The first experiment of a subjective proposal -  - was created 11 days ago and has been in public beta for 4 days so far. As a private beta user I followed the website since day 1, reading most questions (even though I didn't actively participate much), and so far my impression is very good: programmers is a wonderful website to read when you have some time to kill. It's like reading a magazine. In my opinion, reading  is much more fun than reading , and thus it's no surprise that most of the  actually belong on programmers, as they are subjective/argumentative (but have been grand-fathered). I believe that the very nature of subjective answers make them more interesting. Of course there is a (big) place for non-subjective websites where you can get help or help with a specific problem, but I think there should be a (big) place for subjective websites too. It's early to say (this is meant to be an ongoing discussion that will probably last months), but so far programmers seems to be one of the more successful - if not the most successful - proposals ever created. It has , and the only beta website with more views is gaming. So, what do you say? Should subjective proposals be allowed? Can they be successful?
Stuff like polls, recommendations based on subjective constraints, puzzles, webcomics etc. do not belong on the serious main SE sites, where professionals should be considered at work and having just a few spare minutes ("code's compiling") to answer questions, so they should not be distracted by such things. However, I'd also like to have a home for these things still using the SE engine. For the reason I mentioned before, this needs to be a separate place though. Let's call it four.[sitename-here].com.
Plural or singular verb for collective term Let $\ln X \sim \operatorname{Exp}(1)$ and $X,Y$ i.i.d.  What is the distribution of $Z=XY$?  My attempt: $$P(Z\le z)=P(XY\le z)=P(\ln(XY)\le \ln(z))=P(\ln(X)+\ln(Y)\le \ln(z))$$  We need the convolution, since $\ln X $ and $\ln Y$ are independent we get, $$\int_0^{\ln(z)} f_{\ln(X)}\circledast f_{\ln(Y)}=\int_0^{\ln(z)}e^{-y}e^{-x+y}\,dy=e^{-x}ln(z),$$ i.e. $e^{-x}\ln(z)$ is the density of $XY$ I'm reading the proof of the multiplicative property of $$s_k(n)=\sum_{d|(n,k)}f(d)g\bigg( \frac kd\bigg)$$ The book wrote that in order to understand the proof, we need to know if $a,b,k,m$ are integers such that $(a,k)=(b,m)=1$, then $$(ab,km)=(a,m)(b,k).$$  I have written proof, but I don't know is it consistent, and this seems used more tools than it necessarily has to.   My proof: Let $$S_1=\{d: d|(a,m), d&gt;0\}\\S_2=\{d: d|(b,k), d&gt;0\}\\S=\{d:d|(ab,km), d&gt;0\}.$$ I will prove the statement by showing that the function $\phi:S_1\times S_2\to S$ defined as $$\phi(d_1,d_2)=d_1d_2$$ is bijective, and complete the proof by connecting the maximal elements from these partial ordering sets.  Obviously, for $d_1\in S_1, d_2\in S_2$, this tells us $d_1 $ is both divisor of $a$ and $m$, and $d_2$ is both divisor of $b$ and $k$, hence $d_1d_2$ is both divisor of $ab$ and $km$, so we can tell $\phi(S_1\times S_2)\subseteq S$.  To show one-to-one, if we have $c_1,d_1\in S_1$ and $c_2,d_2\in S_2$ such that $$\phi(c_1,c_2)=\phi(d_1,d_2)$$ then $$c_1c_2=d_1d_2$$  In particular, $c_1|d_1d_2$, we need to show $c_1|d_1$. Indeed, if $(c_1,d_2)&gt;1$, this implies $a,k$ have common factor larger than $1$, contradicts the assumption. Therefore $c_1|d_1$. A similar argument implies $d_1|c_1$, therefore $c_1=d_1$. Again a similar argument implies $c_2=d_2$, which shows one-to-one.   To show onto, let $d\in S$, since $d|ab$, we can split $d$ into $d_1d_2$ such that $d_1|a$ and $d_2|b$. Since $(a,k)=1$, we see $(d_1,k)=1$, by property of $S$ we see also $d_1|m$, therefore $d_1\in S_1$, a similar argument implies $d_2\in S_2$. So every number in $S$ has a preimage in $S_1\times S_2$  This completes the proof. Is there any mistake in the proof?     Edit: A proof about the statement: If $d|ab$ then there are $d_1,d_2$ such that $d=d_1d_2$ and $d_1|a, d_2|b$.  Let $ab=p_1^{e_1}\cdots p_r^{e_r}$ for distinct prime factors $p_1,\cdots,p_r$, then we can write $$a=p_1^{x_1}\cdots p_r^{x_r}\\b=p_1^{y_1}\cdots p_r^{y_r}$$ where some of $x_i, y_i$ can be zero, and $x_i+y_i=e_i$ for all $i=1,\cdots,r$.  Since $d|ab$, we can write $$d=p_1^{f_1}\cdots p_r^{f_r}$$ with $f_i\leq e_i$ for all $i=1,\cdots,r$. Then since $$f_i\leq x_i+y_i$$ Split into two cases:   Case 1: $f_i&gt; x_i$, then we can choose $g_i=x_i$ and $h_i=f_i-x_i$.  Case 2: $f_i\leq x_i$, then we can choose $g_i=f_i$ and $h_i=0$.  Then the choice $$d_1=\prod_{i=1}^r p_i^{g_i}, \quad d_2=\prod_{i=1}^r p_i^{h_i}$$ will prove the statement. How do I get the local machine name in C#? I've installed VM VirtualBox v. 4.3.8 on my Ubuntu 12.04 LTS (Lenovo G500S with Intel 1005M processor) and I can't configure any 64-bit guest (nor Windows, neither other OS). Inslalation of Win 8.1 64-bit under 32-bit profile obviously fails... My processor supports VT-x technology, but in my BIOS there is no enable/disable option for VT-x. Is there any way to force VirtualBox to support 64-bit guest ? Persist variables between page loads Find all polynomials $P$ such that $P(x^2+1)=P(x)^2+1$ Find all polynomials $P$ such that   $$P(x^2+1)=P(x)^2+1$$ How do I set a user environment variable? (permanently, not session) This is irritating me. I seen several suggestions (all using different files and syntax) and none of them worked.  