New email template: small typo or you love us? :p
Notification email from stackoverflow contains "<3" after zip code
What is the difference between "information on", "information of", "information about" "Information on something", "information of something", "information about something" — these three usages all sound having the same meaning for me. Are there any differences? Integral closure of $\mathbb{Z}$ in $\mathbb{C}$ is not finitely generated as a $\mathbb{Z}$-module? Let     $$ \mathbb{Z}^{'}_{\mathbb{C}}=\{ z \in \mathbb{C} | \exists f \in \mathbb{Z}[X] \text{ monic such that } f(z)=0\} $$   be the integral closure of $ \mathbb{Z} $ in $ \mathbb{C} $. Prove that $ \mathbb{Z}^{'}_{\mathbb{C}} $ is not finitely generated as a $ \mathbb{Z} $-module.  My attempt: Suppose $ \mathbb{Z}^{'}_{\mathbb{C}}=\mathbb{Z}\alpha_{1}+...+\mathbb{Z}\alpha_{n} $ for some $ \{ \alpha_{i}\}_{i=\overline{1,n}} \subset \mathbb{Z}^{'}_{\mathbb{C}} $. I know that given $ \alpha , \beta \in \mathbb{Z}^{'}_{\mathbb{C}} $ with minimal polynomials of degrees $ m $ and $ n $ respectively, then we can construct a monic polynomial with integral coefficients $ P(z)=\prod(z-(\alpha_{i}+\beta_{j})) $ where $ \alpha_{i},\beta_{j} $ are the conjugates of $\alpha $ , $\beta $ and therefore the minimal polynomial of $ \alpha + \beta $ has degree $ \leq mn $.   I was thinking that then the degrees of the minimal polynomials of the elements of $ \mathbb{Z}\alpha_{1}+...\mathbb{Z}\alpha_{n} $ could be somehow bounded by a certain constant, whereas $ \mathbb{Z}^{'}_{\mathbb{C}}$ contains elements whose degrees of the minimal polynomials are arbitrarily large, take $ 2^{\frac{1}{n}} $ for example,$ n\geq 2$. I think this works when we are asked to prove that the set of all algebraic numbers $ \overline{\mathbb{Q}} $ is not a finitely dimensional $\mathbb{Q}$-vector space, but I don't know how to proceed in my case.  I would really appreciate any ideas, hints or solutions. Thank you very much! Is it a good approach to call return inside using {} statement? Calling a function from a string in C# How can I check for an empty/undefined/null string in JavaScript? How do I verify that a string only contains letters, numbers, underscores and dashes? I know how to do this if I iterate through all of the characters in the string but I am looking for a more elegant method. Change the Ubuntu program that runs when a command can't be found Proving the countability of algebraic numbers I am trying to prove that algebraic numbers are countably infinite, and I have a hint to use: after fixing the degree of the polynomial, consider summing the absolute values of its integer coefficients, and setting the sum less than or equal to $m$, for each $m \in \mathbb{N}$. I am also allowed to use the fact that every polynomial has a finite number of roots. I am not sure where to begin... Perhaps after fixing the degree of the polynomials, I could try enumerating them, and after proving countability of the set that contains the roots of all polynomials of a certain degree, I could state that the union of infinitely many ($\bigcup_{n=1}^{\infty}$, $n \in \mathbb{N}$) countably infinite sets is countable, and thus the algebraic numbers are countably infinite, too, but I am not sure if this is a good approach/how to enumerate the polynomials. Thanks! How to resolve ambiguous column names when retrieving results? RGB and CMYK: Why both? Any of you who have at least little experience with graphic design software, photography or professional printing, must have -almost undoubtedly- have gone through this: 'the struggle' of RGB and CMYK colour spaces.  Now, there are many questions regarding matters of 'which should I choose', 'what is what' and converting problems, but that's not really what I'm after here.  As a graphic designer with only a couple of years of experience, I still have this struggle from time, and find the whole CMYK/RGB choosing/converting/saving situation quite confusing, to say the least. I do know that RGB is meant for digital end purposes, and CMYK is suitable for printing.  I have always been wondering about the neccesity of this whole thing. So, my question is: why are there these two colour profiles, instead of just having one?   Wouldn't it be a lot easier if printers or software could convert any RGB file to a CMYK printing document instead? I'm pretty sure it does already exist, by the way, because printing an RGB file sometimes simply prints the right colours for me. Alas, not always (doesn't seem to be related to the printer of software I print from).    