User talk:Musictheory2math

$Edge$ $of$ $Darkness$ (Painting theory)

Nanas lemma: If $\mathbb{P}$ is the set of prime numbers and $S$ is a set that has been made as below: Put a point on the beginning of each member of $\Bbb{P}$ like $0.2$ or $0.19$ then $S=\{0.2,0.3,0.5,0.7,...\}$ is dense in the interval $(0.1,1)$ of real numbers.$($Nanas is my parrot and I like it so much.$)$

This lemma is a base for finding formula of prime numbers.

There is a musical note on natural numbers that can be discovered by the formula of prime numbers.Alireza Badali 22:21, 8 May 2017 (CEST)

True, $S$ is dense in the interval $(0.1,1)$; this fact follows easily from well-known results on Distribution of prime numbers. But I doubt that this is "This lemma is a base for finding formula of prime numbers". Boris Tsirelson (talk) 22:10, 16 March 2017 (CET)

Dear Professor Boris Tsirelson , in principle finding formula of prime numbers is very lengthy. and I am not sure be able for it but please give me few time about two month for expression my theories.Alireza Badali 22:21, 8 May 2017 (CEST)

You mean, how to prove that $S$ is dense in $(0.1,1)$, right? Well, on the page "Distribution of prime numbers", in Section 6 "The difference between prime numbers", we have $ d_n \ll p_n^\delta $, where $p_n$ is the $n$-th prime number, and $ d_n = p_{n+1}-p_n $ is the difference between adjacent prime numbers; this relation holds for all $ \delta > \frac{7}{12} $; in particular, taking $ \delta = 1 $ we get $ d_n \ll p_n $, that is, $ \frac{d_n}{p_n} \to 0 $ (as $ n \to \infty $), or equivalently, $ \frac{p_{n+1}}{p_n} \to 1 $. Now, your set $S$ consists of numbers $ s_n = 10^{-k} p_n $ for all $k$ and $n$ such that $ 10^{k-1} < p_n < 10^k $. Assume that $S$ is not dense in $(0.1,1).$ Take $a$ and $b$ such that $ 0.1 < a < b < 1 $ and $ s_n \notin (a,b) $ for all $n$; that is, no $p_n$ belongs to the set \[ X = (10a,10b) \cup (100a,100b) \cup (1000a,1000b) \cup \dots \, ; \] all $ p_n $ belong to its complement \[ Y = (0,\infty) \setminus X = (0,10a] \cup [10b,100a] \cup [100b,1000a] \cup \dots \] Using the relation $ \frac{p_{n+1}}{p_n} \to 1 $ we take $N$ such that $ \frac{p_{n+1}}{p_n} < \frac b a $ for all $n>N$. Now, all numbers $p_n$ for $n>N$ must belong to a single interval $ [10^{k-1} b, 10^k a] $, since it cannot happen that $ p_n \le 10^k a $ and $ p_{n+1} \ge 10^k b $ (and $n>N$). We get a contradiction: $ p_n \to \infty $ but $ p_n \le 10^k a $. And again, please sign your messages (on talk pages) with four tildas: ~~~~. Boris Tsirelson (talk) 20:57, 18 March 2017 (CET)

'I have special thanks to Professor Boris Tsirelson for this beauty proof. Sincerely yours, Alireza Badali Sarebangholi'

Theorem $1$: For each natural number like $a=a_1a_2a_3...a_k$ that $a_j$ is j_th digit in the decimal system there is a natural number like $b=b_1b_2b_3...b_r$ such that the number $c=a_1a_2a_3...a_kb_1b_2b_3...b_r$ is a prime number.Alireza Badali 22:21, 8 May 2017 (CEST)

Ah, yes, I see, this follows easily from the fact that $S$ is dense. Sounds good. Though, decimal digits are of little interest in the number theory. (I think so; but I am not an expert in the number theory.) Boris Tsirelson (talk) 11:16, 19 March 2017 (CET)

Now, assume $H$ is a mapping from $(0.1,1)$ on $(0.1,1)$ given by $H(x)=1/(10x)$.

Let $T=H(S)$, $T$ is a interesting set for its members because of, a member of $S$ like $0.a_1a_2a_3...a_n$ that $a_j$ is j-th its digit in the decimal system for $j=1,2,3, ... ,n$ is basically different with ${a_1.a_2a_3a_4...a_n}^{-1}$ in $T$.

Theorem: $T$ is dense in the $(0.1,1)$.Alireza Badali 13:49, 17 May 2017 (CEST)

"Theorem: T=H(P) that P is the set of prime numbers is dense in the (0.1 , 1)." — I guess you mean H(S), not H(P). Well, this is just a special case of a simple topological fact (no number theory needed): A is dense if and only if H(A) is dense (just because H is a homeomorphism). Boris Tsirelson (talk) 18:53, 25 March 2017 (CET)

Let $D=\mathbb{Q} \cap (0.1,1)$

Dear Professor Boris Tsirelson, your help is very valuable to me and I think we can make a good paper together of course if you would like.Alireza Badali 22:21, 8 May 2017 (CEST)

Thank you for the compliment and the invitation, but no, I do not. Till now we did not write here anything really new in mathematics. Rather, simple exercises. Boris Tsirelson (talk) 18:50, 27 March 2017 (CEST)

But do not you think this way about prime numbers is new and for the first time.Alireza Badali 22:21, 8 May 2017 (CEST)

It is not enough to say that this way is new. The question is, does this way give new interesting results? Boris Tsirelson (talk) 21:03, 30 March 2017 (CEST)

Dear Professor Boris Tsirelson, I thank you so much for your valuable help to me and I owe you because more than $10$ years I could not prove the Nanas lemma, but you proved it seemly and guided me honestly that in principle you gave me a new hope to continue.

