数学专业英语答案2.3集合论的基本概念（五篇范例）

第一篇：数学专业英语答案2.3集合论的基本概念

2.3集合论的基本概念

单词、词组

1.1 集set，子集subset，真子集proper subset，全集universal subset，空集void/ empty set，基地集the underlying set

1.2 正数positive number，偶数even integer，图形diagram，文氏图Venn diagram，哑标dummy index，大括号brace

1.3 可以被整除的be divisible by，两两不同的distinct from each other，确定的definite，无关紧要的irrelevant/inessential

1.4 一样的结论the same conclusion，等同的效果equivalent effect，用大括号表示集sets are designated by braces，把这

个图形记作A：this diagram is designated by letter A，区别对象to distinguish between objects，证明定理to prove theorems，把结论可视化to visualize conclusions/consequences

汉译英

2.1由于小于10且能被3整除的正整数组成的集是整数集的子集。

The set consisting of those positive integers less than 10 which are divisible by 3 is a subset of the set of all integers.2.2如果方便，我们通过在括号中列举元素的办法来表示集。

When convenient，we shall designate sets by displaying the elements in braces.2.3用符号￠表示集的包含关系，也就是说，式子A ￠B表示A包含于B。

The relation ￠ is referred to as set inclusion；We also say that A ￠ B means that A is contained in B.2.4命题A￠B并不排除B￠A的可能性。

The statement A￠B does not rule out the possibility that B￠A.2.5基础集可根据使用场合不同而改变。

The underlying set may vary from one application to another according to using occasions.2.6为了避免逻辑上的困难，我们必须把元素x与仅含有元素x的集｛x｝区分开来。

To avoid logical difficulties, we must distinguish between the element x and the set ｛x｝ whose only element is x.2.7图解法有助于将集合之间的关系形象化。

Diagrams often help us visualize relations between sets.2.8定理的证明仅仅依赖于概念和已知的结论，而不依赖于图形。

The proofs of theorems rely only on the definitions of the concepts and known result，not on the diagrams.英译汉

1.If A is the set of all the letters of the alphabet，then listing each of elements would be tedious.So we write A={a,b,c,…,z}.如果A是所有字母的集合，那么把每一个其中的字母列举出来将是很冗长乏味的，因此我们写出A=｛a，b，c，…,z｝。

2.In the set A，the last element is z.Many sets do not have last elements.Two important sets are N , the set of natural numbers , and W , the set of whose numbers.To list all the elements in these sets would be impossible because they go on forever.So we use three dots and write N={1,2,3,…},W={0,1,2,3,…}.在集合A里,最后一个元素是z，许多集合没有最后一个元素，两个重要的集合是N，自然数集合，和W，整数的集合。把这两个集合里所有的元素列举出来是不可能的，因为它们是永远持续下去的，所以我们用三个点来表示，集合N写成N={1,2,3,…}，集合W写成W={0,1,2,3，…}。

3.The whole numbers have many important subsets.A whole number is said to be even if it is divisible by 2；2,6,and 18 are examples of even numbers.A whole number is said to be odd if it is not divisible by 2;1,7,and 13 are examples of odd numbers.The natural numbers greater than 1 are called prime or composite , A number is prime if it is divisible only by 1 and itself , A number is composite if it is divisible by a natural number other than 1 and itself.整数有许多重要的子集。如果一个整数能被2除开就是偶数；2，6，18就是偶数的例子。一个整数如果不能被2整除就是奇数；1，7，13就是奇数的例子。大于1的自然数叫做素数或者合数，如果一个自然数只能被1和它本身整除，那么这个数就是素数（质数），如果一个自然数除了能被1和它本身整除外，还可以被其他的自然数整除，就叫做合数。

第二篇：专业英语答案

UNIT 4

1.土地利用与人类活动密切相关，人们通过利用土地来谋生。

The land use has to do with human activities.Peopleearn their living by using the land.2.衡量人口的指标通常有出生率、死亡率以及人口增长率等。

