集合论存在矛盾的必然性及其证明

自然数理论在无限问题上隐含逻辑矛盾，因为自然数理论是集合论的逻辑基础，所以集合论也隐含逻辑矛盾，这一事实是能够证明的，文章给出了三个不同的证明，它们分别与小学数学、中学数学、大学数学接轨。

Inevitability of Contradiction in the Theory of Sets and Its Proof

In the theory of natural numbers, there lies concealed contradiction of logic on the infinity. Since the theory Of natural numbers is the fundament of logic for the theory of sets, there also lies concealed contradiction of logic in the latter. It is possible to prove this fact. In this article, three different proofs are given, which are connected to the mathematics of the elementary school, middle school and uni- versity respectively.