Double user on Stack Overflow
How can one link / merge / combine / associate two accounts / users? (Anonymous / unregistered / cookie, or Google / Facebook / registered)
Let $U\subset \mathbb{C}$ be a nonempty connected open set such that for every $z\in U$, $\overline z\in U$.  Let $f$ be analytic on $U$. Suppose $f(x)\in\mathbb R$ for every $x\in U\cap\mathbb R$. Prove that $f(\overline{z})=\overline{f(z)}$ for any $z \in U$.    By definition, I know that $f$ analytic on $U$ means that for every $z_0 \in U$, there exists $r&gt;0$ and a sequence of complex numbers $\left(a_n\right)_{n=0}^\infty$ such that $f(z)=\sum_{n=0}^\infty a_n\left(z-z_0\right)^n$ on the disc $D(z_0,r)\subseteq U$. I see that $f$ takes points without imaginary components to other points without imaginary components. But I don't see how this implies a symmetry that $f(\overline{z})=\overline{f(z)}$ for $z \in \mathbb C \setminus \mathbb R$. It seems like a very strong conclusion and I'm not sure how I would prove it.  I have also shown in the preceding question that $U\cap\mathbb R$ contains an open interval, however I am not sure if that detail is meant to be helpful to this question. Applying MVT and IVT (?) to show something about f'''? (edit: actually, Taylor's Theorem using Lagrange remainder) "Compared with" vs "Compared to"—which is used when? Is only one of them correct? Are they used in different situations? Or are they interchangeable? Why am I seeing a bomb icon on my files and folders in Ubuntu? Close Lightning Modal by clicking anywhere outside of it Just wondering whether this is possible? i.e. once a modal is open, close it by clicking anywhere on the grey backdrop?  I've tried invoking my custom close-modal function via: - Adding onclick to the slds-backdrop div - Adding onblur to the slds-modal__container div - Adding onclick to the slds-modal (just wanted to see whether this would work)  None of these seem to work. Can I visit other Schengen countries on a long-term Schengen visa or residency permit? I've always been one to simply use:  List&lt;String&gt; names = new ArrayList&lt;&gt;();   I use the interface as the type name for portability, so that when I ask questions such as these I can rework my code.    When should  be used over  and vice-versa? Why can't helicopters reach mount everest? I know and understand the mean value theorem. But at the moment I don't have the intuition to understand the generalized mean value theorem     If $f$ and $g$ are continuous on the closed interval $[a,b]$ and differentiable on the open interval $(a,b)$, then there exists a point $c\in(a,b)$ where$$[f(b)-f(a)]g'(c)=[g(b)-g(a)]f'(c).$$If $g'$ is never zero on $(a,b)$, then the conclusion can be stated as$$\frac{f'(c)}{g'(c)}=\frac{f(b)-f(a)}{g(b)-g(a)}.$$   What is the intuition? And how can you prove this (generally) ? Why does pdfTeX hang on this file? When is a review task "completed" or "invalidated"? I've noticed that the number of reviews required to remove a post from a queue varies. For example, to accept/reject a suggested edit, you need two votes of the same kind. If the votes are conflicting, the number goes higher. This seems to be the case for the other queues as well. (Additionally, I think that a mod-review is binding) So, my question is: what are the criteria for a review to be marked as a &quot;completed&quot; review? Also, when is a review considered invalidated (i.e. &quot;no longer reviewable&quot;)? Formerly When is a post removed from a review queue?. How can I add certain mobs to a team and make them passive to me if they would normally attack me? I know how to do it in 1.8, but how can I do it now in 1.16.4? Is there an issue tracker for already reported Mathematica bugs? Toggle Switch to swap the connections of two buttons Network reputation graph becomes nervous when clicking quickly, backs away slowly Why did Palpatine wait so long before giving Order 66? Is it possible to open a remote terminal session on a Windows XP machine? Remote desktop is... useable, but I'd like to get a proper remote terminal window open on the Windows XP machine, like I'm able to with Linux. A quick Google points at , but it looks like it's only for Vista/Server. I was just chatting on the Ask Different chat - and the reputation numbers for me and the others chatting don't seem to match any other reputation count I can see on the sites here.  Is there some calculation being made? These numbers are the highest of any other combined reputation I have seen. For me - I'm listed over 10k - but no other aggregate reputation counter I can see is above 8k.  Perhaps I'm unaware how reputation is calculated, but the people there suggested a bug report in case this isn't intended.  (after three lines of text are drawn - a number shows beneath our icons in the left hand side) Determine if two rectangles overlap each other? I am trying to write a C++ program that takes the following inputs from the user to construct rectangles (between 2 and 5): height, width, x-pos, y-pos. All of these rectangles will exist parallel to the x and the y axis, that is all of their edges will have slopes of 0 or infinity.  I've tried to implement what is mentioned in  question but I am not having very much luck.  My current implementation does the following:  // Gets all the vertices for Rectangle 1 and stores them in an array -&gt; arrRect1 // point 1 x: arrRect1[0], point 1 y: arrRect1[1] and so on... // Gets all the vertices for Rectangle 2 and stores them in an array -&gt; arrRect2  // rotated edge of point a, rect 1 int rot_x, rot_y; rot_x = -arrRect1[3]; rot_y = arrRect1[2]; // point on rotated edge int pnt_x, pnt_y; pnt_x = arrRect1[2];  pnt_y = arrRect1[3]; // test point, a from rect 2 int tst_x, tst_y; tst_x = arrRect2[0]; tst_y = arrRect2[1];  int value; value = (rot_x * (tst_x - pnt_x)) + (rot_y * (tst_y - pnt_y)); cout &lt;&lt; "Value: " &lt;&lt; value;     However I'm not quite sure if (a) I've implemented the algorithm I linked to correctly, or if I did exactly how to interpret this?  Any suggestions? windows bat file error