The paper aims to employ a different approach to show that the countable infinite sets are self‐contradictory non‐sets.
The paper discusses the concept.
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.
The concept of Cauchy theater is introduced.
Zhu, W., Lin, Y., Du, G. and Gong, N. (2008), "Modern system of mathematics and special Cauchy theater in its theoretical foundation", Kybernetes, Vol. 37 No. 3/4, pp. 458-464. https://doi.org/10.1108/03684920810863426
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