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计算机英语高手,帮我翻译一篇文章!不要软件翻译……
The concept of set plays a very significant role in all branches of modern mathematics. In recent
Years set theory has become an important area of investigation because of the way in which it permeates so much of contemporary mathematical thought. A genuine understanding of any branch of modern mathematics requires a knowledge of the theory of sets for it is the common foundation of the diverse areas of mathematics.. Sets are used to group distinct objects together .It is necessary that the objects which belong to set are well-defined in the sense that there should be no ambiguity in deciding whether a particular object belongs to a set or not. Thus, given an object, either it belongs to a given set or it does not belongs to it .For example, the first five letters of the English alphabet constitute a set which may be represented symbolically as the set {a,b,c,d,e}.An arbitrary object belongs to this set if and only if it is one of these five letters ,These five distinct Objects can appear in any order in this representation. In other words, this set can also be represented by {d,b,a,e,c}.The objects that belong to a set need not possess a common property. Thus the number 4, the letter x , and the word “book” can constituter a set S which may be represented as S={x,book,4}.A particular day may be cold for one person and not cold for another, so the “collection of cold days in a month “ is not a clearly defined set .Similarly, “the collection of large numbers “and “the collection of tall men” are also not sets.
The term object has been used here without specifying exactly what an object is . From a mathematical point of view, set is a technical term that takes its meaning from the properties we assume that sets possess. This informal description of a set, based on the intuitive notion of an object, was first given by the German mathematician Georg Cantor(1845-1918) toward the end of the nineteenth century and the theory of sets based on his version is known as naïve set theory. In Cantor’s own words, “a set is bringing together into a whole of definite well-defined objects of our perception and these objects are the elements of the set.” The sets considered in this book can all be viewed in this framework of Cantor’s theory.
Thus a set is a collection of distinct objects. The objects in a set are called the elements or members of the set ,If x is an element of a set A, we say that x belongs to A, and this is expressed symbolically as x∈A. The nation y∈A denotes that y is not an element of the set A.
The concept of set plays a very significant role in all branches of modern mathematics. In recent
Years set theory has become an important area of investigation because of the way in which it permeates so much of contemporary mathematical thought. A genuine understanding of any branch of modern mathematics requires a knowledge of the theory of sets for it is the common foundation of the diverse areas of mathematics.. Sets are used to group distinct objects together .It is necessary that the objects which belong to set are well-defined in the sense that there should be no ambiguity in deciding whether a particular object belongs to a set or not. Thus, given an object, either it belongs to a given set or it does not belongs to it .For example, the first five letters of the English alphabet constitute a set which may be represented symbolically as the set {a,b,c,d,e}.An arbitrary object belongs to this set if and only if it is one of these five letters ,These five distinct Objects can appear in any order in this representation. In other words, this set can also be represented by {d,b,a,e,c}.The objects that belong to a set need not possess a common property. Thus the number 4, the letter x , and the word “book” can constituter a set S which may be represented as S={x,book,4}.A particular day may be cold for one person and not cold for another, so the “collection of cold days in a month “ is not a clearly defined set .Similarly, “the collection of large numbers “and “the collection of tall men” are also not sets.
The term object has been used here without specifying exactly what an object is . From a mathematical point of view, set is a technical term that takes its meaning from the properties we assume that sets possess. This informal description of a set, based on the intuitive notion of an object, was first given by the German mathematician Georg Cantor(1845-1918) toward the end of the nineteenth century and the theory of sets based on his version is known as naïve set theory. In Cantor’s own words, “a set is bringing together into a whole of definite well-defined objects of our perception and these objects are the elements of the set.” The sets considered in this book can all be viewed in this framework of Cantor’s theory.
Thus a set is a collection of distinct objects. The objects in a set are called the elements or members of the set ,If x is an element of a set A, we say that x belongs to A, and this is expressed symbolically as x∈A. The nation y∈A denotes that y is not an element of the set A.
