Cauchy theater phenomenon in diagonal method and test principle of finite positional differences

Abstract

Purpose

The paper's purpose is to show a class of well‐used methods in set theory is invalid.

Design/methodology/approach

A conceptual approach is taken.

Findings

Based on the concept of Cauchy theater introduced elsewhere, it is proven that the argument employing the diagonal method for the fact that the set of all real numbers R={x|r(x)}, where r(x)=_df “x is a real number” has an uncountable cardinality, is not valid. The diagonal method has appeared in naive and modern axiomatic set theories.

Originality/value

Point out more paradoxes in the methodology of mathematics.

Citation

Zhu, W., Lin, Y., Gong, N. and Du, G. (2008), "Cauchy theater phenomenon in diagonal method and test principle of finite positional differences", Kybernetes, Vol. 37 No. 3/4, pp. 469-473. https://doi.org/10.1108/03684920810863444