关于无穷大基数的矛盾

通过分析康托尔对角线法证明实数集不可列隐含下述前提:可依次检查完对角线上所有无穷个元素.从认同Ai的元素与集合A]=∪Ai中孪生元素对一一对应,从而A]=2(A),进而证明这一前提出发,证明了集合(A)=∪1 i≤ω1 i<ω了(A)= 0=A]=2 0这一与康托尔矛盾的结果.

On the Contradictions of Infinite Cardinal Numbers

Canter's proof of which real number set is not a countable aggregate is called the diagonal method. The present author discovers that this proof implies a premise that "all the infinite elements on diagonal can be checked in due order." Based on this premise, we can prove that the one to one correspondence between the elements of (A)=∪1i<ωA_iand the pairs of twin elements ofA]=∪1i≤ωA_i, i.e., (A])=2((A)). Thus we have ((A))=_0=(A])=2~(_0), which is contrary to Cantor's results.