离散数学英文版？离散数学(Discrete mathematics)是数学的几个分支的总称，以研究离散量的结构和相互间的关系为主要目标，其研究对象一般地是有限个或可数无穷个元素；因此它充分描述了计算机科学离散性的特点。内容包含：数理逻辑、集合论、代数结构、图论、组合学、数论等。由于数字电子计算机是一个离散结构，那么，离散数学英文版？一起来了解一下吧。
b)的意思是以0作为1和n的像，
c）意思是让1严格作为某一个小于n的正整数的像
a)因为不能保证set1中不同的元素对应不同的set2中不同的像，所以没有一一映射
b)1和n已经选定了像为0，剩下n-2个正整数的像每个有2种选择，一共有2^(n-2)种。n=1时仅仅有一种
c)先选择一个小于n的正整数，选取方法有(n-1)种，剩下n-1个数的像只能选择0.所以一共是n-1种。
嗯，不知道理解得对不对 - -
C）我做错了，LS是对的 - -
Here is an overview of the contents for "Discrete Mathematics and Its Applications (English Edition):"
Preface: The introductory section provides context and an overview of the book's objectives, discussing its relevance and purpose for readers.
About the Author: This part introduces the author, highlighting their background, expertise, and contributions to the field of discrete mathematics.
To the Student: A message is directed to the reader, encouraging them to approach the subject with a clear mindset and providing guidance on how to make the most of the material.
LIST OF SYMBOLS: A comprehensive list of symbols used throughout the book, ensuring readers are familiar with the notation employed.
Chapter 1: The Foundations: Logic and Proofs
- 1.1 Propositional Logic: The basics of logical statements and their relationships are explained.
- 1.2 Propositional Equivalences: Key equivalences in propositional logic are discussed and demonstrated.
- 1.3 Predicates and Quantifiers: Understanding of quantifiers and their role in statements is introduced.
- 1.4 Nested Quantifiers: The intricacies of combining quantifiers in logical expressions.
- 1.5 Rules of Inference: Essential rules for deducing new statements from existing ones.
- 1.6 Introduction to Proofs: A beginner's guide to constructing and evaluating mathematical proofs.
- 1.7 Proof Methods and Strategy: Various proof techniques and strategies are introduced and practiced.
Chapter 2: Basic Structures: Sets, Functions, Sequences, and Sums
- 2.1 Sets: The fundamental concept of sets, their elements, and set operations are explained.
- 2.2 Set Operations: How to combine and manipulate sets using union, intersection, and others.
- 2.3 Functions: The definition of functions and their mappings between sets are discussed.
- 2.4 Sequences and Summations: Introduction to ordered lists and the concept of sums in discrete mathematics.
Each chapter concludes with end-of-chapter material, including exercises, review questions, and additional resources for further study.
1、定义f(x)=e^x.f(x)=f(y),则e^x=e^y,得x=y,所以f是单射.对(0,∞)内任意的正数z,由f(x)=z得x=lnz∈R,所以f是满射.所以f是双射.
2、sinx=1的解是x=2nπ+π/2,n是整数.所以定义f(n)=2nπ+π/2.若f(n)=f(m),则n=m,f是单射.对任意的x∈S,存在整数k,使得x=2kπ+π/2=f(k),所以f是满射.所以f是双射.
3、n为偶数时,f(n)是正整数.n为奇数时,f(n)是负整数或零.
(a)只要证明任取n1,m1;n2,m2.
当2^n1*3^m1=2^n2*3^m2的时候，有n1=n2,m1=m2。
因为(2,3)=1(2,3为互素的），所以2^n1|2^n2*3^m2可以得到2^n1|2^n2。即n1<=n2.
同理得到n2<=n1.n2=n1。
同理有m2=m1。
即
所以映射为单射
(b)只要建立映射f(m)=
This comprehensive textbook, "Discrete Mathematics and Its Applications" (English Edition), serves as an esteemed classic for students seeking to delve into the fundamentals of the subject. Its popularity is unparalleled, with over 600 US institutions relying on it as a core text, marking its significant success. The Chinese edition has also gained traction among domestic universities, widely adopted as a key resource in their curriculum.
The sixth edition, an enhancement from its previous ones, has been meticulously revised, enhancing its efficacy as a teaching tool. Designed for a one to two-semester introductory course, it caters to a diverse range of students, particularly those pursuing mathematics, computer science, computer engineering, and information technology. This book bridges the theoretical concepts with practical applications, making it a pivotal resource in these academic disciplines.
以上就是离散数学英文版的全部内容，1、定义f(x)=e^x.f(x)=f(y),则e^x=e^y,得x=y,所以f是单射.对(0,∞)内任意的正数z,由f(x)=z得x=lnz∈R,所以f是满射.所以f是双射.2、内容来源于互联网，信息真伪需自行辨别。如有侵权请联系删除。
