Modern system of mathematics and general Cauchy theater in its theoretical foundation

The paper aims to show using a different method that any uncountable set is a self‐contradictory non‐set.

The paper discusses the concept.

Elsewhere it is shown that in the framework of ZFC, various countable infinite sets are all self‐contradicting non‐sets. In this paper, the authors will generalize the concept of Cauchy theater, and establish the concept of transfinite Cauchy theaters. After that, employing a new method, they will prove that various uncountable infinite sets, as studied in naive set theory and modern axiomatic set theory, are also self‐contradicting non‐sets.

The concept of general Cauchy theater is introduced.