[1] **viXra:1203.0101 [pdf]**
*submitted on 2012-03-28 18:07:22*

**Authors:** Andrew Banks

**Comments:** 9 Pages.

The debate between process infinity and Cantor’s eigentlich Unendliche “completed infinity” has occurred since before Greek times. Prior to Cantor, the prevailing view of infinity was that it is a process that continues on forever and there is only one type of infinity. Cantor, on the other hand, produced the current foundations of mathematics with his hierarchy of completed infinite objects. In particular, the completed infinite set ω contains all natural numbers and none are missing from the set. This paper will demonstrate, however, a specific method under ZFC of assembling all finite ordinals into the completed set ω such that ω ε ω is a necessary condition of that formation. Then, from ω ε ω, it will be shown ZFC is inconsistent.

**Category:** Set Theory and Logic