Is Ubuntu Touch support available for porting to latest devices that runs Android L or Android M? To run Ubuntu touch on Android devices, some of the components from Android are required (E.g, Modified kernel to support Ubuntu Touch, Android HAL, drivers etc.) The initial Ubuntu Touch port for the list of compatible devices were based on Kitkat.  Is there a working Ubuntu Touch port available for the latest Android devices that runs Android L or Android M? What level of support available from Ubuntu Touch for porting the components (modified kernel, HAL, drivers based on Android L or M) to these devices?
With the announcement of the Ubuntu Phone OS I'd like to know what phone (and tablet) models are supported at this time.  Note from foss &amp; Oli: We are making this the master question for all future "Will this work on &lt;insert random tablet/phone/device here&gt;?!" questions
Prove that any two nontrivial subgroups of $\mathbb{Q}$ have nontrivial intersection I need to prove that any two nontrivial subgroups of $\mathbb{Q}$ have a nontrivial intersection as part of a larger proof that $\mathbb{Q}$ cannot be represented as a nontrivial direct product.    (Yes, I realize that there are other ways to prove that $\mathbb{Q}$ cannot be represented as a nontrivial direct product, but I am not interested in those, and will not accept answers showing me how to do that).  Based on the density of the rationals, I guess this idea kind of makes sense, but I am doing this proof for an abstract algebra class, and I don't think real analysis proofs would be accepted.   Everywhere I've looked online has said this is "trivial" or "easy to see" without bothering to actually prove it for those of us mere mortals who don't see it as such. As for myself, I have literally no idea where to even get started proving this. Could somebody help me figure this out (without giving me cutesy examples that aren't really all that related with the expectation that I should be able to figure it out from looking at those - that's not really how my brain works)?  Thank you. How can I download an older version of Xcode? I am trying to download Xcode from the App Store, but it says that I have to have a newer version of macOS. But I don't have enough space on my computer to upgrade. Its like 8 gigs or something like that and if I only could download Xcode that was compatible with macOS Sierra that would be nice. Are we discouraged from fixing typos and misspellings on Stack Exchange sites? I just attempted to fix a typo on a question on cooking.stackexchange.com and saw this     Oops! Your edit couldn't be submitted because:         Your edit summary must be at least 10 characters   This edit is less than 6 characters; surely more can be improved with your edit?      So, misspelled words have to just be left misspelled?  That could prevent the post from being found in a search. How to delete entry in Auto Complete in Microsoft Edge How do I delete an unwanted entry in AutoComplete in Microsoft Edge?  I have tried everything including highlighting with the down arrows and nothing works. I understand how to define include shared objects at linking/compile time. However, I still wonder how do executables look for the shared object (*.so libraries) at execution time.  For instance, my app a.out calls functions defined in the lib.so library. After compiling, I move lib.so to a new directory in my $HOME.  How can I tell a.out to go look for it there? Prove Inverses not need be Unique if Associativity fails Let $M=\{x, y, z\}$ be a set and let $\circ$ be a binary operation on $M$ such that the identity element is $x$ and $y \circ y = x = y \circ z$. Prove that inverses need not be unique if associativity fails given the multiplication table below.  $x \circ x = x, x \circ y = y, x \circ z = z$  $y \circ x = y, y \circ y = x, y \circ z = x$  $z \circ x = z, z \circ y = x, z \circ z = x$ Is this notification that keeps coming up on my phone a virus? This notification keeps coming up, and i'm not sure if it's real or a virus, or how to stop it coming up. It says 'Android system warning! Google has found serious bugs in your Battery Module!Click on [OK] to view details.'   Screenshot (click for larger variant)  Any help appreciated, thanks. Lauren. Where is the default folder for Apps? I am relatively new to the linux world. I use OSX at home and Windows at work. In those worlds, there is a default folder for applications (C:\Program Files, /Applications). Is there any such directory in Ubuntu?   I understand that this is not very important and any location in the file system should be ok, but was just wondering whether there are such standard locations (I think there would be one). For instance where is Firefox or Libre Office (that are installed by default)?  Got this question when I was trying to install eclipse. Downloaded the zip, and was wondering... How to prove $A+ A^T$ symmetric, $A-A^T$ skew-symmetric. Distribution of a ratio of uniforms: What is wrong? Suppose that  $X$ and $Y$ are two i.i.d. uniform random variables on the interval $[0,1]$  Let $Z=X/Y$, I am finding the cdf of $Z$, i.e. $ \Pr(Z\leq z) $.  