TY  - JOUR
AB  - Purpose– The paper aims to employ a different approach to show that the countable infinite sets are self‐contradictory non‐sets.Design/methodology/approach– The paper discusses the concept.Findings– The concept of infinities in the countable set theory was discussed in Zhu et al. by employing the method of analysis of allowing two different kinds of infinities. What was obtained is that various countable infinite sets, studied in the naïve and modern axiomatic set theories, are all incorrect concepts containing self‐contradictions. In this paper, the authors provide another argument to prove the same conclusion: various countable infinite sets studied in both naïve and modern axiomatic set theories are all specious non‐sets. The argument is given from a different angle on still the same premise of allowing two different concepts of infinities.Originality/value– The concept of Cauchy theater is introduced.
VL  - 37
IS  - 3/4
SN  - 0368-492X
DO  - 10.1108/03684920810863426
UR  - https://doi.org/10.1108/03684920810863426
AU  - Zhu Wujia
AU  - Lin Yi
AU  - Du Guoping
AU  - Gong Ningsheng
ED  - Yi Lin
PY  - 2008
Y1  - 2008/01/01
TI  - Modern system of mathematics and special Cauchy theater in its theoretical foundation
T2  - Kybernetes
PB  - Emerald Group Publishing Limited
SP  - 458
EP  - 464
Y2  - 2024/04/25
ER  -