General Mathematics

The Collapse of Recursive Logic: A Critique of Actual Infinity via the Fixed-Point Singularity of Sequence S

Authors: Kesan Yi

This paper presents a logical critique of the concept of Actual Infinity by analyzing a specific recursive sequence S. By examining the algebraic properties of the limit as a potential member of the set, we demonstrate that the transition from a generative process to a "completed" state results in a fixed-point singularity. This singularity destroys the bidirectional logic of succession and traceability, suggesting that the notion of a completed infinite set is structurally incompatible with the recursive definitions that govern countable sets.

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[v1] 2026-05-11 19:28:52

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