Context:   The  may be the ethically correct thing to do, but there's certainly legal ramifications with it that should not be ignored. While the answer has a bolded disclaimer that points this out, this doesn't change the fact that the content of the answer itself can cause serious harm.  Should such answers be discouraged on this site? Should they be redirected to Law.SE?
If I see an answer that involves some illegal activity, such as breaking license agreements, should I then mark this as Offensive or should I simply down-vote it?
Prove or find a counterexample: For all real numbers x and y it holds that x + y is irrational if, and only if, both x and y are irrational. The following is a Homework Question that I've been working on and I would like some feedback on my answer: Prove or find a counterexample: For all real numbers $x$ and $y$ it holds that $x + y$ is irrational if, and only if, both $x$ and $y$ are irrational.  So I've got (or at least like to think I've got) a counter example.  Let $x = 1$ and $y = \sqrt{2}$.   Thus $x$ is rational and $y$ is irrational. Adding $x$ and $y$ gives us $1 + \sqrt{2}$ which cannot be simplified any further (right?) and is an irrational number.  Thereby proving that $x + y$ can be irrational without both x and y being irrational.   Is this okay? Any feedback is greatly appreciated thank you! Does the verb &quot;provide&quot; always have to be used with &quot;with&quot;? For example,  Can you provide me with some good examples? Can you provide me some good examples? Can you provide some good examples?  I suppose it's a transitive verb, isn't it? Moreover, is the following type of usage correct?  You should provide food for your dog before you go on vacation.  If you could give me some good examples regarding &quot;provide&quot; with different types of usage, I'd appreciate that. How to wrap text around a figure? Deploy Community Builder audience page assignments with ant migration tool? In Community Builder, if you create audiences and assign them to page variations, you cannot deploy these using change sets, according to .  In fact, Audience doesn't even appear in the list of change set components.  On the other hand, Audience metadata can be deployed using the ant migration tool, so I was hopeful that the audience assignments would also be deployable.  Unfortunately, I haven't had success in deploying any audience assignments, either for entire pages or for components on a page.  Has anyone found a workaround for deploying audience assignments for Community Builder pages?  I should say that I'm using the Build Your Own template.  If it can't be deployed, is there at least a way to get a list of audience assignments so I don't have to open every single page in the Community Builder to check?  Here's what I'm using in my package.xml manifest.  All the community builder page variations and all the audiences are created correctly, but the assignments are not.  &lt;types&gt;     &lt;members&gt;*&lt;/members&gt;     &lt;name&gt;Audience&lt;/name&gt; &lt;/types&gt; &lt;types&gt;     &lt;members&gt;*&lt;/members&gt;     &lt;name&gt;CustomSite&lt;/name&gt; &lt;/types&gt; &lt;types&gt;     &lt;members&gt;*&lt;/members&gt;     &lt;name&gt;SiteDotCom&lt;/name&gt; &lt;/types&gt; Typesetting A when a register is 1, B when 2, etc I have a register \count0=&lt;some-value&gt; and need to get the letter of the alphabet on the index of \count0. That is, if it is 1, I need an A, if 2, a B, etc.  Is this possible?  I'm reluctant sharing an MWE as it seems to overcomplicate things a bit:  \begin{tikzpicture} \node[regular polygon, regular polygon sides=7, minimum size=5cm] (A) {}; \foreach \i in {1,...,7}{     \count0=8     \advance\count0 by -\i     \node[circle, label=above:\scriptsize\the\count0, fill=black, minimum size=4pt, inner sep=0pt] (\the\count0) at (A.corner \i) {}; } \end{tikzpicture}   With the tikz package and the shapes.geometric tikz library.  