There are always some indexes such as the birth rate, the death rate and the growth rate to measure the population.3.医疗条件的改善、技术的进步以及人口的迁移导致人口近年来的迅速增长。The improved medical care, the progress of technology and the migration have led to the rapid increase of population in the recent years.4.人口在全球的分布是不均衡的，可以用人口密度来衡量人口分布的情况。The population distributes unevenly around world, which can be measured by the density of population.5有的发展中国家后来发现了其他国家和地区缺少的资源，如石油。他们利用通过石油赚取的财富来发展教育和医疗，结果是许多人的预期寿命大大延长了。Some developing counties in time discovered theresourcessuch as petroleum which are in shortages in the other countries.They use the treasures earned from petroleum to develop education and medical care, resulting in a much longer life expectancy.英语作业：环境问题的根源在于人口增长还是资源的过度消耗？

Which is the cause of the environment problem, population explosion or overuse of resources?

UNIT 5

1.在空中，你可以凭借地面闪烁的灯光将城市与其他地区区别开来。

In the air, you can tell a city from the other regions by the glowing lights on the horizon.2.世界绝大多数的人口都集中分布在城市地区，这是人口分布不均衡的显著特征。

Most of the people in the world densely distribute in the urban areas, which is the distinguished feature of the uneven distribution of p

opulation.3.城市的区位受到很多因素的影响，包括环境、交通、防御以及接近原料和资源产地。

A lot of factors have influenced on the location of a city, including environment, transportation, defense and nearness to resources and raw materials.4.许多古代城市都有城墙来抵御敌人的进攻。近代，由于新式武器的产生，防御对于城市来讲不再像以前那么重要了。

Many ancient cities had walls to protect them against the enemy’s attack.In time, due to the invention of new weapon, defense is less important to cities than it used to.5.世界主要的宗教有基督教、佛教、犹太教和伊斯兰教。宗教对于城市的产生和定位起到了十分重要的影响和作用，形成和发展了像耶路撒冷、梵蒂冈等这样的宗教中心城市。

The major religions are Christianity, Buddhism, Judaism and Islam.The religion made a great difference location of cities, which made and developed the religious center cities such as Vatican and Jerusalem.有第四课和第五课的作业参考答案，给大家看看 吧

第三篇：2.3数学归纳法

理：§2.3数学归纳法(1)

1.了解数学归纳法的原理，并能以递推思想作指导，理解数学归纳法的操作步骤;

2.能用数学归纳法证明一些简单的数学命题，并

能严格按照数学归纳法证明问题的格式书写;3.数学归纳法中递推思想的理解.反思：数学归纳法是一种特殊的证明方法,主要用于研究与正整数有关的数学问题.关键：从假设n=k成立，证得n=k+1成立.※ 典型例题

例1 用数学归纳法证明

122232n2

n(n1)(2n1),nN*

6一、课前准备

（预习教材P104~ P106，找出疑惑之处）复习1：在数列{an}中，a

a11,an1n,(nN*)，先算出a2，a3，a4的1an值，再推测通项an的公式.复习2：f(n)n2n41，当n∈N时，f(n)是否都为质数？

二、新课导学

※ 学习探究

探究任务：数学归纳法 问题：在多米诺骨牌游戏中,能使所有多米诺骨牌全部倒下的条件是什么?

新知：数学归纳法两大步：

（1）归纳奠基：证明当n取第一个值n0时命题成立;

（2）归纳递推：假设n=k（k≥n0，k∈N*）时命题成立，证明当n=k+1时命题也成立.只要完成这两个步骤，就可以断定命题对从n0开始的所有正整数n都成立.原因：在基础和递推关系都成立时，可以递推出对所有不小于n0的正整数n0+1，n0+2，…，命题都成立.试试：你能证明数列的通项公式an这个猜想吗?

n

变式：用数学归纳法证明

1427310n(3n1)n(n1)2,nN*

小结：证n=k+1时，需从假设出发，对比目标，分析等式两边同增的项，朝目标进行变形.例2 用数学归纳法证明:

