天津财经珠江学院数学系毕业论文：无穷的发展史
无穷的发展史
中铁四局六公司内容摘要
公司收入证明无穷的探索在数学史的发展上有着举足轻重的作用。本文从历史发展的角度展示了无穷的发展历程。从古希腊时期的初步探索，到在微积分中大放异彩，再到集合论的惊世骇俗。无穷的每一次新的探索都伴随着数学思想的跳跃性的发展。通过对无穷史的展示，引发对无穷本质的思考。最初，无穷对于人们来说是不可理解的是，甚至是恐惧的，正因为如此人们才会如此惧怕以至于不敢承认无理数??无限不循环小数的存在。然而好奇心促使人们开始了解它，应用它。尤其是微积分的出现，使得无穷走进数学的大舞台，但最初的微积分显然没有解决无穷小的问题，也因此引发了第二次数学危机。经过后期的完善特别是分析的严格化，无穷小终于有了自己精确的定义。然而无穷的探究仍未停止，康托尔提出集合论，指出了无穷大的谱系，构建了数学大厦的根基。但集合论也存在着致命的硬伤??罗素悖论，这引发了第三次数学危机，并至今未被完全解决。对于无穷，仍然存在着太多的未知。
【关键词】：无穷极限微积分集合论
龙珠壁纸
Infinite history
Abstract白领的堕落
那一次我真Endless exploration in the history of mathematics in development has a pivotal role. This paper, from the perspective of the development of history shows the endless development process. From the ancient Greece's preliminary exploration, to topping in calculus, again to t theory of pedophilia. Boundless each time the new exploration are accompanied with mathematical thought the development of the narrative.
Through the history of the infinite show, leading to the nature of the infinite thinking. At first, it is not infinite for people to understand is, and even fear, becau of this people will be so afraid that can't admit that irrational Numbers-not the existence of infinite repeating decimals. However curiosity makes people begin to understand it, u it. Especially the emergence of calculus, which went into the stage of infinite math, but the first of the infinitesimal calculus obviously not solve the problem, which, therefore, the cond mathematical crisis. Through the analysis of the late perfect especially the strict, an infinitesimal finally had a preci definition. But endless explore is still not stop, cantor's propod t theory, and points out that the infinite genealogy, constructed the mathematical building foundation. But t theory, there are also took a deadly-Rusll paradox, which prompted a third mathematical crisis, and has not been fully resolved. For endless, there are still a too much of the un
known.
【Key words】:Infinite limit calculus t theory
目录
引言 (1)
恐惧??关于无穷的悖论和无理数的发现 (1)
发展??穷竭法、无穷级数和微积分 (3)
危机??第二次数学危机和分析的严格化 (5)
改革??康托尔的集合论和第三次数学革命 (7)
结束语 (10)
中国粮食现状参考文献 (11)
致谢 (12)
无穷的发展史表外资产
引言
数学是门严谨的学科。数学家近乎偏执的证明、完善各种数学问题，又不断产生新的悖论、问题。数学就是在这一次次悖论、证明、危机、改革中发展和完善起来的。然而数学中有这么一个概念??无穷，它在几千年前就被人们发现和使用却至今未被人完美的证明，它被用来证明最严谨的数学问题本身却是科学中最模糊的概念。有人说无穷是数，有人说无穷是一种思想，甚至有人说它是消逝的量的鬼魂。
借用大卫?希尔伯特的话“无穷大!任何一个其他问题都不曾如此深刻的影响人类的精神；任何一个其他观点都不曾如此有效的激励人类的智力；然而，没
