无穷的发展史 毕业论文.docVIP

无穷的发展史 内容摘要 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 Infinite history Abstract 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 Greeces preliminary exploration, to topping in calculus, again to set 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, because of this people will be so afraid that cant admit that irrational Numbers-not the existence of infinite repeating decimals. However curiosity makes people begin to understand it, use 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 second mathematical crisis. Through the analysis of the late perfect especially the strict, an infinitesimal finally had a precise definition. But endless explore is still not stop, cantors proposed set theory, and points out that the infinite genealogy, constructed the mathematical building foundation. But set theory, there are also took a deadly-Russell paradox, which prompted a third mathematical crisis, and has not been fully resolved. For endless, there are still a too much of the unknown. 【Key words】：Infinite limit calculus set theory 目录 引言…………………………………………………………（