首项是a1,公差是d的等差数列的通项公式是anan项和的公式是1(n1)d,前

n(n1)

Snna1d.2变式：用数学归纳法证明:

首项是a1,公比是q的等差数列的通项公式是

ana1q

n

1a1(1qn),前n项和的公式是Sn.(q1)

1q

小结：数学归纳法经常证明数列的相关问题.※ 动手试试

练1.用数学归纳法证明:当n为整数时, 135(2n1)n

2练2.用数学归纳法证明:当n为整数时, 12222n12n1

三、总结提升

※ 学习小结

1.数学归纳法的步骤

2.数学归纳法是一种特殊的证明方法,主要用于研究与正整数有关的数学问题.※ 知识拓展

意大利数学家皮亚诺总结了正整数的有关性质,并提出了关于正整数的五条公理,后人称之为“皮亚诺公理”.数学归纳法的理论依据是皮亚诺公理.※ 自我评价 你完成本节导学案的情况为（）.A.很好B.较好C.一般D.较差 ※ 当堂检测（时量：5分钟 满分：10分）计分： 1.用数学归纳法证明：

1an22n

11aaa(a1)，在验证n1

1a

时，左端计算所得项为

A.1B.1aa2C.1aD.1aa2a3 2.用数学归纳法证明

(n1)(n2)(n3)(nn)2n13(2n1)(nN*)

时，从n=k到n=k+1，左端需要增加的代数式为

2k12k

3A.2k1 B.2(2k1)C.k1 D.k1 3.设

f(n)(nN*)，那么

n1n22n

f(n1)f(n)等于（）

A.2n1B.2n

21111



C.2n12n2D.2n12n2

4.已知数列{an}的前n项和Snnan(n2)，而a11，通过计算a2,a3,a4，猜想an

1122

5.数列{xn}满足x11,x2，且

xn1xn1xn3（n2），则xn

1.用数学归纳法证明: 1111n 133557(2n1)(2n1)2n1

2.用数学归纳法证明:

1n2(n1)3(n2)n1n(n1)(n2)

6理：§2.3数学归纳法(2)

1.能用数学归纳法证明一些简单的数学命题，并能

严格按照数学归纳法证明问题的格式书写;

2.数学归纳法中递推思想的理解.一、课前准备

（预习教材P107~ P108，找出疑惑之处）复习1：数学归纳法的基本步骤？

复习2：数学归纳法主要用于研究与有关的数学问题.二、新课导学

※ 学习探究

探究任务：数学归纳法的各类应用 问题：已知数列 1111，,,，猜想Sn的1447710(3n2)(3n1)表达式，并证明.新知：数学归纳法可以应用于：(1)数列的先猜后证;(2)证明不等式;(3)证明整除性问题;(4)证明几何问题.试试：已知数列

1111，,，,计算S1,S2,S3,由1223314n(n1)

此推测计算Sn的公式.反思：用数学归纳法证明时,要注意从nk时的情形到nk1的情形是怎样过渡的.※ 典型例题

例1平面内有n个圆，任意两个圆都相交于两点，任何三个圆都不相交于同一点，求证这n个圆将平面分成f(n)=n2－n+2个部分

变式：证明凸n边形的对角线的条数

1f(n)n(n3)n(4)

小结：用数学归纳法证明几何问题的关键是找项,即几何元素从k到k1所证的几何量增加多少.例2 证明:n35n(nN*)能被6整除.变式：证明:x2n1y2n1能被xy整除.小结：数学归纳法证明整除性问题的关键是凑项,而采用增项、减项、拆项和因式分解的手段，凑出nk的情形，从而利用归纳假设使问题获证.※ 动手试试

练1.已知f(n)1

1,求证: 23n

※ 自我评价 你完成本节导学案的情况为（）.A.很好B.较好C.一般D.较差 ※ 当堂检测（时量：5分钟 满分：10分）计分：

n

21.使不等式2n1对任意nk的自然数都

n

f(2n)(nN*)

练2.证明不等式|sinn|n|sin|(nN*)

