Compactness & countable dense subset
Showing a compact metric space has a countable dense subset
Can't clean a full /boot because of unmet dependencies I got an error message explaining my /boot is full. trying to clean up old image files always seems to fail because of disk full errors or dependency errors. Could someone explain where I’m going wrong.   $ sudo apt-get autoremove Reading package lists... Done Building dependency tree        Reading state information... Done You might want to run ‘apt-get -f install’ to correct these. The following packages have unmet dependencies.  linux-image-extra-3.13.0-44-generic : Depends: linux-image-3.13.0-44-generic but it is not installed  linux-image-extra-3.13.0-45-generic : Depends: linux-image-3.13.0-45-generic but it is not installed  linux-image-generic : Depends: linux-image-3.13.0-45-generic but it is not installed E: Unmet dependencies. Try using -f.  $ ls /boot abi-3.13.0-32-generic         initrd.img-3.13.0-43-generic abi-3.13.0-36-generic         lost+found abi-3.13.0-37-generic         memtest86+.bin abi-3.13.0-39-generic         memtest86+.elf abi-3.13.0-40-generic         memtest86+_multiboot.bin abi-3.13.0-43-generic         System.map-3.13.0-32-generic config-3.13.0-32-generic      System.map-3.13.0-36-generic config-3.13.0-36-generic      System.map-3.13.0-37-generic config-3.13.0-37-generic      System.map-3.13.0-39-generic config-3.13.0-39-generic      System.map-3.13.0-40-generic config-3.13.0-40-generic      System.map-3.13.0-43-generic config-3.13.0-43-generic      vmlinuz-3.13.0-32-generic grub                          vmlinuz-3.13.0-36-generic initrd.img-3.13.0-32-generic  vmlinuz-3.13.0-37-generic initrd.img-3.13.0-36-generic  vmlinuz-3.13.0-39-generic initrd.img-3.13.0-37-generic  vmlinuz-3.13.0-40-generic initrd.img-3.13.0-39-generic  vmlinuz-3.13.0-43-generic initrd.img-3.13.0-40-generic   I used   kernelver=$(uname -r | sed -r 's/-[a-z]+//') dpkg -l linux-{image,headers}-"[0-9]*" | awk '/ii/{print $2}' | grep -ve $kernelver   to get   linux-headers-3.13.0-32 linux-headers-3.13.0-32-generic linux-headers-3.13.0-36 linux-headers-3.13.0-36-generic linux-headers-3.13.0-37 linux-headers-3.13.0-37-generic linux-headers-3.13.0-39 linux-headers-3.13.0-39-generic linux-headers-3.13.0-40 linux-headers-3.13.0-40-generic linux-headers-3.13.0-44 linux-headers-3.13.0-44-generic linux-headers-3.13.0-45 linux-headers-3.13.0-45-generic linux-image-3.13.0-32-generic linux-image-3.13.0-36-generic linux-image-3.13.0-37-generic linux-image-3.13.0-39-generic linux-image-3.13.0-40-generic   Then picking the first image to remove   $ sudo apt-get purge linux-image-3.13.0-32-generic Reading package lists... Done Building dependency tree        Reading state information... Done You might want to run 'apt-get -f install' to correct these: The following packages have unmet dependencies.  linux-image-extra-3.13.0-32-generic : Depends: linux-image-3.13.0-32-generic but it is not going to be installed  linux-image-extra-3.13.0-44-generic : Depends: linux-image-3.13.0-44-generic but it is not going to be installed  linux-image-extra-3.13.0-45-generic : Depends: linux-image-3.13.0-45-generic but it is not going to be installed  linux-image-generic : Depends: linux-image-3.13.0-45-generic but it is not going to be installed E: Unmet dependencies. Try 'apt-get -f install' with no packages (or specify a solution). How did Toru and Koji pass the entrance exam in My Hero Academia? I have seen some comments and speculations about the robot having an off switch or whatever. But I want to know if there is any source material or comment from the author on how they managed to pass the exam.  I have only seen the actual author's comment on Mineta:     But I was wondering if there are author notes for the other characters. What are some of the rule changes that Pathfinder brings in comparison to D&amp;D 3.5?  I am curious what changes were made so I can explain to my group what it has to offer. Early 80s anthology book about human kind being feared by other races in space I always thought the book was Manifest Destiny but its not. The story that sticks in my head was a human in a cage over a pit? Aliens walk in and discuss how dangerous humans were. He eventually escapes. Man I miss this book. wish I wouldve written down every book I ever read. Ugh How to find a starting point for root finding in complex plane? The function $f(x) = x^2 +1$ has zeros in the complex plane at $x = +i$ and $x = -i$. Is there a real starting point for complex Newton's method such that the iterates converge to either of these zeros? Is there a complex starting point too?  