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《Journal of Huaiyin Teachers College(Natural Science Edition)》 2014-01
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The Falsity of Continuum Hypothesis2~(ω~(0)) = ω_1 The Mathematical Justification for All Numbers are Countable 2~(ω~(0)) = ω_0

CHEN Zi-li;Haining Construction Bureau & Zhejiang Huaheng ArchitecturalDesign CO. LTD;  
By the falsity of"Theorem: ω1is a cardinal"and the falsity of Cantor Theorem or Improper use of the diagonal method obtani the main results are the following: 2ω0equal to ω1( 2ω0= ω1) ? Cantor thought it was true,which means [0,1]is uncountable. We call it Continuum Hypothesis. This article first rocks the cornerstone of Continuum Hypothesis,that is to say,the basic principle and method adopted in this hypothesis. Then to clarify the problem,several methods are used to prove that the continuum [0,1]is countable. A new mathematical proof of continuum: 2ω0= ω0; To prove 2ω0is countable by using decimal method; To prove the countability of the set of real numbers [0,1]by using the rule of one-one correspondence
【CateGory Index】: O177
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