三、总结提升

成立的最小k值为（）

A.2B.3C.4D.5 2.若命题p(n)对n=k成立，则它对nk2也成立，又已知命题p(2)成立，则下列结论正确的是 A.p(n)对所有自然数n都成立 B.p(n)对所有正偶数n成立 C.p(n)对所有正奇数n都成立

D.p(n)对所有大于1的自然数n成立

3.用数学归纳法证明不等式111127

成立，起始值至少应取为 1n1

2426

4A.7B.8C.9D.10

4.对任意nN*,34n2a2n1都能被14整除,则最小的自然数a=.5.用数学归纳法证明等式

123(2n1)(n1)(2n1)时,当n1时左边表达式是;从kk1需增添的项的1.给出四个等式: 1=11-4=-(1+2)

1-4+9=1+2+31-4+9-16=-(1+2+3+4)„„

猜测第n个等式，并用数学归纳法证明.2.用数学归纳法证明:

1(11)(1)(1)nN*)

32n1

※ 学习小结

1.数学归纳法可以证明不等式、数列、整除性等问题;

2.数学归纳法是一种特殊的证明方法,主要用于研究与正整数有关的数学问题.※ 知识拓展

不是所有与正整数有关的数学命题都可以用数学归纳法证明,例如用数学归纳法证明

(1)n(nN*)的单调性就难以实现.n

第四篇：§2.3数学归纳法

县直高中选修2-2理科导学案第二章推理与证明编写：秦新亮

理：§2.3数学归纳法(2)

1.能用数学归纳法证明一些简单的数学命题，并能严格按照数学归纳法证明问题的格式书写;

.107108，找出疑惑之处）复习1：数学归纳法的基本步骤？

复习2：数学归纳法主要用于研究与.二、新课导学

※ 学习探究

探究任务：数学归纳法的各类应用

问题：已知数列

1111，,,，猜想Sn的表达式，并证明.1447710(3n2)(3n1)

新知：数学归纳法可以应用于：(1)数列的先猜后证;(2)证明不等式;(3)证明整除性问题;(4)证明几何问题.试试：已知数列

1111，,，,计算S1,S2,S3,由此推测计算Sn的公式.1223314n(n1)

反思：用数学归纳法证明时,要注意从nk时的情形到nk1的情形是怎样过渡的.※ 典型例题

例1平面内有n个圆，任意两个圆都相交于两点，任何三个圆都不相交于同一点，求证这n个圆将平面分成f(n)=n2－n+2个部分

变式：证明凸n边形的对角线的条数f(n)n(n3)(n4)

小结：用数学归纳法证明几何问题的关键是找项,即几何元素从k到k1所证的几何量增加多少.例2 证明:n35n(nN*)能被6整除.变式：证明:x2n1y2n1能被xy整除.小结：数学归纳法证明整除性问题的关键是凑项,而采用增项、减项、拆项和因式分解的手段，凑出nk的情形，从而利用归纳假设使问题获证.※ 动手试试

2练1.已知f(n)1,求证:

nf(2n)(nN*)212131n

练2.证明不等式|sinn|n|sin|(nN*)

三、总结提升

※ 学习小结

1.数学归纳法可以证明不等式、数列、整除性等问题;

2.数学归纳法是一种特殊的证明方法,主要用于研究与正整数有关的数学问题.※ 知识拓展

不是所有与正整数有关的数学命题都可以用数学归纳法证明,例如用数学归纳法证明1(1)n(nN

*)的单调性就难以实现.※ 自我评价 你完成本节导学案的情况为（）.A.很好B.较好C.一般D.较差

※ 当堂检测（时量：5分钟 满分：10分）计分：

n21.使不等式2n1对任意nk的自然数都成立的最小k值为（）

A.2B.3C.4D.5

2.若命题p(n)对n=k成立，则它对nk2也成立，又已知命题p(2)成立，则下列结论正确的是

A.p(n)对所有自然数n都成立

B.p(n)对所有正偶数n成立

C.p(n)对所有正奇数n都成立

D.p(n)对所有大于1的自然数n成立

3.用数学归纳法证明不等式11

2141127成立，起始值至少应取为 n1264

A.7B.8C.9D.10

4.对任意nN*,34n2a2n1都能被14整除,则最小的自然数a5.用数学归纳法证明等式

123(2n1)(n1)(2n1)时,当n1时左边表达式是;从kk1需增添的项的1.给出四个等式: 1=1

1-4=-(1+2)