I know that Newton's method for finding roots is $x_{n+1} = x_n - \frac {f(x)}{f'(x)}$. But I don't know how to find the proper starting point. I have a virtual machine running ubuntu and I am trying to host some files on ubuntu and map the drive in windows PC.  Following the steps , I am able to see (from windows) the "work" folder after typing in \ubuntu_ip. But when trying to access or map it with "svc_acct" from windows, I get "0x80070043 error the network name cannot be found". I guess I am not accessing correctly from windows.   SAMBA config below (svc_acct is an account set up under linux). When accessing the folder from windows, I get prompted for username/password. Not sure what credential to type in exactly.  samba config: [work] path = /home/svc_acct/work valid users = svc_acct available = yes read only = no browsable = yes public = yes writable = yes force user = svc_acct create mask = 0777 directory mask = 0777   UPDATE:  All I did to resolve this is by changing samba config's path from path = /home/svc_acct/work to path = /home/svc_acct following  post  (last sentence). Then no more prompt for password in windows when I try to click into the folder. Thanks to @sancho.s for suggesting the link. Why can't photons have a mass? Why can't photons have a mass? Could you explain this to me in a short and mathematical way? 3-manifold examples of homomorphisms between fundamental groups that are not induced by continuous maps Count days between two dates, excluding weekends (MySQL only) WiFi problems (Atheros driver) with FreeBSD 11 With FreeBSD 10.3 my Atheros card worked fine and showed up as /dev/ath0. Now with FreeBSD 11 this is no longer the case, though the module is loaded and it seems the system recognizes the card:  root@igloo:~ # sysctl net.wlan.devices net.wlan.devices: ath0   Still, ath0 cannot be used:  root@igloo:~ # ifconfig wlan0 create wlandevice ath0 ifconfig: must specify a parent device (wlandev) when creating   What must I do to use the card? How do I disable search-as-you-type text in Ubuntu 17.10 and later? I cannot find enable-interactive-search in    gsettings set org.gnome.nautilus.preferences enable-interactive-search true.     I searched using    gsettings list-recursively | grep search     and    gsettings list-recursively | grep interactive     but no such option.  Can you help me disable this in Ubuntu 17.10 and later? Performing multiple layer intersection in QGIS? ASP.NET "special" tags What is the official name for the "special" ASP.NET tags like this:  &lt;%# %&gt; &lt;%= %&gt; &lt;%@ %&gt; &lt;%$ %&gt;   I can't seem to figure out the conceptual or well known name for these, so I'm having trouble searching for more info.  As a bonus, can anyone give me a quick rundown of all of the possible "special tags" and what each one of them does (or point me to a resource)? How can I check if a word is contained in another string using PHP? Is there any matrix $2\times 2$ such that $A\neq I$ but $ A^3=I$? Is there any $2 \times 2$ matrix $A \neq I$ such that $A^3=I$?  In my opinion: no. Thank you very much. SQL Server 2008 server cannot connect to itself with alias name or "localhost" We have a SQL Server 2008 ENT 64bit SP3 server running Server 2008 R2 Standard SP1 64-bit.  This is also a windows/sql clustered environment.  There is the cluster alias for the server, and then we have 2 AD DNS aliases as well for the server  Suddenly I can't connect to the sql instance in Management Studio, or with a Powershell Invoke-SQLcmd IF I am doing it from that actual server, when using one of the dns alias names, or "localhost".  If I use the Cluster alias name it works and if I use the other dns alias name it works.  Using management studio with the non-working dns alias I get "Login failed. The login is from an untrusted domain and cannot be used with Windows authentication."  If I use localhost, I get "A network-related or instance-specific error occurred while establishing a connection to SQL Server. The server was not found or was not accessible. Verify that the instance name is correct and that SQL Server is configured to allow remote connections. (provider: Named Pipes Provider, error: 40 - Could not open a connection to SQL Server) (Microsoft SQL Server, Error: 2)"    Shared Memory and TCPIP are enabled in SQL Server Config manager but named pipes is not.  