Why do clouds not fall?
The Density of Clouds
How to divide aleph numbers Recently, I was wondering how division of aleph numbers would work. First, I thought about how finite cardinality division would work. What I came up with was that the result of $A/B$ where $A$ and $B$ are both cardinalities, is the number of times that each element of $B$ had to be mapped to an element of $A$ in order to ensure that all elements of $A$ were mapped to.  Extending this to aleph numbers, specifically, I thought that $\aleph_1/\aleph_0$ would be $\aleph_1$. The reasoning behind this is that there are an infinite ($\aleph_1$) number of real numbers between any two natural numbers. As such, that mapping would need to be applied.  Can anyone validate this idea? Is this how division of aleph numbers actually works, or am I totally off base?  Thanks. According to the definition on , a multiple  is a root with  $n\geq 2$. For example, in the equation $(x-1)^2 = 0$, $1$ it the multiple (double) root.  Question: Why is $x = 1$ the multiple root of $(x-1)^2 = 0$?  What does multiplicity mean in this case? According to Wolfram multiplicity is the number of values for which a condition holds, or the number of times for which a polynomial equation has a root at a given point. In what way does the polynomial $x^2 - 2x + 1 = 0$ have multiple roots? Let $G$ be a non abelian group of order $p^3$, with $p$ prime.  I'm proving that $Z(G)$ (its center) is of order $p$. I already know how to do it by saying that its order can't be $p^3$, nor 1, and if it's $p^2$ then $G/Z(G)$ is cyclic then G is abelian, Abs!  But I've been reading another way of proving it and the author supposes that $|Z(G)|=p^2$. Then, she says: "$\exists\ x$ outside the center of $G$, of order $p$." Could someone give me a hint? Thanks! Exponent and abelian groups Of Half-elven and mortal life When half-elvens choose mortal life, how would their bodies behave?  Half-elven are always elves by nature. Ever since they're born, their physical body and behaviour would be elvish - they have keen senses, they don't get physically weary, no illness, and so on.  Half-elvens are then offered a choice - Immortal elvish lives or mortal fate of men. When they choose the latter, like Elros and Arwen did, what would happen to their elvish nature? Would they lose it? I don't think they would lose their pointy ears, but what about the other elvish features that I mentioned before?  Are there any canonical references? I've working LDAP authentication with the following setup   AuthName            "whatever"  AuthType            Basic  AuthBasicProvider   ldap  AuthLDAPUrl         "ldap://server/OU=SBSUsers,OU=Users,OU=MyBusiness,DC=company,DC=local?sAMAccountName?sub?(objectClass=*)"  Require ldap-group  CN=MySpecificGroup,OU=Security Groups,OU=MyBusiness,DC=company,DC=local   This works, however I've to put all users I want to authenticate into MySpecificGroup. But on LDAP server I've configured that MySpecificGroup also contains the group MyOtherGroup with another list of users.  But those users in MyOtherGroup are not authenticated, I've to manually add them all to MySpecificGroup and basically can't use the nested grouping. I'm using Windows SBS 2003.  Is there a way to configure Apache LDAP to do this? Or is there a problem with possible infinite recursion and thus not allowed? What part of speech is “there” when used in “There is (blah blah)”? What part of speech is there in the sentence “There is a book on the table?”  Also, while typing it out, another question pops up vis-à-vis punctuation. In my complete first sentence above, I ended it with a question mark since my main sentence is a question. The quote is not a question, but it looks like it because of the question mark. Is this the right way to punctuate? How do I delete all empty directories in a directory from the command line? Say I have a directory named foo/. This folder includes subdirectories. How can I delete all the empty directories in one command? I am Indian passport holder living in Hungary for 4 years and I have been issued a Temporary residence permit (EU Schengen).  Can I go to visit Dublin without any visa, or do I need to apply for a UK visa? I know Ireland still in Schengen but part of United Kingdom. Parental controls with different settings for different users Does anyone know of a good way to set up some sort of parental controls so that one user account is subject to them, but not another?  A couple of friends of mine use Ubuntu and have kids (7 to 10 years old) who use the family computer. They'd like to have some blocking of adult sites. They're not going to supervise all the time, which I know might be ideal, but there we go. And they're not particularly technical, so they don't want to have to run scripts to turn the parental controls on and off regularly, but they can cope with having different accounts for different people. I haven't found a great way of doing this. I am pretty technical, so I'm happy to spend some time at the command line to set it up, but then it needs to just work.  