关于连续统假设若干史实的注记

A Note on Some Historical Facts of Continuum Hypothesis

结合 3个基本事实 ,考察分析了连续统问题的起源、发展和现有的结论 .由此得知 :1.康托尔为了对无限集进行分类提出连续统猜想时间上是合理的 ;2 .希尔伯特的证明失误反映了历史的局限性 ,同时蕴含了有用的证明思想 ;3.哥德尔在解决连续统问题的过程中承上启下的作用是独特的 ,他的思想主导着该领域的发展方向 .历史地看待 3位数学家的贡献有助于做出公允的评判 ,从而对连续统问题的演化和发展有一个正确地认识 .

Through three basic facts,the origin,the evolution and the present results are explored.The conclusions are drawn as follows:1.The time when Cantor raised the Continuum Problem is suitable;2.The faults in Hibert's proof for the Continuum Hypothesis reflect the historic limitation,but suggests a possible solution.3.Gdel's role as a connecting link between the preceding and the following is unique and remarkable.Bsed on these results,the contributions of the three mathematicians are fairly judged and commented on,thus the evolvement and development of the Continuum Problem can correctly be understood.