摘要
关于两个数学问题:(ⅰ)呈0/0型函数的连续性问题;(ⅱ)中国数学家在非标准数学方面是否有过工作的问题;对前者给出探讨性结论,对后者给出考证。前者探讨性结论是:在某点呈0/0型的函数在该点有确定的值,且在该点连续,而传统观点则是:这类在某点呈0/0型的函数在该点没有确定的值,在该点不连续。后者的考证结果是:华罗庚的1nx之无穷大之阶是个非标准数——中国数学家华罗庚早在1957年就以实例证实了这类非标准数的存在,比现代非标准分析创始人A·Robinson用数理逻辑方法证明出这类非标准数存在早3年;然而华罗庚在这方面的工作在国内外数学界竟没有被正视过。
In this paper, we discuss two math problems: (ⅰ)On the continuity of function which displays 0/0 type on certain point (ⅱ) If China mathmaticiam Hua Luogeng did the work on the nonstandard number. We give conclusion of discussion for(ⅰ)and verify for(ⅱ). The conclusionn for(ⅰ)is that: The function which displays 0/0 type on certain point has certain value adn continues on the point. But traditional view is that: The function which displays of Onoyep certain point has not cerat value andnot continues on the point. Verify for(ⅱ)is that: Order of infinity of lnx is nonstandard number. About that, China mathmaticiam Hua Luogeng show existance of nonstadaard number by example in 1957. It is earlier3 Years than modern nonstandard analysis beginner A Robinson who proof it by method of mathmatical logic. But Hun Luogeng's work come to internal and external math circle notice.
关键词
连续性
无穷大的阶
非标准数
continuity, order of infinty, nonstadnard number
