Is this set dense on the positive half of the real line?
Are fractions with prime numerator and denominator dense?
What does "if not" mean in the given sentence Let there be given this sentence (which came from an ):     The contest has become personalised, if not bitter.   Then what does the phrase if not mean?   Seeking after is a general guide or rule of such usage. I could not install my modem driver so I have to update and install applications offline. For this I want to use keryx but to install keryx, Python and wxPython have to be installed first. So how do I install Python and wxPython offiline on Ubuntu 13.04?  Note : I don't have internet connection in Ubuntu. So I'll have to download the required file from my Windows 7. So, I know that there is a race in Lord of the Rings of Peredhil  (half elf). Also, in the Hobbit (film trilogy, not book), there is a romance between a dwarf and an elf.  My question is, how do man/elf or dwarf/elf offspring work? Can they not be born? Are they born infertile because they are from parents of two different species? Are elves, dwarves, and men only different "races" of one single primordial species, and can thus reproduce any number of ways? To my knowledge, this isn't addressed in the books or films. Duplicity Backup Browse I have made a duplicity backup with Ubuntu 14.04 in another laptop of my home directory.  I copied all duplicity back files to my current laptop to "/home/user/Ubuntu-backup"  How do i browse the content of that backup see if it is worth restoring? I want to restore how do i restore from those files. Are common cryptographic hashes bijective when hashing a single block of the same size as the output? Can command substitution be nested in variable substitution? Irreducible Components of the Prime Spectrum of a Quotient Ring and Primary Decomposition Dropping Internet connection on Realtek Semiconductor Co., Ltd. RTL8821AE I have continuous problems of network dropping connections on wifi with ubuntu 16.04, I have an ASUS R510J, this is my network card:  ##### lspci #############################  03:00.0 Network controller [0280]: Realtek Semiconductor Co., Ltd. RTL8821AE 802.11ac PCIe Wireless Network Adapter [10ec:8821]         Subsystem: AzureWave RTL8821AE 802.11ac PCIe Wireless Network Adapter [1a3b:2161]         Kernel driver in use: rtl8821ae  04:00.1 Ethernet controller [0200]: Realtek Semiconductor Co., Ltd. RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller [10ec:8168] (rev 12)         Subsystem: ASUSTeK Computer Inc. RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller [1043:200f]         Kernel driver in use: r8169   sudo service network-manager restart doesnt's help, as I never regain internet connection after it drops, and I have to restart the PC. On Ethernet cable I have no problem.  What do you think is the issue? drivers?  thank you Is it feasible to transform each variable differently while doing multiple regression Command prompt as SYSTEM user (Windows 7) How can I get a command prompt as the SYSTEM user on Windows&nbsp;7?  Context: I'm testing a computer startup script, and I need to figure out the behavior of a command when run as SYSTEM rather than my user account.  I've seen ways to do this with at and psexec, but those methods only appear to work on Windows&nbsp;XP or Windows&nbsp;Vista.  I'm using Windows&nbsp;7 Pro SP1. resizable serial console window? I'm trying to determine if 1317 and 116 can be written as the sum of three squares?  I have the condition that if it is not of the form $4^{\alpha}(8k+7)$ then it can be written as a sum of three squares, but how do I use this condition to work it out?  Thank you A clock near the surface of the earth will run slower than one on the top of the mountain.  If the equivalence principal tells us that being at rest in a gravitational field is equivalent to being in an accelerated frame of reference in free space, shouldn't the clock near the earth run increasingly slower than the other clock over time?  If those two clocks are considered to be in two different frames of acceleration, the one near the earth will have a greater acceleration than the one on the mountain, and thus over time, their relative velocity will increase over time which will increase the time dilation.  Or is this not a proper use of the equivalence principle? I need to prove that the center of $A_n$ is trivial for $n \geq 4$.  $Z(A_3) = A_3$, since $A_3 = \mathbb{Z}/3\mathbb{Z}$ is commutative.  One idea is two use "counting" technique. First of, all we count cojugacy classes of even permutations in $S_n$. It's the classes correspodning to the types $[\lambda_1, ..., \lambda_r]$ where $n \equiv r \mod 2$  Now, the conjugacy class in $S_n$ correspoding to the type $[\lambda_1, ..., \lambda_r]$ splits into two equal-sized classes in $A_n$ if $\lambda_1, ..., \lambda_r$ are distinct odd numbers. If they aren't then it is preserved in $A_n$.  Then we can use "the counting formula"(  ) of elements in each "even" class of $S_n$ and divide one by $2$ if needed.  Still, I'm not sure if it can be done. Seems to be a lot of work there. Maybe there are other, he easier ways? Or, maybe, it is the way, in this case, I wouild appreciate any advices. If the distribution of test statistic is bimodal, does p-value mean anything? Pros and cons of AppSettings vs applicationSettings (.NET app.config / Web.config) When developing a .NET Windows Forms Application we have the choice between those App.config tags to store our configuration values. Which one is better?  &lt;configuration&gt;    &lt;!-- Choice 1 --&gt;   &lt;appSettings&gt;     &lt;add key="RequestTimeoutInMilliseconds" value="10000"/&gt;   &lt;/appSettings&gt;    &lt;!-- Choice 2 --&gt;   &lt;configSections&gt;     &lt;sectionGroup name="applicationSettings" type="System.Configuration.ApplicationSettingsGroup, System, Version=2.0.0.0, Culture=neutral, PublicKeyToken=b77a5c5612342342" &gt;         &lt;section name="Project1.Properties.Settings" type="System.Configuration.ClientSettingsSection, System, Version=2.0.0.0, Culture=neutral, PublicKeyToken=b77a5c5612342342" requirePermission="false" /&gt;     &lt;/sectionGroup&gt;   &lt;/configSections&gt;   &lt;applicationSettings&gt;     &lt;Project1.Properties.Settings&gt;       &lt;setting name="TABLEA" serializeAs="String"&gt;         &lt;value&gt;TABLEA&lt;/value&gt;       &lt;/setting&gt;     &lt;/Project1.Properties.Settings&gt;   &lt;/applicationSettings&gt;  &lt;/configuration&gt; What is the normal operating temperature for the MacBook (2016 generation)? I'm a C++ newbie, but I wasn't able to find the answer to this (most likely trivial) question online.  I am having some trouble compiling some code where two classes include each other.  To begin, should my #include statements go inside or outside of my macros?  In practice, this hasn't seemed to matter.  However, in this particular case, I am having trouble.  Putting the #include statements outside of the macros causes the compiler to recurse and gives me "#include nested too deeply" errors.  This seems to makes sense to me since neither class has been fully defined before #include has been invoked.  However, strangely, when I try to put them inside, I am unable to declare a type of one of the classes, for it is not recognized.  Here is, in essence, what I'm trying to compile:  A.h  #ifndef A_H_ #define A_H_  #include "B.h"  class A {     private:         B b;      public:         A() : b(*this) {} };  #endif /*A_H_*/   B.h  #ifndef B_H_ #define B_H_  #include "A.h"  class B {     private:             A&amp; a;      public:         B(A&amp; a) : a(a) {}  };  #endif /*B_H_*/   main.cpp  #include "A.h"  int main() {     A a; }   If it makes a difference, I am using g++ 4.3.2.  And just to be clear, in general, where should #include statements go?  I have always seen them go outside of the macros, but the scenario I described clearly seems to break this principle.  Thanks to any helpers in advance!  Please allow me to clarify my intent if I have made any silly mistakes! I've asked several questions about 4th Edition D&amp;D because I may be able to start a game. However, I'd need to purchase (some) materials. I am aware of the 4 book set (core) and the expected Essentials Red Box.  So now I need to know: presumably buying either the 4 book set or essentials will be enough to get my game on. Would there be something 'lacking' though? Would I be missing character types, for instance, as I've seen that the splatbook strategy is still in effect?  I'm an experienced player and GM and plenty creative, so many holes I'd be able to fill in myself. I just don't want to get sucked into too much financial impact. Order of some quotient ring of Gaussian integers