一个群G,称Ⅲ中的e为群G的单位元,称Ⅳ中的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/856b4ab24ff3b7d9e0b4d1c945232aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/655c66701407d942ef38d482e6b3ffd7.png)
(2)同一个对称变换的符号语言表达形式不唯一,如
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/317369bcdd0bc35e2ca45ff7ee37ec09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7703f78bf42acd363d895107b6edae18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54ec72c22e432256b92c8c87f31f4bd2.png)
①证明集合S对于给定的代数运算*来说作成一个群;
②已知H是群G的一个子群,e,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3377b3f59d9c7ac048d59262ecbaf389.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15c2fe2621766b6e71a4e61686f3bea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/856b4ab24ff3b7d9e0b4d1c945232aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e90425090dfd36313d564a97289b3b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3377b3f59d9c7ac048d59262ecbaf389.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/856b4ab24ff3b7d9e0b4d1c945232aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e90425090dfd36313d564a97289b3b1.png)
③写出群S的所有子群.
您最近一年使用:0次
2024-03-20更新
|
1338次组卷
|
5卷引用:安徽省芜湖市安徽师范大学附属中学2024届高三第二次模拟考试数学试题
安徽省芜湖市安徽师范大学附属中学2024届高三第二次模拟考试数学试题安徽省天域全国名校协作体2024届高三下学期联考(二模)数学试题山东省菏泽市单县第一中学2024届高三下学期3月月考数学试题(已下线)安徽省天域全国名校协作体2024届高三下学期联考(二模)数学试题变式题16-19(已下线)压轴题01集合新定义、函数与导数13题型汇总-2
7 . 群的概念由法国天才数学家伽罗瓦(1811-1832)在19世纪30年代开创,群论虽起源于对代数多项式方程的研究,但在量子力学、晶体结构学等其他学科中也有十分广泛的应用.设
是一个非空集合,“
”是一个适用于
中元素的运算,若同时满足以下四个条件,则称
对“
”构成一个群:(1)封闭性,即若
,则存在唯一确定的
,使得
;(2)结合律成立,即对
中任意元素
都有
;(3)单位元存在,即存在
,对任意
,满足
,则
称为单位元;(4)逆元存在,即任意
,存在
,使得
,则称
与
互为逆元,
记作
.一般地,
可简记作
可简记作
可简记作
,以此类推.正八边形
的中心为
.以
表示恒等变换,即不对正八边形作任何变换;以
表示以点
为中心,将正八边形逆时针旋转
的旋转变换;以
表示以
所在直线为轴,将正八边形进行轴对称变换.定义运算“
”表示复合变换,即
表示将正八边形先进行
变换再进行
变换的变换.以形如
,并规定
的变换为元素,可组成集合
,则
对运算“
”可构成群,称之为“正八边形的对称变换群”,记作
.则以下关于
及其元素的说法中,正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/655c66701407d942ef38d482e6b3ffd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/655c66701407d942ef38d482e6b3ffd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c9cbad1e8b405feac6e8fe403f024b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/459aa90a6c76081e2150c67d8ac00fc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a11fc62e2874e9ef25a9d62bfc9704a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a2d02e70b2af37d2d226b3c608566bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25e6faeeed98a19d7012c921ca71a046.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/572f76c63e3a74a90a1e6ca5ae401cf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a34726666c0499373270f6ca37136f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/572f76c63e3a74a90a1e6ca5ae401cf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5463eaf01a62bc6a772301d9e2ad19c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28099032d4c04bae47985cd2d4d6d013.png)
![](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/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/856b4ab24ff3b7d9e0b4d1c945232aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e7b60314b50ef35a3d723f67b6f55a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6e21737c7c4bb66c7bd47c584b6b5cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feea1bf2a87ab88ef7cef5dd660c5661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b367f647833446cf684c3ddedb1592.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d17d4a6cf11cda87b3dfafaecdec683f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/655c66701407d942ef38d482e6b3ffd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e675e81d1b5fa38080ddefcbe94b132e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/276509f01529d982ab21e479a4619268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d285dfc71eccabb3730b4d7a2e844fe6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e43bf250b8d68f26a3c2f6fb5f92cc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/655c66701407d942ef38d482e6b3ffd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4424f7a126daa000c5940787ee564521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4424f7a126daa000c5940787ee564521.png)
A.![]() ![]() |
B.![]() ![]() |
C.![]() |
D.![]() |
您最近一年使用:0次
8 . 设A,B是两个非空集合,如果对于集合A中的任意一个元素x,按照某种确定的对应关系
,在集合B中都有唯一确定的元素y和它对应,并且不同的x对应不同的y;同时B中的每一个元素y,都有一个A中的元素x与它对应,则称
:
为从集合A到集合B的一一对应,并称集合A与B等势,记作
.若集合A与B之间不存在一一对应关系,则称A与B不等势,记作
.
