Edit: I've actually just figured out the answer to the question I was going to ask, so I no longer require any assistance finding a site to ask it on. I am very thankful for the suggestions I received in the comments, however, as I will now have a better idea of where to go if I have a similar question in the future.  I have recently written a computer algorithm which, at its core, is driven by a well established mathematical function (The Cantor pairing function). I am struggling to develop a functional reversal of my algorithm, and I've come to realize that I do not posses the mathematical or reverse engineering knowledge necessary to solve my problem. This had lead me to seek help on one of the stack exchange sites.  My question involves code, math, and the reverse engineering of an algorithm, which seems to point me in the direction of either  or the  site, but I'm truly not sure where I should go. Any suggestions?
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There seems to be more than a few computer science/programming Stack Exchange networks (is that the correct term?). Stack Overflow, being the first, has by far the most users, questions, and answers.  What is the reasoning for creating the others, and are there clear guidelines for which kinds of questions should be posted? I can see a large amount of potential overflow, many cases of people not getting a good answer to their question, because the person who has the answer isn't browsing that particular network at the moment.  I understand that they were probably created for organizational purposes, but wouldn't it almost make more sense to just have them as categories under Stack Overflow, keep them separated but still connected, instead of making people have to create multiple 'account's, one for each network?  I am sure there was a very good reason to break them up, but as someone that is new to SE, it can be somewhat intimidating to decide which one to post in to ensure you get a good answer. For example, if I am a computer science student, my first instinct might to be to post in the computer science network, until I see that it literally has 1% of the users as the Stack Overflow network, which still seems to be for programming/computer science related questions.  So my second instinct would then to be to post it into the Stack&nbsp;Overflow site on the basis that I have a significantly higher chance of my question being seen and getting a good answer. Then I notice that there is also a 'programmers' network, and I don't even begin to know where that fits in. I, and I am assuming most people, will probably just post on Stack&nbsp;Overflow to be safe.  My question is, other than the short little description blurb of each one, is there a clear cut set of guidelines which what each network is intended for, what kinds of questions should go to each one, and is anything being done to encourage people to post in these newer, smaller (more specialized?) networks as opposed to just posting in big daddy Stack Overflow?  Now again, this is for computer science/programming/"why isn't this code doing what I want?" related questions, I am not saying that if I had a question about Linux or WordPress or something I would have the same confusion.
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In the article  the author claims that he discovered classical algorithm for factoring integers in polynomial time. The Quantum Report mentioned  that it has similar performance to Shor algorithm which is often considered to ignite interest in quantum computers. Of course, the new classical algorithm has to be examined closely before it is confirmed that it is really so fast as claimed. However, I would like to know if there are other quantum algorithms besides Shor and quantum binary optimization based. Has it been proven that Shor algorithm is optimal or could there be another even faster quantum algorithms for integers factoring?
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This is a homework question. But I am completely stuck.  My only intuition was to go about it inductively from a "greedy algorithm" maybe know as the deletion-contraction algorithm. And to somehow use the information about the jth cycle to solve the j+1th. But I'm not sure how I'd do it. Thank you very much for looking this over.
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Could you give me an example of function $ f \colon \mathbb N \to \mathbb Z$ that is both one-to-one and onto? Does this work: $f(n) := n \times (-1)^n$?  N starts with zero.
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Does there exist a good reference on the algorithms used by calculators, especially on the trigonometric and transcendental functions?  I would still like to know how Casio generates its random numbers. I still wonder if they are any good.
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Let $C_k$ be the set obtained in the $k-$th stage of building the Cantor set, where  $$C_1=[0,\frac{1}{3}]\cup[\frac{1}{3},\frac{2}{3}]$$  $$C_2=[0,\frac{1}{9}]\cup[\frac{2}{9},\frac{1}{3}]\cup[\frac{2}{3},\frac{7}{9}]\cup[\frac{8}{9},1]$$  $$\dots$$  So we have   $$C_k=\bigcup_{j=1}^{2^k}I_{k,j}$$  where $I_{k,j}$ are pairwise disjoint closed intervals of length $3^{-k}$ in $[0,1]$, let  $$[0,1]\setminus C_k=\bigcup_{j=1}^{2^k-1}J_{k,j}$$  where $J_{k,j}$ are pairwise disjoint open intervals and each $J_{k,j}$ are located between intervals $I_{k,j},I_{k,j+1}$  define  $$F_k:[0,1]\to[0,1]$$  where  $$F_k(0)=0,F_k(1)=1,F_k(x)=\frac{j}{2^k}\quad x\in J_{k,j}$$  and $F_k$ is linear on each subinterval of $C_k$. We can show that $F_k$ converges to the Cantor function $F:[0,1]\to[0,1]$. Moreover, it can be shown that  $$|F_k(x)-F_k(y)|\leq\frac{3^k}{2^k}|x-y|$$  How can we show that $F$ is Hölder continuous of order $\log_32$ ?