But we've NEVER had named pipes enabled, and don't have it enabled on any of our other sql servers and they're set up the same (clustering, dns aliases...etc) and are having no issues.  I've Googled around and had a view people suggest listing what other SQL servers it can see (cmd prompt sqlcmd -L)  If it do it from a good server I see all other servers on my network including the "bad" one.  If I do that command from the "bad" server, I get no results at all.  Pretty much checked everything from this blog and it's all ok except the sqlcmd -L issue I just mentioned above.    Windows firewall is not enabled.  This was working just fine for a couple of years.  I'm not sure when this started happening, but I know that at some point, it was not happening.  And the other kicker...it's only happening locally to this server.  If I connect with management studio or run a powershell Invoke-Sqlcmd from another machine, or my local machine connecting to the "bad" server, it works fine no matter what alias I use.  I'm stumped.  I think it sounds like an issue with the AD alias (there are 2 ad aliases, 1 works locally the other doesn't)...but not being able to connect with localhost makes me question that.  any help is greatly appreciated. Proof that $1729$ is the smallest taxicab number Isomorphism between $\mathbb{C}^* $ under multiplication with $\mathbb{C}$ under addition. Does there exists an Isomorphism between $\mathbb{C}^* $ under multiplication with $\mathbb{C}$ under addition.  Attempt In my opinion It does not exists.  If there exists such an isomorphism say $\phi :\mathbb{C}^* \to \mathbb{C}$ then, from the fact that Isomorphism takes identity to identity we have $$\phi \left( 1 \right)=0$$  From the fact      Given $\phi:G \to H$ be an isomorphism, then For a fixed integer $k$ and a fixed group element $b$ in $G$, the   equation $x^k=b$ has the same number of solutions in $G$ as does   the equation $x^k=\phi\left(b\right)$ in $H$.   We have $x^4=1$ and $x^4=0$ must have same number of solutions, but the solutions to these equations are 4 and 1 only. How to plot a surface from a set of data? Disclaimer: I already read questions like  and  but these did not solve my problem.  I have this set of data:  x       y       z 2.17    0.001   0.82044815 2.17    0.002   0.82345825 2.17    0.004   0.82679255 2.17    0.008   0.83334715 2.17    0.016   0.84395915 2.17    0.032   0.8584953 2.21    0.001   0.77582165 2.21    0.003   0.78520505 2.21    0.009   0.80205985 2.21    0.027   0.83085105 2.24    0.001   0.7227885 2.24    0.002   0.73391615 2.24    0.005   0.7543979 2.24    0.015   0.78798745 2.24    0.003   0.74176635 2.24    0.009   0.77064805 2.24    0.027   0.81042375 2.26    0.001   0.66545585 2.26    0.003   0.7012046 2.26    0.005   0.721067 2.26    0.009   0.7447984 2.26    0.015   0.76715245 2.26    0.027   0.794177 2.27    0.001   0.62916195 2.27    0.003   0.6774642 2.27    0.009   0.72961785 2.27    0.027   0.7861086 2.28    0.001   0.5750828 2.28    0.003   0.65059675 2.28    0.005   0.6802631 2.28    0.009   0.7145367 2.28    0.015   0.74447695 2.28    0.027   0.7774403 2.29    0.001   0.51357255 2.29    0.002   0.581053 2.29    0.003   0.6173075 2.29    0.009   0.6972096 2.29    0.027   0.76793225 2.31    0.001   0.36997965 2.31    0.002   0.474415 2.31    0.003   0.53649295 2.31    0.009   0.6587164 2.31    0.016   0.70870255 2.31    0.027   0.7482423 2.31    0.05    0.7912395 2.34    0.001   0.2204104 2.34    0.002   0.316308 2.34    0.003   0.39256745 2.34    0.004   0.45240835 2.34    0.009   0.5883453 2.34    0.016   0.6590771 2.34    0.027   0.71444205 2.34    0.05    0.7690014 2.38    0.001   0.13286995 2.38    0.002   0.1828288 2.38    0.004   0.2980268 2.38    0.008   0.4507145 2.38    0.016   0.58417075 2.38    0.032   0.6833616   And if I plot it in Mathematica (with ListPlot3D[data]) it looks, without further tweaking and fiddling around, like:    But if I try this pgfplots code  \begin{tikzpicture}   \begin{axis}     \addplot3 [surf] table {data.txt};   \end{axis} \end{tikzpicture}   I only get this:    What do I have to do to get a surface like in Mathematica (color, smoothness, style, etc. does not matter, just a closed surface)? I have to submit a manuscript to a journal, and I just realized that they want every single part of the paper to be in 12 pt font. This includes tables text, footnotes, acknowledgements etc. Is there a way to force all text to be the same size?