PR
Keyword Search
▼キーワード検索
再生核研究所
再生核研究所声明
Calendar
Comments
Freepage List
2017.05.16
カテゴリ： カテゴリ未分類
How will be the idea of Brahmagupta (598 -668 ?) ?:
Confusions as in the attached:
The division by zero has a long and mysterious story over the world (see, for example, H. G. Romig \cite{romig} ) with its physical viewpoints since the document of zero in India on AD 628. In particular, note that Brahmagupta (598 -668 ?) established the four arithmetic operations by {\bf introducing $0$ and at the same time he defined as $0/0=0$} in Brāhmasphuṭasiddhānta. Our world history, however, stated that his definition $0/0=0$ is wrong over 1300 years. We will see that his definition is right and suitable.
Indeed, we will show typical examples:
The conditional probability $P(A|B)$ for the probability of $A$ under the condition
that $B$ happens is given by the formula
$$
P(A|B) = \frac{P(A \cap B)}{P(B)}.
$$
If $P(B) = 0$, then, of course, $P(A \cap B) =0$ and $P(A|B) = 0$ and so, $0/0=0$.
For the differential equation
$$
\frac{dy}{dx} = \frac{2y}{x},
$$
we have the general solution with constant $C$
$$
y = Cx^2.
$$
At the origin $(0,0)$ we have
$$
y^{\prime}(0) = \frac{0}{0} =0.
$$
For three points $a,b,c$ on a circle with center at the origin on the complex $z$-plane with radius $R$, we have
$$
|a + b + c| = \frac{|ab + bc + ca|}{R}.
$$
If $R =0$, then $a,b,c =0$ and we have $0=0/0$.
For the second curvature
\begin{equation}
K_2 = \left((x ^{\prime \prime})^2 + (y^{\prime \prime})^2 + (z^{\prime \prime})^2 \right)^{- 1}\cdot
\begin{vmatrix}
x^\prime & y^\prime & z^\prime\\
x ^{\prime \prime}& y^{\prime \prime}& z^{\prime \prime}\\
x^{\prime \prime \prime} & y{\prime \prime \prime}& z{\prime \prime \prime}
\end{vmatrix},
\end{equation}
if $ (x ^{\prime \prime})^2 + (y^{\prime \prime})^2 + (z^{\prime \prime})^2 =0$; that is, when for the case of lines, then $0 = 0/0$.
For the function
sign $x$ $= x/|x|$,
we have, {\bf automatically}, sign $x = 0$ at $x=0$.
We have many and many concrete examples.
The division by zero is uniquely and reasonably determined as 1/0=0/0=z/0=0 in the natural extensions of fractions. We have to change our basic ideas for our space and world
Division by Zero z/0 = 0 in Euclidean Spaces
Hiroshi Michiwaki, Hiroshi Okumura and Saburou Saitoh
International Journal of Mathematics and Computation Vol. 28(2017); Issue 1, 2017), 1
-16.
http://www.scirp.org/journal/alamt http://dx.doi.org/10.4236/alamt.2016.62007
http://www.ijapm.org/show-63-504-1.html
http://www.diogenes.bg/ijam/contents/2014-27-2/9/9.pdf
http://okmr.yamatoblog.net/…/announcement%20326-%20the%20di…
http://okmr.yamatoblog.net/
Relations of 0 and infinity
Hiroshi Okumura, Saburou Saitoh and Tsutomu Matsuura：
http://www.e-jikei.org/…/Camera%20ready%20manuscript_JTSS_A…
Confusions as in the attached:
The division by zero has a long and mysterious story over the world (see, for example, H. G. Romig \cite{romig} ) with its physical viewpoints since the document of zero in India on AD 628. In particular, note that Brahmagupta (598 -668 ?) established the four arithmetic operations by {\bf introducing $0$ and at the same time he defined as $0/0=0$} in Brāhmasphuṭasiddhānta. Our world history, however, stated that his definition $0/0=0$ is wrong over 1300 years. We will see that his definition is right and suitable.
Indeed, we will show typical examples:
The conditional probability $P(A|B)$ for the probability of $A$ under the condition
that $B$ happens is given by the formula
$$
P(A|B) = \frac{P(A \cap B)}{P(B)}.
$$
If $P(B) = 0$, then, of course, $P(A \cap B) =0$ and $P(A|B) = 0$ and so, $0/0=0$.
For the differential equation
$$
\frac{dy}{dx} = \frac{2y}{x},
$$
we have the general solution with constant $C$
$$
y = Cx^2.
$$
At the origin $(0,0)$ we have
$$
y^{\prime}(0) = \frac{0}{0} =0.
$$
For three points $a,b,c$ on a circle with center at the origin on the complex $z$-plane with radius $R$, we have
$$
|a + b + c| = \frac{|ab + bc + ca|}{R}.
$$
If $R =0$, then $a,b,c =0$ and we have $0=0/0$.
For the second curvature
\begin{equation}
K_2 = \left((x ^{\prime \prime})^2 + (y^{\prime \prime})^2 + (z^{\prime \prime})^2 \right)^{- 1}\cdot
\begin{vmatrix}
x^\prime & y^\prime & z^\prime\\
x ^{\prime \prime}& y^{\prime \prime}& z^{\prime \prime}\\
x^{\prime \prime \prime} & y{\prime \prime \prime}& z{\prime \prime \prime}
\end{vmatrix},
\end{equation}
if $ (x ^{\prime \prime})^2 + (y^{\prime \prime})^2 + (z^{\prime \prime})^2 =0$; that is, when for the case of lines, then $0 = 0/0$.
For the function
sign $x$ $= x/|x|$,
we have, {\bf automatically}, sign $x = 0$ at $x=0$.
We have many and many concrete examples.
The division by zero is uniquely and reasonably determined as 1/0=0/0=z/0=0 in the natural extensions of fractions. We have to change our basic ideas for our space and world
Division by Zero z/0 = 0 in Euclidean Spaces
Hiroshi Michiwaki, Hiroshi Okumura and Saburou Saitoh
International Journal of Mathematics and Computation Vol. 28(2017); Issue 1, 2017), 1
-16.
http://www.scirp.org/journal/alamt http://dx.doi.org/10.4236/alamt.2016.62007
http://www.ijapm.org/show-63-504-1.html
http://www.diogenes.bg/ijam/contents/2014-27-2/9/9.pdf
http://okmr.yamatoblog.net/…/announcement%20326-%20the%20di…
http://okmr.yamatoblog.net/
Relations of 0 and infinity
Hiroshi Okumura, Saburou Saitoh and Tsutomu Matsuura：
http://www.e-jikei.org/…/Camera%20ready%20manuscript_JTSS_A…
お気に入りの記事を「いいね！」で応援しよう
Last updated
2017.05.16 05:47:17
【毎日開催】
15記事にいいね！で1ポイント
© Rakuten Group, Inc.
