Cauchy theater phenomenon in diagonal method and test principle of finite positional differences
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 vertical bar r(x)}, were r(x) =(df) "x is a real number" has an uncountable cardinality, is not valid. The diagonal method has appeared in naive and modem axiomatic set theories. Originality/value - Point out more 'paradoxes in the methodology of mathematics.
set theory cybernetics