Now, I came up with two ways of doing this. One produces a correct answer consistent with the pdf here: , the other does not. Why is the second method wrong?  First Method  $\newcommand{\rd}{\mathrm{d}} \Pr(Z\leq z) = \Pr(X/Y\leq z) = \Pr(X\leq zY) = \int^{1}_{0}\int^{\min(1,zy)}_{0} \rd x \rd y = \int^{1}_{0}\min(1,zy)\ \rd y$ $  = \left\{      \begin{array}{lr}        \int^{1/z}_{0}zy\ \rd y + \int^{1}_{1/z} \rd y&amp; : z &gt; 1\\        \int^{1}_{0}zy\ \rd y &amp; : z \leq 1      \end{array}    \right. $ $  = \left\{      \begin{array}{lr}        1 - \frac{1}{2z} &amp; : z &gt; 1\\        \frac{z}{2} &amp; : z \leq 1      \end{array}    \right. $  This appears correct.  Second Method  $\Pr(X/Y\leq z) = \Pr(X \leq zY\ |\ zY \geq 1)\Pr(zY \geq 1) + \Pr(X \leq zY\ |\ zY &lt; 1)\Pr(zY &lt; 1) $ by total probability  $ = \Pr(X \leq zY\ |\ zY \geq 1)\Pr(Y \geq 1/z) + \Pr(X \leq zY\ |\ zY &lt; 1)\Pr(Y &lt; 1/z)$  Taking $z&gt;1$ yields $ (1)(1-\frac{1}{z}) + (\int^{1/z}_{0}\int^{zy}_{0} \rd x \rd y)(\frac{1}{z}) = 1-\frac{1}{z} + (\int^{1/z}_{0}zy\ \rd y)(\frac{1}{z}) = 1-\frac{1}{z} + \frac{1}{2z^{2}}$  This is already different. Why is this wrong?  Thanks! Why is the voltage across a capacitor and the current across an inductor continuous? Why is the voltage across a capacitor (as a function of time) continuous? Why is the current across an inductor (as a function of time) continuous? Simulating draws from a Uniform Distribution using draws from a Normal Distribution I recently purchased a  in which one of the probability questions was as follows:     Given draws from a normal distribution with known parameters, how can you simulate draws from a uniform distribution?   My original thought process was that, for a discrete random variable, we could break the normal distribution into K unique subsections where each subsection has an equal area under the normal curve. Then we could determine which of K values the variable takes by recognizing which area of the normal curve the variable ends up falling into.   But this would only work for discrete random variables. I did some research into how we might do the same for continuous random variables, but unfortunately I could only find techniques like inverse transform sampling that would use as input a uniform random variable, and could output random variables from some other distribution. I was thinking that perhaps we could do this process in reverse to get uniform random variables?  I also thought about possibly using the Normal random variables as inputs into a linear congruential generator, but I'm not sure if this would work.  Any thoughts on how I might approach this question? Reputation misaligned in new topbar In the sites dropdown, the reputation scores are misaligned:    This seems to happen only on Firefox (56.0), both on macOS (10.13) and Windows (7, 10) (thanks @Tom and @MonicaCellio). I've tested a couple of other browsers which do not have this problem. I've already cleared my cache. A matrix and its transpose have the same set of eigenvalues/other version: $A$ and $A^T$ have the same spectrum In Section 9 of Chapter 6, Lang constructrs for the first time a non-abelian extension as a splitting field $K$ of $X^n - a$ when the ground field $k$ does not contain primitive $n$-th roots of unity $\zeta_n$. He constructs an injective homomorphism of the Galois group $G(K/k)$ into the matrices of type   $$ M=\begin{pmatrix} 1 &amp; 0 \\ b &amp; d \end{pmatrix} \quad \hbox{with}\ b\in \mathbb{Z}/n\mathbb{Z} \quad \hbox{and} \quad d\in (\mathbb{Z}/n\mathbb{Z})^*,$$  where $(\mathbb{Z}/n\mathbb{Z})^*$ the multiplicative group of integers modulo n.  Afterwards, he states in Theorem 9.4 that if $n$ is an odd positive integer prime to the characterstic and $[k(\zeta_n):k]=\varphi(n)$ (i.e, the primitive roots of unity are not in the ground field), then the above homomorphism is, in fact, an isomorphism. Besides, the commutator group is $G(K/k(\zeta_n))$, so $k(\zeta_n)$ is the maximal abelian subextension of $K$.  Lang proves the theorem inductively over the number of prime factors in the decomposition of $n$ (i.e. if $n=9= 3\cdot 3$, then the proof "would take two steps" to complete). The induction start with $n$ prime is written clearly and I agree with it.   Now come the questions:   I do not understand Lang's argument to prove that the commutator subgroup is the subgroup $\begin{pmatrix}1 &amp; 0 \\ b &amp; 1\end{pmatrix}$, $b\in \mathbb{Z}/n\mathbb{Z}$. What is this projection on the diagonal and how does one see that the factor group of the commutator group is isomorphic to $(\mathbb{Z}/n\mathbb{Z})^*$?   By the way, direct computation of $x\, y\, x^{-1}\, y^{-1}$ for two arbitrary matrices $x=\begin{pmatrix} 1 &amp; 0 \\ b &amp; d \end{pmatrix}$, $y=\begin{pmatrix} 1 &amp; 0 \\ c &amp; e \end{pmatrix}$ yields a matrix $\begin{pmatrix} 1 &amp; 0 \\ b(1-e)+c(d-1) &amp; 1 \end{pmatrix}$. As $n$ is odd, $2 \in (\mathbb{Z}/n\mathbb{Z})^*$, so taking $e=1$ and $d=2$, we indeed reconstruct the above-mentioned group.   The second (inductive) part of the proof is a complete mystery to me with virtually every sentence being a Theorem which needs an extra proof. Can someone give me some hints?   