摘要
讨论了2个最基本的数学问题,分别给出了明确的答案."存在最大的自然数吗"?答案是:最大的自然数,在现实中不存在,但为了研究无穷集合必须假设它存在于理想中;"自然数集中的任何自然数都是有限的吗"?答案是:自然数集中的任何自然数并非都是有限的.还用简单的方法排除了超限数悖论,断言它们都是佯悖.指出所谓最大序数悖论和最大基数悖论中出现的矛盾,是由于悖论的认为者进行了错误的推理所造成的,他们混淆了无穷存在的现实和理想、混淆了无穷构造的进程和终结.还阐述了无穷研究新方案中一些基本创新点.
Two basic mathematic problems are discussed in this article, and clear conclusions are drawn accordingly as to ＂Is the largest natural number existed？＂ The answer is the largest natural number does not existed in the real world, but to research the infinite sets, it is necessary to assume its existence in ideality, ＂Is any natural number in the set of natural number finite？＂ The answer is： not any natural number in the set of natural number is finite. This paper also uses a simple method to exclude the Paradox of transfinite numbers, declares them as false paradoxes, and points out that the so-called contradiction in the paradoxes of the largest ordinal and the largest cardinal is caused by the faulty reasoning, which confuses the ideality and reality of the infinity existence, as well as the process and finalization of the infinity construction. Some basic innovations are also introduced in the new method of infinity research.
出处
《重庆工学院学报（自然科学版）》
2009年第7期146-152,共7页
Journal of Chongqing Institute of Technology
关键词
自然数
无穷
集合
元素
natural numbers
infinity
set
element
