Two most important essays by the famous German mathematician: one provides an arithmetic, rigorous foundation for the irrational numbers, thereby a rigorous meaning of continuity in analysis. The other is an attempt to give logical basis for transfinite numbers and properties of the natural numbers.
I regard the whole of arithmetic act, that of counting, and counting itself as nothing else than the successive creation of the infinite series of positive integers in which each individual is defined by the one immediately preceding; the simplest act is the passing from an already-formed individual to the consecutive new one to be formed. (查看原文)
0 有用 ae 2011-05-03 12:55:18
前一半
0 有用 Caesura 2011-05-18 12:04:45
戴德金对无理数的纯算术方法推导。排列有理数用到了数轴。所以数轴不算一个geometrical intuition哦？然后从数轴这个line推断有理数是不连续的，它们的gap里面还有其他数即无理数。这个move不算stretching an analogy哦？
0 有用 面条超人 2011-05-17 05:36:25
只读了第一篇和第二篇的前言
0 有用 废梁 2018-12-07 04:40:05
Continuity and Irrational Numbers 一篇
1 有用 宣棋 2016-12-12 23:27:43
Which one is the primary, geometry of algebra? Are numbers truly different from geometry? What is the number?
0 有用 Bidasari 2024-05-12 23:57:23 美国
两篇都很精彩；第一篇的typo严重影响理解；另外，认为这还是在依赖几何直观的还是放弃治疗吧，没救了
0 有用 SS 2024-04-21 17:53:32 美国
美丽而优雅
0 有用 初繁言 2021-12-28 17:50:33
极致优雅与严谨——同意geometric intuition还是挺强的。又引起了一些对于proof的思考，赶紧记下来有空问
0 有用 Agilulfo 2020-04-22 18:55:43
Continuity and Irrational numbers. 非常优美的策略。关键概念的征用来自解决问题的实际需要。数学气息＞哲学气息。相当依赖geometric intuition.
0 有用 废梁 2018-12-07 04:40:05
Continuity and Irrational Numbers 一篇