Assume $S_1$={ $a/10^n$ | $a\in{S}$ for $n$=$0,1,2,3,...$ } & $T_1$={ $a/10^n$ | $a\in{T}$ for $n=0,1,2,3,...$ }.

Theorem: $S_1$ and also $T_1$ are dense in the interval $(0,1)$. Proof by the Axiom of Choice and the Nanas lemma.

Assume $T_1$ is the dual of $S_1$ so the combine of both $T_1$ and $S_1$ make us so stronger.

Let $W$={ $±(z+a)$ | $a\in{S_1 \cup T_1}$ for $z=0,1,2,3,...$ } & $G=\mathbb{Q} \setminus W$

Theorem $2$: $W$ and also $G$ are dense in the $\mathbb{Q}$ and also $\mathbb{R}$.

Conjecture: For each member of $G$ like $g$, there are two members of $W$ like $a,b$ in the interval $(g-0.5,g+0.5)$ such that $g=(a+b)/2$.

Of course it is enough that the conjecture just is proved for the interval $(0,1)$ namely assume $g\in{(0,1) \cap {G}}$.

Therefore if a continuous mapping from $D$ on $S$ is found, we must make some topological spaces by the Euclidean topology, into the $(0.1,1)×(0.1,1)$ of Euclidean page such that some topological properties particularly around the sequences is transferred to the set $S$. And now I must say that the formula of prime numbers is equal to an unique painting in the $(0.1,1)×(0.1,1)$.

Alireza Badali 22:21, 8 May 2017 (CEST)

About Painting theory

Theorem: $S×S$ is dense in the $(0.1,1)×(0.1,1)$. Similar theorems are right for $S×T$ & $T×T$.Alireza Badali 13:49, 17 May 2017 (CEST)

"Theorem: C=S×S is dense in the (0.1 , 1)×(0.1 , 1) similar theorems is right for C=S×T and C=T×S and C=T×T." — This is also a special case of a simple topological fact: $A\times B$ is dense if and only if $A$ and $B$ are dense. Boris Tsirelson (talk) 18:53, 25 March 2017 (CET)

Theorem: $D$ and $S$ are homeomorph by the Euclidean topology.

For each member of $D$ like $w=0.a_1a_2a_3...a_ka_{k+1}a_{k+2}...a_{n-1}a_na_{k+1}a_{k+2}...a_{n-1}a_n...$ that $a_{k+1}a_{k+2}...a_{n-1}a_n$ repeats and $k=0,1,2,3,...,n$ , assume $t=a_1a_2a_3...a_ka_{k+1}...a_n00...00$ is a natural number such that $k$ up to $0$ is inserted on the beginning of $t$ , now by the induction axiom and theorem 1 , there is the least number in the natural numbers like $b_1b_2...b_r$ such that the number $a_1a_2a_3...a_ka_{k+1}...a_{n}00...00b_1b_2...b_r$ is a prime number and so $0.a_1a_2a_3...a_ka_{k+1}...a_{n}00...00b_1b_2...b_r\in{S}$.♥ But there is a big problem, where is the rule of this homeomorphism.

Theorem: $D$ and $T$ are homeomorph by the Euclidean topology.

An important question: Is there any real infinite subset of $S$ such that it is dense in the interval $(0.1,1)$ of real numbers?

Assuming $P_1$={ $p$ | $p$ is a prime number & number of digits of $p$ is a prime number } that $P_1$ is called the set of primer numbers, now whether $P_1$ is dense in the $(0.1,1)'"`UNIQ-MathJax2-QINU`"'f(t)=\begin{cases} 2t\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,t\lt 0.5 \\0.2t\,\,\,\,\,\,\,\,\,\,\,\,\,\,t\gt 0.5 \\0.5\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,t=.05 \end{cases}$$

Assuming correctness the new version of Goldbach`s conjecture, it is a way for finding formula of prime numbers, because it explains behavior of prime numbers, and a discussion about A new version of Goldbach`s conjecture is started here.

Alireza Badali 23:51, 11 May 2017 (CEST)

"On the co(girth) of a connected matroid"

Strangely, I see three authors of that work: Jung Jin Cho, Yong Chen, Yu Ding (rather than Alireza Badali). But you wrote it is your thesis. Do I misunderstand something? Boris Tsirelson (talk) 16:10, 19 May 2017 (CEST)

Dear Professor Boris Tsirelson, my mean was this that I have worked on this paper as a thesis only, of course I have not written it, my English is so weak, okay I must edit it, and I thank you for this right point.Alireza Badali 17:45, 19 May 2017 (CEST)