1-4+9=1+2+3

1-4+9-16=-(1+2+3+4)

……

猜测第n个等式，并用数学归纳法证明.2.用数学归纳法证明:

11(11)(1)(1)nN*)32n1

第五篇：2012专业英语试卷答案

学号：_____________ 班级：__________ 姓名：_______________ 专业：__________

湖北医药学院2014-2015学年第 一 学期

专业 12 级本科课程结业考试

《

专业英语 》试卷（A）

I.Choose the best answer from the four choices marked A, B, C and D(40points)1.Which of the following suffixes does not mean “pertaining to”? A.-ic

B.-al

C.-ar

D.-our 2.Which of the following combining forms means cell? A.-cyte

B.cyt/o

C.cel/o

D.both a and b 3.Which of the following forms means tissue? A.erythr/o

B.immun/o

C.hist/o

D.vascul/o 4.An-means ______.A.up

B.down

C.apart

D.without 5.The suffix-itis means _______.A.infammation

B.inflammation

C.inflammazed

D.instrument 6.The combining form of radi/o means _________.A.radar

B.x-ray

C.radio

D.both B and C 7.The instrument for viewing is –scope whereas the instrument for cutting is_____.A.–scopy

B.–tome

C.–meter

D.–graph 8.Which of the following forms refers to “surgical incision of ?” A.–tomy

B.-stomy

C.–tome

D.–ectomy 9.A record of electric wave occurring in the brain is called _______.A.electroencephogram B.electromyogram

C.electrocardiogram

D.electroencephalogram 10.Stethalgia means the pain of chest, which can also be expressed in ____.A.stethodynia

B.thoracalgia

C.thoracodynia

D.all of the above 11.Which of the following forms means fungus? A.my/o

B.myel/o

C.myc/o

D.none of the above 12.The combining form meaning “the skin” is _______.A.dem/o

B.derm/o

C.dermat/o

D.both B and C 13.Which of the following combining vowel means blood vessels ? A.vascul/o

B.angi/o

C.chromat/o

D.Both A and B 14.The term meaning “pertaining to secretion” is _______.A.crinogenic

B.endocrine

C.crinologic

D.endocardial 15.The disease of having too many white blood cells is referred to as _______.A.leukocyte

B.leukemia

C.leukogenesis

D.erythrocyte 16.Inflammation of liver is known in English as ________.A.bronchitis

B.pneumonitis

C.gastritis

D.hepatitis 17.-plasm means _______.A.treatment

B.knowledge

C.diagnosis

D.growth 18.Mammo/o refers to _______.A.mother

B.thymus gland

C.thyroid gland

D.breast 19.Which of the following does not mean “within or in”? A.en-

B.endo-

C.intra-

D.none of the above 20._______ means surgical repair of an organ.A.phag/o

B.–plasm

C.–plasty

D.–pathy

21.Spir/o is a combining form meaning ______.A.see

B.sight

C.breath

D.sport 22.Inflammation of lungs is known as _______.A.pneumonitis

B.pneumonia

C.pulmonitis

D.All of the above 23.Which of the following forms means “protection or safe” ?

A.immun/o

B.lymph/o

C.erythr/o

D.None of the above 24.Cardiopathy means _________.A.heart failure

B.heart disease

C.brain disease

D.skeletal disease 25.Which of the following combining forms does not refer to an organ?

A.hepat/o

B.gastr/o

C.psych/o

D.nephr/o 26.The color of something best expressed in medical terminology is _______.A.chrom/o

B.chromomat/o

C.chramat/o

D.Both A and B 27.Which of the following means “cell”?

