# Set Theory and Logic

## 1709 Submissions

[2] **viXra:1709.0391 [pdf]**
*submitted on 2017-09-26 10:31:21*

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

**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

[1] **viXra:1709.0076 [pdf]**
*submitted on 2017-09-07 11:08:35*

### P Versus Np's Answer.

**Authors:** Gokulakannan.P

**Comments:** 2 Pages. Please, leave comments below. For further enquiries, mail @ sbsp181107@gmail.com .

Always think simple to answer a question which is being seem tough.

**Category:** Set Theory and Logic