## A New Axiom for ZFC Set Theory that Results in a Problem

**Authors:** Andew Banks

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

**Comments:** 5 Pages.

**Download:** **PDF**

### Submission history

[v1] 2017-09-26 10:31:21

**Unique-IP document downloads:** 32 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary.
In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution.
Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*