Whenever an arbitrary positive quantity 𝞮 is assigned,we can make off an interval |x - x0| < 𝞭 so small that for any x which belongs both to the domain of f and to that interval the inequality |f(x) - η| < 𝞮 holds. (查看原文)
if f(𝞷) is defined, then lim(x -> 𝞷) f(x), if it exists at all, must have the value f(𝞷). Indeed, the definition of η = lim(x -> 𝞷)f(x) implies in particular | f(𝞷) - η |<𝞮 for every positive 𝞮 and hence f(𝞷) = η (查看原文)
Whenever an arbitrary positive quantity 𝞮 is assigned,we can make off an interval |x - x0| < 𝞭 so small that for any x which belongs both to the domain of f and to that interval the inequality |f(x) - η| < 𝞮 holds.引自 The Concept of Limits for Functions of a Continuous Variable
恩......似乎看起来不是他看错了，原作这段的确没有大于0......
然而下一段就打脸了
if f(𝞷) is defined, then lim(x -> 𝞷) f(x), if it exists at all, must have the value f(𝞷). Indeed, the definition of η = lim(x -> 𝞷)f(x) implies in particular | f(𝞷) - η |<𝞮 for every positive 𝞮 and hence f(𝞷) = η 引自 The Concept of Limits for Functions of a Continuous Variable
rational numbers: The word 'rational' here does not mean reasonable or logical but is derived from the word 'ratio' meaning the relative proportion of two magnitudes. There is always a point existed in the infinitely nested intervals, which are divided by natural numbers. The understanding of continuum, limit and infinity can eventually be traced back to natural numbers. How amazing it is. It i...
2019-11-14 05:45
rational numbers:
The word 'rational' here does not mean reasonable or logical but is derived from the word 'ratio' meaning the relative proportion of two magnitudes.
There is always a point existed in the infinitely nested intervals, which are divided by natural numbers. The understanding of continuum, limit and infinity can eventually be traced back to natural numbers. How amazing it is. It is a shame that once translated into Chinese "有理数", the very point of ratio is lost.
rational numbers: The word 'rational' here does not mean reasonable or logical but is derived from the word 'ratio' meaning the relative proportion of two magnitudes. There is always a point existed in the infinitely nested intervals, which are divided by natural numbers. The understanding of continuum, limit and infinity can eventually be traced back to natural numbers. How amazing it is. It i...
2013-03-10 11:11
rational numbers:
The word 'rational' here does not mean reasonable or logical but is derived from the word 'ratio' meaning the relative proportion of two magnitudes.引自 Introduction
There is always a point existed in the infinitely nested intervals, which are divided by natural numbers. The understanding of continuum, limit and infinity can eventually be traced back to natural numbers. How amazing it is. It is a shame that once translated into Chinese "有理数", the very point of ratio is lost.
Whenever an arbitrary positive quantity 𝞮 is assigned,we can make off an interval |x - x0| < 𝞭 so small that for any x which belongs both to the domain of f and to that interval the inequality |f(x) - η| < 𝞮 holds.引自 The Concept of Limits for Functions of a Continuous Variable
恩......似乎看起来不是他看错了，原作这段的确没有大于0......
然而下一段就打脸了
if f(𝞷) is defined, then lim(x -> 𝞷) f(x), if it exists at all, must have the value f(𝞷). Indeed, the definition of η = lim(x -> 𝞷)f(x) implies in particular | f(𝞷) - η |<𝞮 for every positive 𝞮 and hence f(𝞷) = η 引自 The Concept of Limits for Functions of a Continuous Variable
rational numbers: The word 'rational' here does not mean reasonable or logical but is derived from the word 'ratio' meaning the relative proportion of two magnitudes. There is always a point existed in the infinitely nested intervals, which are divided by natural numbers. The understanding of continuum, limit and infinity can eventually be traced back to natural numbers. How amazing it is. It i...
2019-11-14 05:45
rational numbers:
The word 'rational' here does not mean reasonable or logical but is derived from the word 'ratio' meaning the relative proportion of two magnitudes.
There is always a point existed in the infinitely nested intervals, which are divided by natural numbers. The understanding of continuum, limit and infinity can eventually be traced back to natural numbers. How amazing it is. It is a shame that once translated into Chinese "有理数", the very point of ratio is lost.
Whenever an arbitrary positive quantity 𝞮 is assigned,we can make off an interval |x - x0| < 𝞭 so small that for any x which belongs both to the domain of f and to that interval the inequality |f(x) - η| < 𝞮 holds.引自 The Concept of Limits for Functions of a Continuous Variable
恩......似乎看起来不是他看错了，原作这段的确没有大于0......
然而下一段就打脸了
if f(𝞷) is defined, then lim(x -> 𝞷) f(x), if it exists at all, must have the value f(𝞷). Indeed, the definition of η = lim(x -> 𝞷)f(x) implies in particular | f(𝞷) - η |<𝞮 for every positive 𝞮 and hence f(𝞷) = η 引自 The Concept of Limits for Functions of a Continuous Variable
Nunc Dimittis
科学出版社2001版
子非鱼
科学出版社2005版
咱是想来质疑某篇一星书评的评价的......本来也是因为这个一星评价担心了一下本书严谨性，结果似乎他的一个论据实际上...... 论据原文:【最基本的一开始的极限严格定义都写得错的！！！！应该是大于0，居然没有！！！！！！这就是所谓的名著？？？？ 】 首先，他这里说的咱想应该是函数极限定义（数列极限对于N,没有大于0)，咱见过的国内教材的确是对于任意的𝞮，存在一个邻域U0(x0,𝞭),亦即 0 < |x - x0| < 𝞭,这...
2 有用 Leuckart 2019-05-19
这是刚进大学时被推荐的一本书。优点是足够详细，但作者似乎有些过于耐心了。节奏太慢，导致这本书的篇幅远远超过同类教材，难免会拖累自学速度，所以我只看了第一卷就没再看了。作者是一位十分优秀的数学家，他的「什么是数学」是本很好的科普书，与希尔伯特合著的「数学物理方法」更不用说了，经典中的经典。
0 有用 leave 2011-04-29
我的数学啊～
1 有用 Tur 2018-11-14
非常给力。
1 有用 Er. 2012-06-16
非常清晰有条理的书
3 有用 reminiscence 2016-01-30
挺容易懂的,有很多的图画。应该是我看的第一本纯粹数学的英文书。
1 有用 我爱巴达兽 2020-01-30
这本书是我最早开始自学的一本书，因为当时刚看完《什么是数学》，觉得柯朗的书应该对读者非常友好。但是我并没有看下去很多，就看到积分，后来也用了别的教材学数学分析。我个人感觉这本书稍微有点老，比起现在大学常用的教材。不过好的地方是一开始就介绍了很多概念，好些我当时没有明白为什么重要，现在也都一一再次碰面了。
1 有用 John 2019-09-26
多年前读的
2 有用 Leuckart 2019-05-19
这是刚进大学时被推荐的一本书。优点是足够详细，但作者似乎有些过于耐心了。节奏太慢，导致这本书的篇幅远远超过同类教材，难免会拖累自学速度，所以我只看了第一卷就没再看了。作者是一位十分优秀的数学家，他的「什么是数学」是本很好的科普书，与希尔伯特合著的「数学物理方法」更不用说了，经典中的经典。
0 有用 未知名的艺术家 2019-04-30
经典之作
1 有用 Tur 2018-11-14
非常给力。