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I know the Solovay-Kitaev algorithm can achieve this. Is there an implementation of this or any other algorithm for the same task in Qiskit? Or perhaps some other library that interfaces well with Qiskit?
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I didn't understand the permutation and of course, I got this question wrong.     Compute the inverse of the following permutation:   $$ \begin{pmatrix}  1&amp;2&amp;3&amp;4&amp;5&amp;6\\ 2&amp;5&amp;4&amp;1&amp;6&amp;3 \end{pmatrix} $$   Could you please help me with this question and provide an explanation?  Furthermore, is it possible to compute the direct permutation, not the inverse one? If yes, how?  Thank you in advance!
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What are the mainstream techniques borrowed from algebraic geometry (or some other branch of mathematics) which are currently used in cryptography/coding theory? I've only heard about a small subset of elliptic curves and hermitian curves. I've also heard about research of hyperelliptic curves but I don't know if some software has already implemented it.  Could you mention some other branches of mathematics being strongly used in cryptography/coding theory and its state? (mainstream/in research)
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I will use binary.  I claim to have a bijection $f \colon \mathcal{N} \to \left[ 0, 1 \right)$ where $\mathcal{N}$ is the set of natural numbers $\left\{ 0, 1, 10, 11, 100, \dotsc \right\}$ as follows:  $$ \begin{array}{l|l} x \in \mathcal{N} &amp; f(x) \in \left[ 0, 1 \right)\\\hline 0 &amp; 0.0 \\ 1 &amp; 0.1 \\ 10 &amp; 0.01 \\ 11 &amp; 0.11 \\ 100 &amp; 0.001 \\ 101 &amp; 0.011 \\ 110 &amp; 0.101 \\ 111 &amp; 0.111 \\ 1000 &amp; 0.0001 \\ \hspace{.6em}\vdots &amp; \hspace{.9em}\vdots \end{array} $$  It's basically the .  I claim to have everything on this list.  Diagonalization?  Go ahead!  Constructing a number that differs from $f(i + 1)$ in its $i$-th fractional digit yields $0.11111\!\ldots = 0.\overline{1}$ which is $1$, and that should not be on the list anyway!  Why does this not work? I think it has something to do with integers supposedly not having infinite digits, while reals supposedly do.
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Recently, I answered to this problem:     Given $a&lt;b\in \mathbb{R}$, find explicitly a bijection $f(x)$ from   $]a,b[$ to $[a,b]$.   using an "iterative construction" (see below the rule).  My question is: is it possible to solve the problem finding a less exotic function?  I mean: I know such a bijection cannot be monotone, nor globally continuous; but my $f(x)$ has a lot of jumps... Hence, can one do without so many discontinuities?    W.l.o.g. assume $a=-1$ and $b=1$ (the general case can be handled by translation and rescaling). Let:  (1) $X_0:=]-1,-\frac{1}{2}] \cup [\frac{1}{2} ,1[$, and  (2) $f_0(x):=\begin{cases}     -x-\frac{3}{2} &amp;\text{, if } -1&lt;x\leq -\frac{1}{2} \\ -x+\frac{3}{2} &amp;\text{,     if } \frac{1}{2}\leq     x&lt;1\\ 0 &amp;\text{, otherwise} \end{cases}$,  so that the graph of $f_0(x)$ is made of two segments (parallel to the line $y=x$) and one segment laying on the $x$ axis; then define by induction:  (3) $X_{n+1}:=\frac{1}{2} X_n$, and  (4) $f_{n+1}(x):= \frac{1}{2} f_n(2 x)$  for $n\in \mathbb{N}$ (hence $X_n=\frac{1}{2^n} X_0$ and $f_n=\frac{1}{2^n} f_0(2^n x)$).  Then the function $f:]-1,1[\to \mathbb{R}$:  (5) $f(x):=\sum_{n=0}^{+\infty} f_n(x)$  is a bijection from $]-1,1[$ to $[-1,1]$.  Proof: i. First of all, note that $\{ X_n\}_{n\in \mathbb{N}}$ is a pairwise disjoint covering of $]-1,1[\setminus \{ 0\}$. Moreover the range of each $f_n(x)$ is $f_n(]-1,1[)=[-\frac{1}{2^n}, -\frac{1}{2^{n+1}}[\cup \{ 0\} \cup ]\frac{1}{2^{n+1}}, \frac{1}{2^n}]$.  ii. Let $x\in ]-1,1[$. If $x=0$, then $f(x)=0$ by (5). If $x\neq 0$, then there exists only one $\nu\in \mathbb{N}$ s.t. $x\in X_\nu$, hence $f(x)=f_\nu (x)$. Therefore $f(x)$ is well defined.  iii. By i and ii, $f(x)\lesseqgtr 0$ for $x\lesseqgtr 0$ and the range of $f(x)$ is:  $f(]-1,1[)=\bigcup_{n\in \mathbb{N}} f(]-1,1[) =[-1,1]$,  therefore $f(x)$ is surjective.  iv. On the other hand, if $x\neq y \in ]-1,1[$, then: if there exists $\nu \in \mathbb{N}$ s.t. $x,y\in X_\nu$, then $f(x)=f_\nu (x)\neq f_\nu (y)=f(y)$ (for $f_\nu (x)$ restrited to $X_\nu$ is injective); if $x\in X_\nu$ and $y\in X_\mu$, then $f(x)=f_\nu (x)\neq f_\mu(y)=f(y)$ (for the restriction of $f_\nu (x)$ to $X_\nu$ and of $f_\mu(x)$ to $X_\mu$ have disjoint ranges); finally if $x=0\neq y$, then $f(x)=0\neq f(y)$ (because of ii). Therefore $f(x)$ is injective, hence a bijection between $]-1,1[$ and $[-1,1]$. $\square$
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In the 70's I had a stack of old Amateur Radio magazines (50s-60s), and for a long time I saved an article about using the  to combine a number of resistors to achieve a specific value. Does anyone recall and have a copy of this article, or know how the Euclidean algorithm is applied to solve this problem?
