关于连续统假设2ω0＝ω1的证伪凡数皆可数2ω0＝ω1的证明

摘要

通过破连续统假设的基石即其中的基本定理与基本方法，得到主要结果：证伪“定理：ω1是基数”；康托定理的证伪；对角线法不可取；从正面几个角度几种方法来证明连续统[0，1]是可数的．得出关于连续统的一个新证明：2ω0＝ω0．用进制法证明2ω0可数；用一一对应法证明[0，1]实数区间的可数性．%By the falsity of “Theorem:ω1 is a cardinal”and the falsity of Cantor Theorem or Improper use of the diagonal method obtani the main results are the following:2ω0 equal toω1 (2ω0 =ω1 ) Cantor thought it was true, which means [0, 1] is uncountable.We call it Continuum Hypothesis .This article first rocks the cor-nerstone 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 2ω0 is 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.