1离散数学及其应用(英文版第5版) 作者: Kenneth H. rosen著出版社:机械工业出 版社 2组合数学(英文版·第4版)—经典原版书库 作者:(美)布鲁迪( Brualdi,R.A.)著出版社: 机械工业出版社 3离散数学暨组合数学(英文影印版) Discrete Mathematics with Combinatorics James A Anderson, University of South Carolina, Spartanburg 大学计算机教育国外著名教材系列(影印 版)清华大学出版社
1.离散数学及其应用（英文版·第5版） 作者：Kenneth H.Rosen 著出版社：机械工业出 版社 2.组合数学（英文版·第4版）——经典原版书库 作者：（美）布鲁迪（Brualdi,R.A.） 著出版社： 机械工业出版社 3,离散数学暨组合数学（英文影印版） Discrete Mathematics with Combinatorics James A.Anderson,University of South Carolina,Spartanburg 大学计算机教育国外著名教材系列（影印 版） 清华大学出版社
I Introduction to Set Theory The objects of study of Set Theory are sets. As sets are fundamental objects that can be used to define all other concepts in mathematics. Georg Cantor(1845--1918) is a German mathematician Cantor's 1874 paper, On a Characteristic Property of All Real Algebraic Numbers marks the birth of set theory. paradox
ⅠIntroduction to Set Theory The objects of study of Set Theory are sets. As sets are fundamental objects that can be used to define all other concepts in mathematics. Georg Cantor(1845--1918) is a German mathematician. Cantor's 1874 paper, "On a Characteristic Property of All Real Algebraic Numbers", marks the birth of set theory. paradox
twentieth century axiomatic set theory naive set theory Concept Relation. function. cardinal number paradox
twentieth century axiomatic set theory naive set theory Concept Relation,function,cardinal number paradox
Chapter 1 Basic Concepts of Sets 1.1 Sets and subsets What are sets? A collection of different objects is called a set SA The individual objects in this collection are called the elements of the set We write“teA” to say that t is an element ofa, and we write“tgA” to say that t is not an element ofA
Chapter 1 Basic Concepts of Sets 1.1 Sets and Subsets What are Sets? A collection of different objects is called a set S,A The individual objects in this collection are called the elements of the set We write “tA” to say that t is an element of A, and We write “tA” to say that t is not an element of A
Example: The set of all integers, Z Then3∈Z,-8∈Z,6.5gZ These sets, each denoted using a boldface letter, play an important role in discrete mathematics: N=0, 1, 2,, the set of natural number FF(,2, -1, 0, 1, 2 ., the set of integers F=Z=1, 2, ., the set of positive integers Z=1, -2,, the set of negative integers Q={p/qlp∈Z2q∈Z,q≠0}, the set of rational numbers Q, the set of positive rational numbers Q, the set of negative rational numbers
Example:The set of all integers, Z. Then 3Z, -8Z, 6.5Z These sets, each denoted using a boldface letter, play an important role in discrete mathematics: N={0,1,2,…}, the set of natural number I=Z={…,-2,-1,0,1,2,…}, the set of integers I +=Z+={1,2,…}, the set of positive integers I -=Z-={-1,-2,…}, the set of negative integers Q={p/q|pZ,qZ,q0}, the set of rational numbers Q+ , the set of positive rational numbers Q- , the set of negative rational numbers