The purpose of this site is to publish announcements on the theory of division by zero

Institute of Reproducing Kernels

Kawauchi-cho, 5-1648-16,

Kiryu 376-0041, Japan

August 21, 2017For this fundamental idea, we should consider the

\begin{equation}

\omega_0 = \exp \left(\frac{\pi}{0}i\right)=1, \quad \frac{\pi}{0} =0.

\end{equation}

For the mean value

$$

M_n = \frac{x_1 + x_2 +... + x_n}{n},

$$

we have

$$

M_0 = 0 = \frac{0}{0}.

$$

4 Fruitful world

5 From $0$ to $0$; $0$ means all and all are $0$

6 Impossibility

\begin{equation}\tag{6.1}

ax =b

\end{equation}we have $x=0$ for $a=0, b\ne 0$ as the standard value, or the Moore-Penrose generalized inverse. This will mean in a sense, the solution does not exist; to solve the equation $($6.1$)$ is impossible. We saw for different parallel lines or different parallel planes, their common points are the origin. Certainly they have the common points of the point at infinity and the point at infinity is represented by zero. However, we can understand also that they have no solutions, no common points, because the point at infinity is an ideal point.

\begin{equation}

m\frac{d^2x}{dt^2} =0, m\frac{d^2y}{dt^2} =-mg

\end{equation}

with the initial conditions, at $t =0$

\begin{equation}

\frac{dx}{dt} = v_0 \cos \alpha , \frac{d^2x}{dt^2} = \frac{d^2y}{dt^2}=0.

\end{equation}Then, the highest high $h$, arriving time $t$, the distance $d$ from the starting point at the origin to the point $y(2t) =0$ are given by

\begin{equation}

h = \frac{v_0 \sin^2 \alpha}{2g}, d= \frac{v_0\sin \alpha}{g}

\end{equation}and

\begin{equation}

t= \frac{v_0 \sin \alpha}{g}.

\end{equation}

For the case $g=0$, we have $h=d =t=0$. We considered the case that they are the infinity; however, our mathematics means zero, which shows impossibility.

These phenomena were looked many cases on the universe; it seems that

[11] Announcement 185 $($2014.10.22$)$: The importance of the division by zero $z/0=0$.

[12] Announcement 237 $($2015.6.18$)$: A reality of the division by zero $z/0=0$ by geometrical optics.

[13] Announcement 246 $($2015.9.17$)$: An interpretation of the division by zero $1/0=0$ by the gradients of lines.

[14] Announcement 247 $($2015.9.22$)$: The gradient of y-axis is zero and $\tan (\pi/2) =0$ by the division by zero $1/0=0$.

[15] Announcement 250 $($2015.10.20$)$: What are numbers? - the Yamada field containing the division by zero $z/0=0$.

[16] Announcement 252 $($2015.11.1$)$: Circles and curvature - an interpretation by Mr. Hiroshi Michiwaki of the division by zero $r/0 = 0$.

[17] Announcement 281 $($2016.2.1$)$: The importance of the division by zero $z/0=0$.

[18] Announcement 282 $($2016.2.2$)$: The Division by Zero $z/0=0$ on the Second Birthday.

[19] Announcement 293 $($2016.3.27$)$: Parallel lines on the Euclidean plane from the viewpoint of division by zero 1/0=0.

[20] Announcement 300 $($2016.05.22$)$: New challenges on the division by zero z/0=0.

[21] Announcement 326 $($2016.10.17$)$: The division by zero z/0=0 - its impact to human beings through education and research.

[22] Announcement 352 $($2017.2.2$)$: On the third birthday of the division by zero z/0=0.

[23] Announcement 354 $($2017.2.8$)$: What are $n = 2,1,0$ regular polygons inscribed in a disc? -- relations of $0$ and infinity.

[24] Announcement 362$($2017.5.5$)$: Discovery of the division by zero as $0/0=1/0=z/0=0$.

PR