Please don't just link to DansGuardian. If your answer doesn't address the different user account aspect, I will vote it down. If you want to talk about general parental controls that apply to all users then please start a new question - I'm sure that plenty of people would be interested in it, and I'll link to it from this question. Enable HTTP DELETE requests on Apache server I need to configure my server to permit the http delete method.  currently, I get the following error when I attempt to make this call:    HTTP/1.1 405 Method Not Allowed Date: Mon, 11 Apr 2011 20:56:23 GMT Server: Apache/2.2.17 (Win32) PHP/5.3.5 Allow: GET,HEAD,POST,OPTIONS,TRACE Content-Length: 233 Keep-Alive: timeout=5, max=98 Connection: Keep-Alive Content-Type: text/html; charset=iso-8859-1     I have searched far and wide and have not been able to come up with an answer as to how I can configure the server to allow this request.  Someone please help as it has put a stop to my project. Alignment issue for the last modified information in the "Top Questions" page In the  (homepage), the asked/modified X mins ago text was left-aligned next to the tags. Previously the text was right-aligned. Seems some alignment issue introduced on that page recently. Screenshot for reference:      Configuration Version     Operating System Windows 10 Pro   Mozilla Firefox 89.0 (64-bit)   Google Chrome 91.0.4472.101 (Official Build) (64-bit)     Update: I see the same alignment issue in all other Stack Exchange site's &quot;Top Questions&quot; page too. Is a droid a ‘he/she’ or an ‘it’? Inspired by  question.  Are droids in the Star Wars universe referred to with gendered pronouns (i.e. he or she), or are they referred to as objects (i.e. it)? Help me to get command or ansibile Regex to fetch below details How large would the steam explosion at Chernobyl have been? So the  of the HBO series began to cover the  that led to them sending three divers into the water below the reactor to drain the tanks.  This occurred after the initial explosion that destroyed the reactor, and after the fire in the core had been put out. But at this point the decay heat and remaining fission reaction kept the core at more than 1200°C, causing it to melt through the concrete floors below the reactor.  And below the reactor were water tanks which contained 7,000 cubic meters of water (according to the TV show. If anyone has a real figure, I'd love to hear). When the lava of the melted core hit it, it would cause an enormous .  Finally, my question: About how large would this explosion have been? The character in the show says "2-4 megatons" (of TNT equivalent, I assume). I'm pretty sure this is absurd and impossible. But real estimates are hard to come by. Other sources vary wildly, some repeating the "megatons" idea, and others saying it would've "". This still seems crazy.  tl;dr:  I know a lot of it hinges on unknowns and the dynamics of the structures and materials involved, so I can simplify it to a constrained physics question:  Assuming 7,000 cubic meters of water instantly flashes to steam, how much potential energy is momentarily stored in that volume of steam occupying the same volume as the water did?  I don't know what to assume the temperature of the steam is. There were hundreds of tons of core material at temperatures near 1200°C, so worst case scenario you could assume all the steam becomes that temperature as the materials mix. Best case scenario, I guess we could assume normal atmospheric boiling point (100°C)? Is there a way to get trig functions without a calculator? In school, we just started learning about trigonometry, and I was wondering: is there a way to find the sine, cosine, tangent, cosecant, secant, and cotangent of a single angle without using a calculator?  Sometimes I don't feel right when I can't do things out myself and let a machine do it when I can't.  Or, if you could redirect me to a place that explains how to do it, please do so.  My dad said there isn't, but I just had to make sure.  Thanks. How to determine which lightdm greeter is in use? I am trying to hide Authoring information, Revision information, Publishing options tabs in create/edit node for any content type. I tried different modules with no luck. Please give me suggestions how to achieve this. Thanks a lot Why does the following code in C work?  const char* str = NULL; str = "test"; str = "test2";   Since str is a pointer to a constant character, why are we allowed to assign it different string literals?  Further, how can we protect str from being modified?  It seems like this could be a problem if, for example, we later assigned str to a longer string which ended up writing over another portion of memory.  I should add that in my test, I printed out the memory address of str before and after each of my assignments and it never changed.  So, although str is a pointer to a const char, the memory is actually being modified.  I wondered if perhaps this is a legacy issue with C? For a command, if using - as an argument in place of a file name will mean STDIN or STDOUT.   But in this example, it creates a file with the name -:  echo hello &gt; -   How can I make - in this example mean STDOUT? Conversely, how can I make - mean a file named - in examples such as:  cat -