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--- 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. altloc: [] chapter: ~ commentary: ~ commref: ~ confdates: ~ conference: ~ confloc: ~ contact_email: ~ creators_id: [] creators_name: - family: Leon given: Antonio honourific: '' lineage: '' date: 2006-08 date_type: published datestamp: 2008-05-11 02:47:06 department: ~ dir: disk0/00/00/60/43 edit_lock_since: ~ edit_lock_until: ~ edit_lock_user: ~ editors_id: [] editors_name: [] eprint_status: archive eprintid: 6043 fileinfo: /style/images/fileicons/application_pdf.png;/6043/1/TheAlephZeroOrZeroDichotomy.pdf|/style/images/fileicons/application_pdf.png;/6043/2/TheAlephZeroOrZerolDichotomy.pdf full_text_status: public importid: ~ institution: ~ isbn: ~ ispublished: ~ issn: ~ item_issues_comment: [] item_issues_count: 0 item_issues_description: [] item_issues_id: [] item_issues_reported_by: [] item_issues_resolved_by: [] item_issues_status: [] item_issues_timestamp: [] item_issues_type: [] keywords: "Zeno's Dichotomies, w-order, topological successiveness, Axiom of Infinity" lastmod: 2011-03-11 08:57:07 latitude: ~ longitude: ~ metadata_visibility: show note: ~ number: ~ pagerange: ~ pubdom: FALSE publication: ~ publisher: ~ refereed: FALSE referencetext: ~ relation_type: [] relation_uri: [] reportno: ~ rev_number: 23 series: ~ source: ~ status_changed: 2008-05-11 02:47:06 subjects: - phil-sci succeeds: 5094 suggestions: ~ sword_depositor: ~ sword_slug: ~ thesistype: ~ title: The Aleph Zero or Zero Dichotomy type: preprint userid: 5458 volume: ~