Authors: Andew Banks
Comments: 5 Pages.
This article adds a new axiom to ZFC that assumes there is a set x which is initially the empty set and thereafter the successor function (S) is instantly applied once in-place to x at each time interval (½ⁿ n>0) in seconds. Next, a very simple question is proposed to ZFC. What is x after one second elapses?
By definition, each time S is applied in-place to x, a new element is inserted into x. So, given that S is applied at each time interval (½ⁿ n>0) then an infinite collection of elements is added to x so, x is countable infinite. On the other hand, since x begins as the empty set and only S is applied to x then x cannot be anything other than a finite natural number. Hence, x is finite. Clearly, in-place counting according to the interval timings (½ⁿ n>0) demonstrates a problem in ZFC
Category: Set Theory and Logic