Collatz - Historia wersji

AndrzejSalwicki o 08:16, 2 kwi 2026

2026-04-02T08:16:39Z

AndrzejSalwicki o 08:12, 2 kwi 2026

2026-04-02T08:12:58Z

AndrzejSalwicki o 08:07, 2 kwi 2026

2026-04-02T08:07:08Z

AndrzejSalwicki o 08:05, 2 kwi 2026

2026-04-02T08:05:09Z

AndrzejSalwicki o 08:01, 2 kwi 2026

2026-04-02T08:01:38Z

AndrzejSalwicki o 07:57, 2 kwi 2026

2026-04-02T07:57:54Z

AndrzejSalwicki o 07:52, 2 kwi 2026

2026-04-02T07:52:35Z

AndrzejSalwicki o 15:44, 30 mar 2026

2026-03-30T15:44:56Z

AndrzejSalwicki o 15:42, 30 mar 2026

2026-03-30T15:42:40Z

AndrzejSalwicki o 15:41, 30 mar 2026

2026-03-30T15:41:10Z

@@ Linia 41: / Linia 41: @@
 					\end{array}\right\rbrace(m=1)} }_{ {the\ computation\   for\ n\ is\ finite} }  \qquad (H)
 </math>   <br />
-   or by another, equivalent formula <br />
+   or by another, equivalent formula with iteration quantifier instead of  '''while''' <br />
-  <math> \qquad  	\underbrace{\boxed{\left\lbrace \begin{array}{l}
-						\{m:=n \div 2^{\kappa(n)} \} \bigcp \left\lbrace \begin{array}{l}
-						\mathbf{if}\ m \neq 1 \\
-						 \mathbf{then}  \\
-						\quad m:=3 \cdot m +1;  \\
-						\quad m:= m \div 2^{\kappa(m)}  \\
-						\mathbf{fi} 	\end{array}\right\rbrace
-					\end{array}\right\rbrace(m=1)} }_{ {the\ computation\   for\ n\ is\ finite} }  \qquad (H)
-</math>   <br />
-−
 There is no finite, traditional proof the following  theorem . <br/>
 <math> \begin{array}{p{14cm}}

@@ Linia 43: / Linia 43: @@
    or by another, equivalent formula <br />
    <math> \qquad  	\underbrace{\boxed{\left\lbrace \begin{array}{l}
-						\{ m:=n \div 2^{\kappa(n)}  \} \bigcup \left\lbrace \begin{array}{l}
+						\{m:=n \div 2^{\kappa(n)} \} \bigcp \left\lbrace \begin{array}{l}
 						\mathbf{if}\ m \neq 1 \\
 						 \mathbf{then}  \\
 						\quad m:=3 \cdot m +1;  \\
 						\quad m:= m \div 2^{\kappa(m)}  \\
 						\mathbf{fi} 	\end{array}\right\rbrace
 					\end{array}\right\rbrace(m=1)} }_{ {the\ computation\   for\ n\ is\ finite} }  \qquad (H)
-</math>
+</math>   <br />
 There is no finite, traditional proof the following  theorem . <br/>

@@ Linia 42: / Linia 42: @@
 </math>   <br />
    or by another, equivalent formula <br />
-   <math> \qquad  	\underbrace{\boxed{\left\lbracket \begin{array}{l}
+   <math> \qquad  	\underbrace{\boxed{\left\lbrace \begin{array}{l}
 						\{ m:=n \div 2^{\kappa(n)}  \} \bigcup \left\lbrace \begin{array}{l}
 						\mathbf{if}\ m \neq 1 \\
@@ Linia 48: / Linia 48: @@
 						\quad m:=3 \cdot m +1;  \\
 						\quad m:= m \div 2^{\kappa(m)}  \\
-						\mathbf{fi} 	\end{array}\right\rbracket
+						\mathbf{fi} 	\end{array}\right\rbrace
 					\end{array}\right\rbrace(m=1)} }_{ {the\ computation\   for\ n\ is\ finite} }  \qquad (H)
 </math>

@@ Linia 42: / Linia 42: @@
 </math>   <br />
    or by another, equivalent formula <br />
-   <math> \qquad  	\underbrace{\boxed{\left( \begin{array}{l}
+   <math> \qquad  	\underbrace{\boxed{\left\lbracket \begin{array}{l}
 						\{ m:=n \div 2^{\kappa(n)}  \} \bigcup \left\lbrace \begin{array}{l}
 						\mathbf{if}\ m \neq 1 \\
@@ Linia 48: / Linia 48: @@
 						\quad m:=3 \cdot m +1;  \\
 						\quad m:= m \div 2^{\kappa(m)}  \\
-						\mathbf{fi} 	\end{array}\right)
+						\mathbf{fi} 	\end{array}\right\rbracket
 					\end{array}\right\rbrace(m=1)} }_{ {the\ computation\   for\ n\ is\ finite} }  \qquad (H)
 </math>

@@ Linia 40: / Linia 40: @@
 						\mathbf{od}
 					\end{array}\right\rbrace(m=1)} }_{ {the\ computation\   for\ n\ is\ finite} }  \qquad (H)
-</math>   or <math> \qquad  	\underbrace{\boxed{\left\lbrace \begin{array}{l}
+</math>   <br />
 						\{ m:=n \div 2^{\kappa(n)}  \} \bigcup \left\lbrace \begin{array}{l}
 						\mathbf{if}\ m \neq 1 \\
@@ Linia 46: / Linia 48: @@
 						\quad m:=3 \cdot m +1;  \\
 						\quad m:= m \div 2^{\kappa(m)}  \\
-						\mathbf{fi} 	\end{array}\right\rbrace
+						\mathbf{fi} 	\end{array}\right)
 					\end{array}\right\rbrace(m=1)} }_{ {the\ computation\   for\ n\ is\ finite} }  \qquad (H)
 </math>

@@ Linia 34: / Linia 34: @@
 <math> \qquad  	\underbrace{\boxed{\left\lbrace \begin{array}{l}
 						m:=n \div 2^{\kappa(n)}; \\
 						\mathbf{while}\ m \neq 1 \\
 						 \mathbf{do}  \\

@@ Linia 4: / Linia 4: @@
 Oto wersja złożona do druku [https://lem12.uksw.edu.pl/images/6/69/CollatzConjecturebecomesTheorem2026-03-15.pdf]<br /><br />
 I odrzucona. <br />
-Artykuł złożono 15 marca 2026.<br />
+Artykuł złożono '''15 marca 2026'''.<br />
 Redaktor naczeelny wyznaczył redaktora odpowiedzialnego za zasiegniecie opinii i podjęcie decyzji 16 marca o godzinie 20:52.<br />
-Redaktor odpowiedzialny podjął decyzję 17 marca 2026 o godzinie 12:17.<br />
+Redaktor odpowiedzialny podjął decyzję '''17 marca 2026 o godzinie 12:17'''.<br />
 Oto cała recenzja i decyzja<br />
-''Unfortunately, we cannot accept it for publication.  The paper belongs to computer science and not mathematics.
+''Unfortunately, we cannot accept it for publication.  The paper belongs to computer science and not mathematics. So the proper venue for its publication should be a computer science journal. It seems to me that the bare argument for the Collatz conjecture presented in your paper is not very complicated (this does not mean that I verified it). Why not extract it, omitting the programming jargon? Then it would be more accessible to mathematicians.''
- So the proper venue for its publication should be a computer science journal. It seems to me that the bare argument for the Collatz conjecture presented in your paper is not very complicated (this does not mean that I verified it). Why not extract it, omitting the programming jargon? Then it would be more accessible to mathematicians.''
 <br />