## On The Non-Real Nature of x.0 (x in R*): The Set of Null Imaginary Numbers

**Authors:** Saulo Jorge

In this work I axiomatize the result of $x \cdot 0$ ($x\in\real_{\ne 0}$) as a number $\inull(x)$ that has a null real part (denoted as $\Re(\inull(x))=0$) but that is not real. This implies that $y+\Re(\inull(x)) = y$ but $y+\inull(x) = y + x\cdot 0 \not=y$, $y\in\real_{\ne 0}$. From this I define the set of null imaginary numbers $\nullset=\{\inull(x)=x\cdot 0|\forall x\in\real_{\ne 0}\}$
and present its elementary algebra taking the axiom of uniqueness as base (i.e., if $x\ne y\Leftrightarrow \inull(x)\ne \inull(y)$).
Under the condition of existence of $\nullset$ I show that division by zero can be defined without causing inconsistencies in elementary algebra.

**Comments:** 7 Pages.

**Download:** **PDF**

### Submission history

[v1] 2018-09-23 23:17:37

[v2] 2018-09-24 10:18:41

[v3] 2018-10-01 16:23:37

[v4] 2018-10-23 08:04:46

[v5] 2019-06-12 14:05:41

**Unique-IP document downloads:** 57 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.*

*
*