sss数学专英课后答案.__2.docVIP

Before 17th century, man confined himself to the elementary mathematics, i. e. , geometry, trigonometry and algebra, in which only the constants were considered. （5）方程与算数的等式不同在于它含有可以参加运算的未知量。 Equation is different from arithmetic identity in that it contains unknown quantity which can join operations. （6）方程又称为条件等式，因为其中的未知量通常只允许取某些特定的值。 Equipment is called an equation of condition in that it is true only for certain values of unknown quantities in it. （7）方程很有用，可以用它来解决许多实际应用问题。 Equations are of very great use. We can use equations in many mathematical problems. （8）解方程时要进行一系列移项和同解变形，最后求出它的根，即未知量的值。 To solve the equation means to move and change the terms about without making the equation untrue, until the root of the equation is obtained, which is the value of unknown term. 2.3 集合论的基本概念 （1）由小于 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）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. （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; AB means that A is contained in B. （4）命题 A B 并不排除 B A 的可能性。 The statement AB does not rule out the possibility that BA. （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. （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}区别开来。 To avoid logical difficulties, we must distinguish between the element x and the set {x} whose only element is x. （7）图解法有助于将集合之间的关系形象化。 Diagrams often help using visualize relationship between sets. （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. 2.4 整数、有理数与实数 整数 （1）严格说，这样描述整数是不完整的，因为我们并没有说明“依此类推”或“反复加 1” 的含义是什么。 Strictly speaking, this description of the positive integers is not entirely complete because we have not explained in detail what we mean by