How do I set an environment variable for a specific user? I am on debian squeeze. What is the exact syntax I should put in the file to make ABC = "123"? Setting nautilus-open-terminal to launch Terminator rather than gnome-terminal Selecting attribute values with html Agility Pack I'm trying to retrieve a specific image from a html document, using html agility pack and this xpath:  //div[@id='topslot']/a/img/@src   As far as I can see, it finds the src-attribute, but it returns the img-tag. Why is that?  I would expect the InnerHtml/InnerText or something to be set, but both are empty strings. OuterHtml is set to the complete img-tag.  Are there any documentation for Html Agility Pack? I'm trying to get past a Snorlax and I need a Poké Flute to wake him up—how do I get one? Learning special relativity and working with Minkowski diagrams for a while now i am still trying to get my head around some oddity.   From my understanding time can often be seen as the dependent variable in those diagrams, so why put it to the vertical axis? What confuses me even more is the apparent convention to denote a point in space time $(t,x)$ even though $x$ is on the horizontal and $t$ is on the vertical axis, so the usual notation would be to refer to that vector as $(x, t)$.  Are there mostly historical reasons or why is it beneficial to use this notation and to violate usual conventions? What exactly is tested when a fire extinguisher is tagged? I am just curious: the obvious is that the  pressure mass   can be inspected /measured to ensure that the device has not been discharged. Is there anything else that is measured \ checked? USB stick mysteriously become write protected So, somehow over the weekend, my 1GB USB flash drive has managed to become write-protected.  There is no switch on the stick, so I'm concluding that something has corrupted at some point.  Obviously I can't format it or remove.  The output from dmesg | tail is:  Buffer I/O error on device sdb1, logical block 328168 lost page write due to I/O error on sdb1 sd 73:0:0:0: [sdb] Unhandled sense code sd 73:0:0:0: [sdb] Result: hostbyte=DID_OK driverbyte=DRIVER_SENSE sd 73:0:0:0: [sdb] Sense Key : Data Protect [current] Info fld=0x0 sd 73:0:0:0: [sdb] Add. Sense: Write protected sd 73:0:0:0: [sdb] CDB: Write(10): 2a 00 00 05 08 00 00 00 01 00 Buffer I/O error on device sdb1, logical block 328200 lost page write due to I/O error on sdb1   I think the second and final lines are a giveaway to corruption, but I don't know how to interpret this output.  Could someone help to see if this output gives any indication?  I usually eject the drive before removing it, but I may have been lax once or twice.  The data isn't critical, it's just bugging me.  Any suggestions on how to fix it (if the drive even can be) would be greatly appreciated. How to start X windows inside "Bash on Ubuntu on Windows" After installing the new feature (still "Beta") called  that is a feature subset of Windows 10 Anniversary edition, I get the following message when trying to start X-Windows using startx :    What do I need to tweak / configure in order for X-Windows to launch?  I noticed that xauth was already installed, however I had to install the rest of the framework as follows :  apt-get install xorg openbox Show that $K[x,xy,xy^2,\dots]$ is not Noetherian Here is the problem I am stuck on: Fix a field $K$ and consider the subring $A \leq K[x,y]$ generated by $K \cup \{x,xy,\dots,\}$. Show that $A$ is not Noetherian.  I figure that taking ideals $I_n = (x,xy,\dots,xy^n)$ should give an infinite strictly ascending chain, which would establish that $A$ is not Noetherian, but I cannot figure out how to show that each $I_n$ is a proper subset of $I_{n+1}$. Any help here? In the course of creating the content for a site, we've ended up with orphaned content nodes that are not linked to from anywhere. I'd like to find and examine these. Surprisingly, I can't find a module for this.  Tiny hypothetical example: I'm building a brochureware site. Someone wrote a "Contact" page, someone else wrote an "About Us", and someone else wrote "Directions". The person writing "Directions" forgot to put it in a menu link or add a link from "About Us" to "Directions". So "Directions" is orphaned: there are no links to it. I'd like to find all such nodes so I can figure out what to do with them. When I go to Settings &gt; Applications &gt; Manage Applications &gt; Downloaded I see an application list. If I select some applications I see button "Force stop" active, but some applications have this button dimmed.  What does it mean? What happens if I press this button?  This button can't mean application running, since the applications with this button are not listed in Running section.  Can I list just applications which have the Force stop button active and uninstall them?    Android version: 3.2 Simple enough question: What math should all game programmers have a firm grasp of in order to be successful?  I'm not specifically talking about rendering math or anything in the niche areas of game programming, more specifically just things that even game programmers should know about, and if they don't they'll probably find it useful.  Note: as there is no one correct answer, this question (and its answers) is a community wiki.  Also, if you would like fancy latex math equations, feel free to use . How to escape  inside  tags I'm trying to write a blog post which includes a code segment inside a &lt;pre&gt; tag. The code segment includes a generic type and uses &lt;&gt; to define that type. This is what the segment looks like:  &lt;pre&gt;     PrimeCalc calc = new PrimeCalc();     Func&lt;int, int&gt; del = calc.GetNextPrime; &lt;/pre&gt;   The resulting HTML removes the &lt;&gt; and ends up like this:  PrimeCalc calc = new PrimeCalc(); Func del = calc.GetNextPrime;   How do I escape the &lt;&gt; so they show up in the HTML?