General Mathematics

A Counterexample to the Universality of Cantor's Diagonal Argument Within Actual Infinity

Authors: Kesan Yi

This paper re-examines the logical foundations of Cantor's diagonal argument. By constructing a countable set S that includes a transfinite limit element under the framework of actual infinity, we demonstrate a paradox: a strictly defined sequential ordering leads the diagonal argument to classify a countable set as uncountable. This paper argues that Cantor's proof relies on two critical implicit assumptions: the completed totality of natural numbers and the presumed invariance of the result across all possible permutations. We conclude that the diagonal argument may reflect the limitations of finite indexing rather than the intrinsic cardinality of the set.

Comments: 3 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)

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[v1] 2026-04-25 19:49:33

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