查询词典 uncountability

There are the seeming paradoxes of countability and uncountability

粗略地讲，悖论可分为可数性悖论和不可数性悖论。

The paper introduces several important notions such as uncountability and halting problem firstly,the fact is proved by contradiction that halting problem is impossible problem,and the same to other relative issues in computer is proved by reduction.

本文先介绍了不可数性和停机问题等重要概念，用反证法证明了停机问题是不可解的，并使用归约法对计算机中的相关问题的不可解性进行了证明。

Through a new analysis on the essential relationship between Russell's Paradox and Cantor's proof on the uncountability of real number set and the proof on the Cantor's Theorem of , a mysterious error was found:the very same logic contradiction was applied in both Russell and Cantor's work.

分析了罗素悖论与康托的实数集合不可数证明及康托定理证明之间的本质性联系，发现康托在这两个非构造性证明中所依赖的、用对角线法所构造出的矛盾其实就是罗素悖论中所揭示的逻辑矛盾。

Through a new analysis on the essential relationship between Russell's Paradox and Cantor's proofs on the uncountability of real number set and the proof on the Cantor's Theorem of ,two mysterious errors were found: The very same idea was applied in both Russell and Cantor's work, but Cantor made wrong use of it with two logical mistakes.

分析了罗素悖论与康托的实数集合不可数证明及康托定理证明之间的本质性联系，发现康托的这两个非构造性证明与罗素悖论有完全相同的思路，但是康托犯了两个逻辑性错误而使他误用了这个悖论思路。

From the defects in the basic theory of present classical infinite theory, the essential relationship between Russell's Paradox and Cantor's proof on the uncountability of real number set and the proof on the Cantor's Theorem of is analyzed and a mysterious error is found:The core of Cantor's above two important proofs in set theory are actually another versions of Russell's paradox and the very same paradoxical idea was applied in both Russell and Cantor's work, and Cantor made wrong use of this paradox idea with two logical mistakes.

从经典无穷理论体系中的缺陷入手，深入分析了罗素悖论与康托的实数集合不可数证明及康托定理证明之间的本质性联系，发现康托在这两个证明里的核心部分实际上是罗素悖论的翻版，它们与罗素悖论有完全相同的思路，并且康托犯了两个逻辑性错误而误用了这个悖论思路。

Russell's Paradox; the uncountability of real number set; Cantor's Theorem of ; infinite theory system; part; all; epistemology; logic

罗素悖论；实数集合不可数性；康托定理；无穷理论体系；部分；全体；认识论；逻辑

Diabetes is a social disease that affects several million people worldwide.

糖尿病是一个社会性疾病，全世界有数百万人罹患此病。

I'll call you on Friday to see if we can reschedule our luncheon meeting at your convenience.

我星期五会给您打电话在您方便的时候我们重新安排我们的午餐约会。