ABSTRACT
For over half a century, it has been commonly believed that the establishment and development of modern axiomatic set theory have provided a method to explain Russell’s paradox. On the other hand, even though it has not been proven theoretically that there will not appear new paradoxes in modern axiomatic set theory, it has been indeed a century that no one has found a new paradox in modern axiomatic set theory. However, when we revisit some well-known results and problems with the thinking logic of allowing two kinds of infinite, the potential and actual infinite, we discover that various infinite sets in the framework of ZFC set theory, widely studied and employed in modern axiomatic set theory, are all specious non-sets.