A.cyt/o

B.cyst/o

C.–cyte

D.Both A and C 28.Bi-means ______.A.life

B.two

C.across

D.Both A and B 29.The form meaning arteries is ________.A.arter/o

B.arteri/o

C.arthr/o

D.artheri/o 30.The prefix with the meaning of bad is ______.A.mal-

B.dys-

C.polio-

D.Both A and B 31.The flesh is expressed in the combining form of _______.A.top/o

B.ten/o

C.thym/o

D.sarc/o 32.The combining vowel for angitis is ____________.A.a

B.o

C.e

D.i 33.Hypo-means having _______ of something.A.too much or too high

B.too little or too low

C.over

D.below 34.Morph/o means ______.A.many

B.maxillae

C.shape

D.head 35.“Pertaining to nourishment or development” is expressed in _________.A.–tropy

B.–trophy

C.-tropic

D.-trophic 36.The process of recording sth is expressed in _________.A.-graph

B.-gram

C.-graphy

D.-scope 37.The formation of blood is also known as ______.A.hematopoiesis

B.hemopoiesis

C.homopoiesis

D.both A and B 38.Because the strands are readily stained with dyes, they are called_______.A.chromosomes

B.protoplasm

C.cytoplasm

D.chromatin

39.The science that deals with cells on the smallest structural and functional level is called _____.A.biology

B.microbiology

C.homostasis

D.molecular biology 40.An instrument for measuring the cell counts of red blood cells is an _______.A.erythrocyte

B.erythrogenesis

C.erythrocytometer

D.erythrocytograph II.Find the best answer to the following abbreviations.(10 points)41.SARS

A.Serious Acute Respiratary Syndrome

B.Severe Acute Respiration System C.Severe Acute Respiratory Syndrome

D.Severe Acute Respiratary Syndrome 42.T.B

A.tuberclosis

B.tubercluosis

C.tubaclosis

D.tuberculosis 43.Ig A.immunoglobin

B.immunogloblin

C.immunoglobulin D.immunoglubin 44.RNA A.ribonuclear acid

B.ribonucleic acid

C.ribanucleic acid D.ribonucleic acid 45.USG A.ultrosonograhy

B.ultrasonograhy

C.ultrosonography

D.ultrasonography 46.ECG

58.光纤技术

A.optic fiber technology

B.fiber optic techonology C.fiber optic technology

D.optic fiber techonology 59.肌肉收缩

A.muscle contraction

B.muscular contraction

C..musclar contraction

D.Both A and B 60.血供

A． supply blood

B.blood supply

C.protein molecule

D.extensor IV.Reading Comprehension.(40 points)A.electrocardiogram

B.electrocardiography

C.electroencephogram D.electroencephalogram 47.CT

A.computed tomograhy B.computed tomography C.computerized tomograhy

D.computerized tomography

48.MRI

A.Magnetic resononce image

B.Magnetic resonance image

C.Magnetic resononce imaging D.Magnetic resonance imaging 49.VD

A.varied disease

B.venareal disease

C.venereal disease

D.vocal disease 50.GI

A.gastrointral

B.gastrointervention

C.gastrointestinal

D.gastrointersectional

III.Find the best answer to the following translations.(10 points)51.心血管疾病

A.cardiavasclar disease

B.cardiavascular disease

C.cardiovasclar disease

D.cardiovascular disease 52.随意肌

A.voluntary muscle

B.involuntary muscle

C.smooth muscle

D.cardiac muscle 53 脉冲信号

A.pulse

B.impulse

C.impulsive

D.pulsive 54.转换

A.transformation

B.transaction

C.transmute

D.transmission 55.功能失调

A.malfunction

B.dysfunction

C.maloperation

D.disoperation 56.局部化的感染

A.local infection

B.localized infection

C.local inflammation

D.localized inflammation 57.乐观的预后

A.optimistic pregnosis

B.optimistic prognosis

C.pessimistic pregnosis D.pessimistic prognosis