2.a. Lang writes $n=p\,m$ and takes $\alpha$ to be the root of $X^n-a$. It is clear that $\beta=\alpha^p$ is a root of $X^m -a$. Now comes the argument "By induction we can apply the theorem to $X^m-a$". I agree that we can apply it here but the result is that $K=k(\beta,\zeta_m)$ is the splitting field of $X^m-a$. In the diagram below, there appears $k(\beta,\zeta_n)$ out of nowhere.   2.b. Now Lang proceeds to apply the theorem on $X^p-\beta$ over $k(\beta)$. Bergman's "Companion" reminds to check that $[k(\beta,\zeta_p):k(\beta)]=\varphi(p)$ before applying the theorem and gives a hint "$[k(\zeta_p):k]$ and $[k(\beta):k]$ are relatively prime". I disagree with this hint. Take $n=21= m p$ where $m=3$ and $p=7$. Then $[k(\zeta_p):k]=\varphi(p)=p-1=6$ but $[k(\beta):k]=m=3$ and both are not co-prime. Can we apply the theorem here at all? Or if so what is the argument? If Bergman's argument is valid, where is the fault in my logic?  2.c. Even assuming that we can apply the theorem in 2.b., then we can say something about $k(\alpha, \zeta_p)$ and not $k(\alpha,\zeta_n)$. How do we proceed to checking everything Lang states in the last section of the proof (basically, everything after the diagram)?  EDIT: I have found the essentially same question Is there a reason why the pin diagram of an RJ-45 looks like this?    I understand that the orange pair is used for Tx and the green pair for Rx. Why is it that the orange pair are kept together while the green pair are separated?  What are the consequences of messing around with this order as long as it is the same at both the ends? I am trying to understand what mathematics is really built up of. I thought mathematical logic was the foundation of everything. But from reading a book in mathematical logic, they use "="(equals-sign), functions and relations.  Now is the "=" taken as undefined? I have seen it been defined in terms of the identity relation.  But in order to talk about functions and relations you need set theory.  However,  seems to be a part of mathematical logic.  Does this mean that (naive) set theory comes before sentential and predicate logic? Is (naive)set-theory at the absolute bottom, where we can define relations and functions and the eqality relation. And then comes sentential logic, and then predicate logic?  I am a little confused because when I took an introductory course, we had a little logic before set-theory. But now I see in another book on introduction to proofs that set-theory is in a chapter before logic. So what is at the bottom/start of mathematics, logic or set theory?, or is it circular at the bottom?  Can this be how it is at the bottom?  naive set-theory $\rightarrow$ sentential logic $\rightarrow $ predicate logic $\rightarrow$ axiomatic set-theory(ZFC) $\rightarrow$ mathematics  (But the problem with this explanation is that it seems that some naive-set theory proofs use logic...)  (The arrows are of course not "logical" arrows.)  simple explanation of the problem:  a book on logic uses at the start: functions, relations, sets, ordered pairs, "="  a book on set theory uses at the start: logical deductions like this: "$B \subseteq A$", means every element in B is in A, so if $C \subseteq B, B \subseteq A$, a proof can be "since every element in C is in B, and every element in B is in A, every element of C is in A: $C \subseteq A$". But this is first order logic? ($(c \rightarrow b \wedge b \rightarrow a)\rightarrow (c\rightarrow a)$).  Hence, both started from each other? How long does it take for police 'presence' to clear when they are alerted? I engaged with some enemy NPCs, and accidentally shot a civilian in the head (though not sure it would've mattered if I hit them somewhere else or not) as they ran across my screen. As a result of this, I was alerted by the game that the NCPD (the police) were automatically en route to 'investigate', and that I could avoid them by leaving the area and &quot;lying low for a while&quot;. How long does it take for the police to stop searching for me, and is there any kind of visual information on the HUD that alerts me to when NCPD is or is no longer looking for me? I used to work as a consultant and have been spoiled with nice looking slides. For instance, being able to create slides that have 2, 3, or 4 graphs (perfectly positioned and with nice headers!) at the click of a mouse button via macros.  Similarly, there are many other kinds of word slides that had multiple columns, etc. that would be nice to recreate as well as objects like "main point" boxes at the bottom that summarize a main point and ways to add a transparent highlight to any part of the screen.  Is this kind of functionality far beyond anything that LaTeX presentations can do or is there an archive somewhere of code for making more intricate presentations? Tags on badge question list I'm trying to get the Weed-Eater hat on Stack Overflow. To do so, I'm looking at the list of questions . The problem is, no tags show up there, and so it's rather difficult to see which ones I have a shot at. Any chance of showing the tags on this page?  I realize that getting this before Winter Bash is over would be difficult, but it would be good to keep such things in mind for the future.