This draws seven nodes labelled 1 .. 7 on a circle. I need to have A .. G instead of 1 .. 7. $D_8$ as a derived subgroup Every undergraduate student knows that there are (exactly) two non-abelian groups of order 8: Dihedral ($D_8$) and Quaternion ($Q_8$). The group $Q_8$ has many interesting properties; simple of them are: it has unique element of order $2$, all subgroups are normal, etc. A property, which is strange and not obvious, the group $Q_8$ has, is that there is no group $G$ such that $G/Z(G)$ is isomorphic to $Q_8$. On the other hand, $D_8$ has no such property; there are (infinitely many) groups $G$ such that $G/Z(G)$ is isomorphic to $D_8$; example - $D_{16}$.   The question, I would like to ask, is related to a property of $D_8$, which is not shared by $Q_8$. There are (infinitely many) groups whose derived subgroup is $Q_8$; example- $SL_2(3)$. For groups $G$ of order &lt;100, one can check on GAP that $D_8$ is not a derived subgroup of any group. The natural question is then:  Question 1: Does there exist a finite/infinite group whose derived subgroup is equal to $D_8$?  Question 2: Does there exist a finite/infinite group whose derived subgroup is equal to (general) dihedral group $D_{2n}$ of order $2n$ ($n&gt;2$)? I wish to show that $\mathbb{Q}(\sqrt2, \sqrt3)$ is not isomorphic to $\mathbb{Q}(\sqrt[4]2)$.    What I did so far was to show that $\mathbb{Q}(\sqrt2,\sqrt3) =\text{span}\{1,\sqrt2,\sqrt3,\sqrt6\}$.  Assuming they are isomorphic, denoting $f$ the isomorphism, then $f(1) = 1$, so $x^2-3$ has a root in $\mathbb{Q}(\sqrt2,\sqrt3)$ so $\sqrt 3\in\mathbb{Q}(\sqrt[4]2)$. ($\sqrt2 \in \mathbb{Q}(\sqrt[4]2)$, $\sqrt[4]2\cdot\sqrt[4]2=\sqrt2)$.   Thus under the assumption, $\mathbb{Q}(\sqrt2, \sqrt3)\subseteq \mathbb{Q}(\sqrt[4]2)$. As a vector spaces of the same dimension over $\mathbb{Q}$, it means that $\mathbb{Q}(\sqrt2, \sqrt3)= \mathbb{Q}(\sqrt[4]2)$.  Now all is left to do it to show a contradiction: $\sqrt[4]2\in\mathbb{Q}(\sqrt2,\sqrt3)$, then $\sqrt[4]2 = a+b\sqrt2+c\sqrt3+d\sqrt6$ so $2=(a+b\sqrt2+c\sqrt3+d\sqrt6)^4$, I believe that opening the expression, I would find out that it can't be an element of $\mathbb{Z}$. However this is a really inelegant way (if it really works), and I wish for a better way to do so.  An other approach: $\mathbb{Q}(\sqrt2,\sqrt3) = \mathbb{Q}(\sqrt2 + \sqrt3)$ by the irreducibility of $x^4-10x^2+1$ over $\mathbb{Q}$ (an some dimension theorem usage). Also, $x^4-10x^2+1$ splits in $\mathbb{Q(\sqrt2, \sqrt3)}$.   Is there a way to show that this polynomial doesn't split over $\mathbb{Q}(\sqrt[2]4)$? with different method then assuming that $\sqrt3\in\mathbb{Q}(\sqrt[4]2)$ and getting a contradiction? Maybe the fact that $\sqrt[4]2$ has complex roots might help? Is there an online course in Mathematical Methods for Physics, Covering Matrices and Vector Analysis? I am taking a course in Mathematical Methods for physicsPhysics (Junior Level).   We are working from   > Mathematical Methods for physicists, George B.Arfken .    I just need online resources covering ( Matrices, Determinants, Vector Analysis, Tensors and differential forms and Vector spaces...etc) to study and understand from. Citrix receiver error 1000119 I am trying to run Citrix receiver on the Xenial version of Ubuntu, but I am getting this error below  ERROR: Cannot connect to &quot;0.0.0.2 - Remote Desktop Connection&quot; Unknown error 1000119. Verify your connection settings and try again.  What should I do? If $f$ is entire and $|f|\geq 1$, then show $f$ is constant. I know I'm going to use Liouville's Theorem, but my main question is why is $1/|f(z)|$ entire as well if $f$ is entire? Is this just a basic property: if $f$ is entire, then $1/f$ is entire? Thanks for the help. Curved mesh topology 2 I am trying to model a violin belly and I am intrigued, how is it possible to make faces with soft / rounded edges?    The edges I do are totally straight (see the blue amoeba).  