组的观念在现代数学的所有部门中担任一个非常重要的角色. 在最近的
因为方式数年集合论已经变得一个调查的重要区域在哪一个它弥漫大多数的同时代的数学想法. 因为它是数学的不同区域的共同基础,现代数学的任何部门的真正理解需要组的理论知识. 设定用来一起聚集清楚的物体.它是必需的属于组的物体是定义明确的在某种意义上在决定一个特别的物体是否属于组方面应该没有不明确. 因此, 被给的一个物体, 或它属于给定的组或者它不属于它.举例来说, 英国字母的最初五封信构成一设定哪一个可能象征性地被表现当做固定的 {a 、 b 、 c 、 d,e}.如果而且只有当如果它是这些五封信之一,一个任意的物体属于这组,这些五个清楚的物体能在这表现中任何的次序中出现. 换句话说, 这组也能被表现被 {d 、 b 、 a 、 e,c}.属于固定的需要的物体不持有通常的财产. 如此 4 号,信 x 和”书”那个字能 constituter 可能当做 S 被表现的固定的 S={x ,书,4}.一个特别的日子可能对一个人是寒冷的和不是寒冷为另外一,因此 " 寒冷的天的收集在一个月中 " 不是清楚地定义的组.同样地, " 收集大大地数 " 和 " 高男人的收集 " 也不是组.
期限物体不需要完全地叙述什么一个物体是就已经在这里被用. 从数学观点,组是采取来自我们承担组持有的特性的它的意义的一个技术上的期限. 组,以物体的直觉观念为基础的这非正式描述, 首先藉着德国数学家 Georg 有接近十九世纪末的合唱指挥家 (1845-1918) 和以他的版本为基础的组的理论即是 na?ve 集合论. 在合唱指挥家的自己字, "组正在一起进入我们的知觉的明确定义明确物体的全部之内带来,而且这些物体是组的元素." 在这一本书中被考虑的组能全部在合唱指挥家的理论的这一个结构中被看.
如此组是一个清楚物体的收集. 在组的物体叫做组的元素或者成员 ,如果 x 是元素一设定一, 我们说 x 属于一, 和这象征性地被表达当 x ∈ A. 国家 y ∈一指示 y 不是元素那设定一.
因为方式数年集合论已经变得一个调查的重要区域在哪一个它弥漫大多数的同时代的数学想法. 因为它是数学的不同区域的共同基础,现代数学的任何部门的真正理解需要组的理论知识. 设定用来一起聚集清楚的物体.它是必需的属于组的物体是定义明确的在某种意义上在决定一个特别的物体是否属于组方面应该没有不明确. 因此, 被给的一个物体, 或它属于给定的组或者它不属于它.举例来说, 英国字母的最初五封信构成一设定哪一个可能象征性地被表现当做固定的 {a 、 b 、 c 、 d,e}.如果而且只有当如果它是这些五封信之一,一个任意的物体属于这组,这些五个清楚的物体能在这表现中任何的次序中出现. 换句话说, 这组也能被表现被 {d 、 b 、 a 、 e,c}.属于固定的需要的物体不持有通常的财产. 如此 4 号,信 x 和”书”那个字能 constituter 可能当做 S 被表现的固定的 S={x ,书,4}.一个特别的日子可能对一个人是寒冷的和不是寒冷为另外一,因此 " 寒冷的天的收集在一个月中 " 不是清楚地定义的组.同样地, " 收集大大地数 " 和 " 高男人的收集 " 也不是组.
期限物体不需要完全地叙述什么一个物体是就已经在这里被用. 从数学观点,组是采取来自我们承担组持有的特性的它的意义的一个技术上的期限. 组,以物体的直觉观念为基础的这非正式描述, 首先藉着德国数学家 Georg 有接近十九世纪末的合唱指挥家 (1845-1918) 和以他的版本为基础的组的理论即是 na?ve 集合论. 在合唱指挥家的自己字, "组正在一起进入我们的知觉的明确定义明确物体的全部之内带来,而且这些物体是组的元素." 在这一本书中被考虑的组能全部在合唱指挥家的理论的这一个结构中被看.
如此组是一个清楚物体的收集. 在组的物体叫做组的元素或者成员 ,如果 x 是元素一设定一, 我们说 x 属于一, 和这象征性地被表达当 x ∈ A. 国家 y ∈一指示 y 不是元素那设定一.