I have gone trough some RGB vs. CMYK-related questions and found this, a.o., (), an answer of user DKuntz2 (thanks DKuntz2):     RGB is a light-based theory. All colors begin with black "darkness",   to which different color "lights" are added to produce visible colors.   RGB "maxes" at white, which is the equivalent of having all "lights"   on at full brightness (red, green, blue).      CMYK is a color-based theory. All colors start with white "paper", to   which different color "inks" are added to produce output colors. CMYK   "maxes" at black, at which point all "inks" are applied at 100% (cyan,   magenta, yellow, black).   Not sure if this is entirely right, though, because some people disagreed with DKuntz2:     I disagree. With RGB you start with black - the absence of light; with   CMYK you start with white paper.   – e100  Although this does clarify the differences fairly well, I still don't see the point of the two colour profiles(/spaces)    Side question: What happens when you work in an RGB document in photoshop, then press ctrl+y? Photoshop says the document is RGB/8/CMYK, but it can't be both. Right?  EDIT:  Big thanks for the answers, the (current) three below are very informative and interesting. I understand the whole thing a bit better, although it's all very complicated and in-depth to me. Especially when I read about terms like colour models, colour profiles, colour spaces, colour spectra and gamut all one after another.  As much as I would like to accept an answer as the desired one, I feel that my question in the core isn't fully answered yet. What I would really like to emphasize is what I asked about earlier: Wouldn't it be a lot easier if printers or software could convert any RGB file to a CMYK printing document instead?. As Alan Gilbertson explained, the reason is - if I understand correctly - basically a 'lost-in-translation' thing that makes the conversion not 100% accurate, and the colours to possibly be a bit distorted.  However, I still don't see how the solution cannot be an automated conversion done by a printer. Should be possible with modern technology; if you can convert RGB to CMYK in Photoshop, why can't a printer do the exact same for you? As was also said in the answers, the slightest differences in colours and colour spaces, can not be seen by the human eye. And that's what it all comes down to: what we want to see. Be it on a screen or on a sheet of paper.  The fact that this question has three very long answers, or even moreso the fact that there are so many questions about these two colour models (I now know the right term, yay) kind of proves that this is way more complicated than it should be. Simple Math Problem A bat and ball cost \$1.10.  The bat costs a dollar more then the ball.  How much does the ball cost?  If this is not the correct place to ask a question like this please tell me and I will remove it :)     The ball costs \$0.05, not \$0.10 LINQ's Distinct() on a particular property set session - custom variable to store user id I want to store user id in custom session variable and use it (read) in trigger procedures to authorize user actions. I found something like this:  set session "myapp.user" = '12345'; ... SELECT current_setting('myapp.user');   and it seems to work - I thought that "myapp.user" should be declared in .conf file but it seems that I can create session variables on the fly (I didn't change .conf file at all).  Is there any disadvantage of doing like this? Catch multiple exceptions at once? I am working on a large C++ project in Visual Studio 2008, and there are a lot of files with unnecessary #include directives. Sometimes the #includes are just artifacts and everything will compile fine with them removed, and in other cases classes could be forward declared and the #include could be moved to the .cpp file.  Are there any good tools for detecting both of these cases? Why does the Cauchy distribution have no mean? Need hint for $\lim_{x\to 0} \frac{(x+1)^\frac{1}{x}-e}{x}$ Please give me some hints or solution for this limit. I had it on my exam and I'm curious how to solve it. $$ \lim_{x\to 0} \frac{(x+1)^\frac{1}{x}-e}{x} $$ Modify TikZ coil decoration Can I modify the existing tikz coil decoration, so that the downstrokes are not drawn in a certain interval, to produce a picture like this?    Edit: Previous attempts, code and MWE has been moved to or superseded by my own answer. How do I instantiate a string array object into a Spring.Net container? Draw power from a portable mobile charger to power circuits