Also, do you have some idea on how to avoid the edge loops getting too "compressed" in the middle of the model (see the red amoeba) ?    I know the Subdivision surface modifier, but I want curved edges after applying the modifier... like in this picture :  Any help will be very appreciated. Thank you in advance!  Marcos  2nd part  In fact, I've tryied to model using nurbs and bezier curves, but I wasn't able to find any tool similar to loft that works with curves, then I was forced to convert it in meshes, the results were not terrific and I've started to move the vertices manually, a real pain... Unlike a guitar, each edge loop is on a diferente elevation on z axis and I have to keep the original dimensions, So I have to be extremely careful when using the subdivision suface modifier. I've already modeled this think on three different CAD softwares, but the meshes are far from good... I want to improve the edge loops, but it will be a long path... Thank you again. How to draw a border around character in a formula? So far everything I found on the matter of borders only applies to the text mode.  I want to be able to do something like  $x_i = y$   so the result will be like the ordinary "xi = z" formula with the border around "i"?  The common answers seems to be the fbox or boxed commands. Yet they render their argument in the standart mode, unless specified to do otherwise with the specific mode. For example, the following code  \[ x_i, \boxed{x}_i, x_{\boxed{i}}, \boxed{x}_{\boxed{i}} \]   produces two normal xi figures, and another two with an oversized i. Does $f(x)$ is continuous and $f = 0$ a.e. imply $f=0$ everywhere? I wanna prove that   "if $f: \mathbb{R}^n \to \mathbb{R}$ is continuous and satisfies $f=0$ almost everywhere (in the sense of Lebesgue measure), then, $f=0$ everywhere."  I am confident that the statement is true, but stuck with the proof. Also, is the statement true if the domain $\mathbb{R}^n$ is restricted to $\Omega \subseteq \mathbb{R}^n$ that contains a neighborhood of the origin "$0$"? How to install Eclipse J2EE IDE from a tarball? I have downloaded Eclipse 3.6.1 as a tar.gz file from eclipse site. Then I extract using  cmd: tar -zxvf eclipse-jee-helios-SR1-linux-gtk.tar.gz  after execute this cmd I got eclipse folder in this there is eclipse file. When I double click on this eclipse file I'm getting following error:     Could not display "/media/D-DEVELOPME/eclipse/eclipse".   There is no application installed for executable files   is there any solution for it? The comment pop-up is too far away When you click the add a comment button when you don't have enough rep, you get a pop-up saying that you need more rep in able to comment. Except, it is too far away and users might be confused for a while before realizing the pop-up is on the other side of the page:     Clearly, that is very inconvenient for a lot of people, like me. Can we move the pop-up to be right next to the add a comment button? Responsive Breakpoints? Twitter Bootstrap uses these break points for responsive design:  Large Display: 1200px Default: 980px Tablet: 768px Mobile: 480px  A client said they are using 1280px for their Large Display breakpoint.  Is there an industry standard for these or are they just made up as we go right now? Always sort Recent Places by date modifed I've noticed confusing definitions about permutation and substitution, preventing me from understanding the difference.  A permutation changes the order of distinct elements of a set, but this can be written as a function changing one element by another, exactly as a substitution.  So, how exactly can we distinguish between these two notions?  This question is interesting since we have these two notions in block ciphers, in which S-boxes perform substitution. The problem is that this table is used to replace one element by another, exactly like a permutation. How does Router know where to forward packet How to zero out a drive?