康托对康托
Cantor versus Cantor
摘要：
本文考察了将康托尔关于实数集的不可数性质的两个论点扩展到其真可数子集之一：有理数集的可能性。本文证明，除非满足一定的限制条件，这两种扩展是可能的。因此，证明这些条件在康托的超限集合理论中实际上是满足的是必不可少的。否则这个理论就不一致了。
英文摘要：
This paper examines the possibilities of extending Cantor's two arguments on the uncountable nature of the set of real numbers to one of its proper denumerable subsets: the set of rational numbers. The paper proves that, unless certain restrictive conditions are satisfied, both extensions are possible. It is therefore indispensable to prove that those conditions are in fact satisfied in Cantor's theory of transfinite sets. Otherwise that theory would be inconsistent.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