例如:对于集合
,
,存在一一对应关系
,因此
.
(1)已知集合
,
,试判断
是否成立?请说明理由;
(2)证明:①
;
②
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42acae4bf2a6bead9d904b70d0480fc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0915685a3eae67d5c6bc3bd722030876.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79aedd00413c6ff9b2696a63a854867.png)
例如:对于集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aac2c0e4c6fc7ae8950a38098cb062f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8794b3ea2ca1d6d2b70dcec2a991dd3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/210402b31fd895e4fd6921cb25c1ee88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0915685a3eae67d5c6bc3bd722030876.png)
(1)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cf4f47caab35fc473167ca17c7b5f4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eae2c499889a4619a5102a4b2e6b8129.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e386b0005c8f091434060361a07955d8.png)
(2)证明:①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b06ec5553f5aeef37ec8ca6f0d9caba8.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/229c5c40da18cb86a81e709d802d4c1e.png)
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2024-04-18更新
|
975次组卷
|
4卷引用:浙江省台州市2024届高三下学期第二次教学质量评估数学试题
浙江省台州市2024届高三下学期第二次教学质量评估数学试题(已下线)压轴题01集合新定义、函数与导数13题型汇总 -1河北省名校联盟2024届高三下学期4月第二次联考数学试题 (已下线)情境10 存在性探索命题
9 . 对于给定的一个
位自然数
(其中
,
),称集合
为自然数
的子列集合,定义如下:
{
且
,使得
},比如:当
时,
.
(1)当
时,写出集合
;
(2)有限集合
的元素个数称为集合
的基数,一般用符号
来表示.
(ⅰ)已知
,试比较
大小关系;
(ⅱ)记函数
(其中
为
这
个数的一种顺序变换),并将能使
取到最小值的
记为
.当
时,求
的最小值,并写出所有满足条件的
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6be3d8ff4885ce8cf21ed3b7e4c9059.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4ab89a62749697c6a67e4fe8e6f3c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12b0e3b00fe47801afb53ec56706c21a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5123cae73867329882792f626287b970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d688a7cacda715fc5c2fad9a2adaddee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab691edda624f588e85d493423b3e398.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76fb6d4810762396e3fbe728687a0794.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba7a9e06bedb3aca590121cc47e64e52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e534ff8ca5451dce6629223e002d5878.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d407ed5fd8a5fd413426fc1fc118422.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeaa1b4ec60977b69d48d3d023f5d731.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5123cae73867329882792f626287b970.png)
(2)有限集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc8279d9dd0b7750953cb9e2098b3b90.png)
(ⅰ)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b43ea4161df6e6178c26c524935af465.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b53fe2a5d83d2e3e97f3a49d1f845370.png)
(ⅱ)记函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2a7d5abc0e14bf1da403fba5b27644.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c558c7204d256c96b74b9c991c0e5c1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086eb439f6a1578fdba904825340772d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aad1bf0868f56ad3bda73d4ca5851cb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbf91726683a3963e941231877c8c6ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e731e11a03c0f5d2768e87a3442634d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c326b4a68d5148e8e5a5ebc15d3b132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aad1bf0868f56ad3bda73d4ca5851cb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e731e11a03c0f5d2768e87a3442634d.png)
您最近一年使用:0次
10 . 给定整数
,由
元实数集合
定义其随影数集
.若
,则称集合
为一个
元理想数集,并定义
的理数
为其中所有元素的绝对值之和.
(1)分别判断集合
是不是理想数集;(结论不要求说明理由)
(2)任取一个5元理想数集
,求证:
;
(3)当
取遍所有2024元理想数集时,求理数
的最小值.
注:由
个实数组成的集合叫做
元实数集合,
分别表示数集
中的最大数与最小数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a74fd362793540afbf0d97d96e34f86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19a004e53d6da57977a26325a5336e6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(1)分别判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/798fbe13094bfa183eb57fae77647508.png)
(2)任取一个5元理想数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b942b7722c385c79c70ba8928d38af.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd2861d53cafb06f076c59b25bdfd857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
注:由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcc0cbd6a65ad74e65716c682d6985cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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