The Aleph-zero or zero dichotomy

TL;DR

This paper explores a topological dichotomy related to w-order that results in paradoxical conclusions similar to Zeno's Dichotomy, highlighting inherent contradictions in such logical structures.

Contribution

It introduces a new dichotomy derived from topological successiveness of w-order and demonstrates its paradoxical implications.

Findings

Derives a contradiction from the first Zeno's Dichotomy

Establishes a dichotomy based on topological successiveness of w-order

Shows the resulting paradoxes are similar to Zeno's Dichotomy II

Abstract

This paper proves the existence of a dichotomy which being formally derived from the topological successiveness of w-order leads to the same absurdity of Zeno's Dichotomy II. It also derives a contradictory result from the first Zeno's Dichotomy.