pgfplots: undefined control secquence in a foreach loop
PGFplots foreach equivalent to TikZ's with multiple variables separated by a slash
Cardinality of set of real continuous functions Why no tag Badges for Good questions Why not make  but for questions too?  I love that everything is well though behind SO but I can't see no reason as to why great questions can't be prized with "Badges by subject". Why is $\frac{1}{2\pi i}\int_{\gamma}\frac{f'(z)}{f(z)}dz$ an integer? Let $f$ be holomorphic in an open $\Omega \subset \mathbb{C}$ and $\gamma$ a closed curve in $\text{int}(\Omega)$, along which $f$ is never zero.   Are these hypotheses enough to claim $\frac{1}{2\pi i}\int_{\gamma}\frac{f'(z)}{f(z)}dz$ is an integer? If not, what are the necessary and sufficient conditions for that?  I can prove that's an integer for some particular cases, for example when $\Omega$ is convex and  $\gamma$ is a circle. But I've seen people claming this in many other contexts, like when $\Omega$ is an annulus around $0$ and $\gamma $ is an arbitrary curve inside it. This isn't obvious to me at all.  Thanks! Suppose $\sum{a_n}$ converges. How do I prove that $\sum{\frac{\sqrt{a_n}}{n}}$ converges.  So I know that just because  $\sum{a_n}$ converges, do not mean I can say anything about the converges of its square root. So I know that I can prove that if  $\sum{\sqrt{a_n}}$ converges then $\sum{\frac{\sqrt{a_n}}{n}}$ converges by Abel's Test, but I do not know where to start for the case where  $\sum{\frac{\sqrt{a_n}}{n}}$ diverges How can I hide username and computer in terminal command prompt?   In Terminal it says  Last login: Mon Jan 13 00:00:14 on ttys000 Whatever:~ UserName$    Is it possible to show just the current folder and $ sign? Suppose $G$ is a group generated by elements $x$ and $y$ where $xy^2 = y^3x$ and $yx^3 = x^2y$ What can you prove about $G$? Suppose $G$ is a group generated by elements $x$ and $y$ where $xy^2 = y^3x$ and $yx^3 = x^2y$ What can you prove about $G$?  I've just been playing around with the relations but I can't seem to get anywhere. It seems as if I'm going in circles. I don't know what to look for in terms of how the equations should look in order to give me an insight into the structure of the group.  So given a group presentation, are there any general strategies of what to look for in the relations (as in how to rearrange them) in order to obtain insight about the group? What is the relation between linear purity and von Neumann entropy of a state? Given a density matrix $\rho$, its linear purity is $\mathrm{Tr} \rho^2$, its von Neumann entropy is $-\mathrm{Tr} \rho \log \rho$. Knowing one how do I calculate the other?  Edit:   My thought is that the linear purity and the von Neumann entropy are a parallel set of benchmarks for mixedness. Their inter-conversion should be like unit conversion.  See it this way, as a state goes from a pure state to a maximally mixed state, $\mathrm{Tr} \rho^2$ goes from $1$ to $0$, and $-\mathrm{Tr} \rho \log \rho$ goes from $0$ to $\log d$, like two rulers. A point on one should correspond to a point on the other. How to link data to a polygon ArcMap 10.3 I have a map with different polygons (118). Each of this polygons represent diferent vegetation types.  For each of those polygons I have data of which species there is and how abundant they are (the abundance is measured with a scale from 1 to 3).  I would like to "link" (I am sorry if its not the correct way of name it) the data of which species and abundance there is in each of those polygons.   I would like afterwards to be able of selecting the different polygons containing the same abundance and species.  In the polygons I created there is no atributes associated other than (FID, shape and Id. the 3 of them created alone by the program when I drew them) and the tables I have in excel with the data I want to "link" to the polygons contain a column called species and another abundance.  As you can see, I'm pretty new using the program...    As I have tried to do what you all suggest in the comments down here, and I couldn't achieve what I was wanting to do (provably because of my bad explanation before...)  I leave a picture:  As you can see in the attribute table, that is how every attribute table of each polygon (which represents one area) looks like. On the right there is how I have my data in excel. Could you please suggest something I could do in order to add to the polygons attribute table the data belonging of species and its abundances (polygon number 1 has to have all the species (Acer mons, Acer pseu, Acer repens….) and its abundance (which are the numbers of the row Area1). number of edges induction proof Proof by induction that the complete graph $K_{n}$ has $n(n-1)/2$ edges.   I know how to do the induction step I'm just a little confused on what the left side of my equation should be. $E = n(n-1)/2$  It's been a while since I've done induction. I just need help determining both sides of the equation. How do you teleport a certain player to spawn after they win a 1v1 I managed a KitPvP server in Minecraft and everything works fine except when players wants to duel each other. They get sent to a room where they will be dueling. The main problem is when the winner wins, I have no idea how to teleport them back to spawn. We found this skull on a beach in southwestern Sweden, and are curious as to what kind of animal it was. Resize Move Partitions on Dual Boot System Does mass distribution/center of mass affect free fall? An everyday is example would be cars. If you were to drop a car, not taking air resistance into account, would a front-heavy car tumble forward as it fell? And a car with a perfect 50/50 front/rear weight distribution fall straight? Does mass distribution/center of mass affect free fall? Or would they both fall straight down without tumbling? Can you explain why please? Unable to boot into Windows after installing Ubuntu, how to fix? Extrude and bevel an imported svg curve I can write  VAR=$VAR1 VAR=${VAR1} VAR="$VAR1" VAR="${VAR1}"   the end result to me all seems about the same. Why should I write one or the other? are any of these not portable/POSIX? Extruding a circular shape from a non-circular object I need to extrude a circular shape from a surface that's basically just a grid of quads. What's the best practice to do this without screwing up the topology too much?  I basically want to have a circular face I can extrude, in order to have a cylinder like protuberance on the object, something like this: Where can I rent a decent mountain bike in Zürich? I am going for a 4 day trip in Zürich and I would like to bike quite a lot. Though biking is quite advertised, I failed to find a decent bike rental shop in the city. Would highly appreciate some tips! What does the comma operator , do? What does the , operator do in C? SQL Server nvarchar(max) vs nvarchar(n) affects performance