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If you read enough mathematics, you eventually come across several so-called "special functions". I'm always left wondering what on Earth these things are actually for.  We have the Euler Gamma function, the Beta function, the infamous Riemann zeta function, the Airy functions, the Möbius function, the Bessel functions, the Jacobi theta functions, the digamma and polygamma functions, the polylog, the Chebyshev polynomials, Weierstrass's elliptic functions, the Dedekind eta function, the hypergeometric functions, etc etc etc.  If you try looking any of these functions up, you generally get a huge page of dense, complex-looking formulas recounting the sixteen different ways to define the function, the myriad of properties and identities it has, and so on and so forth. But nowhere does it mention why this is useful.  I have just about figured out that the Euler Gamma function extends the factorial to non-integer values. I still don't know how that's "useful" in some way. Bessel J somehow appears at random in a few unrelated contexts, as do the Chebyshev polynomials. And that's about as far as I've got.  Obviously, I'm not expecting anyone to give an exhaustive explanation of what every single special function ever invented actually does. I suppose that if you don't know what a function does, that means you probably don't need it yet. But I would like to have some basic intuition as to why all these millions of functions have been defined, and what people use them for.
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Can you give a definition of the Conway base-$13$ function better than the one actually presented on , which isn't clear? Maybe with some examples?
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I'm actually in a course of Abstract Algebra, and the teacher asked some interesting questions at the end of a course on the material we had seen. I found the answer to the first question, but the other two leave me perplexed. Could you give me your opinion on the questions (2) and (3)?  (1) Is the function $f : \mathbb{N} \to \mathbb{N} $ such that $$f= \begin{pmatrix} 1 &amp; 2 &amp; 3 &amp; 4 &amp; ...\\ f(1) &amp; f(2) &amp; f(3) &amp; f(4) &amp; ... \end{pmatrix} = \begin{pmatrix} 1 &amp; 2 &amp; 3 &amp; 4 &amp; ...\\ 2 &amp; 3 &amp; 4 &amp; 5 &amp; ... \end{pmatrix}$$ is a permutation? Answer : no, because $1$ isn't an element in the image.  (2) Is there a function $ f \in S_E$  that is factorisable into disjoint cycle of infinite order such that $\mid \{n \in \mathbb{N} : f(n) \not= n\}\mid &lt; \infty$ ?  Definitions :    $S_E$ is the set of all permutation of E.  Let the set $E \not= \emptyset$. W say that a map $f : E \to E$ has an inverse function, if there is a mapping $g : E \to E$ such that both composition $f \circ g$ and $g \circ f$ are the application identity for each $x$ element of $E$. We say that $f$ is a permutation (bijection) of $E$ .    (3) Does the subset of functions $\in S_{\mathbb{N}}$ ($S_E$ with $E=\mathbb{N}$) consistent with $\mid \{n \in \mathbb{N} : f(n) \not= n\}\mid &lt; \infty$ form a group?
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I'm currently doing a research on generating functions, but I have only found few books on this topic. Can anyone provide references (if possible, trying to assess the level of math competence required) on generating functions?   Ideally, what is the context of the referenced book and further details to help to put the book itself in context would be much appreciated.
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I want to find a function $f:[0,1] \to [0,1]$ such that $f$ takes on each value in $[0,1]$ exactly twice. I think this means there are an infinite number of discontinuities. Can anyone help me figure this one out?  Anyone have any pointers?