Show that $L^{\infty}$ space does not have a countable dense set.
Why is $L^{\infty}$ not separable?
Lualatex and bm package I've updated my latex packages yesterday and have now issues with lualatex. One problem arising for me now is, that lualatex does not print bold characters using the bm package.  When I compile the following MWE with pdflatex everything looks okay, but for lualatex it doesn't:  \documentclass{article} \usepackage{bm} \begin{document} % Bold $\bm{E}$ \\ Normal $E$ % \end{document}   Output using pdflatex    using lualatex    Also trying to fall back to an earlier version of lualatex by using \RequirePackage{luatex85} does not work for me.  When having a look at the log file, there are the suspicious messages   LaTeX Font Info:    Redeclaring math alphabet \mathbf on input line 142. LaTeX Info: Redefining \bm on input line 208. [...] Missing character: There is no х (U+0445) in font cmmi10!   Can anyone tell me, what is going on here and what I need to do to solve this problem, since I am quite sure lualatex and bm worked before? Software Tester Skill Matrix with Levels I would like to know if there's a standard Skill set for Skill Matrix for a Software Tester of different levels, like for example, what are the skills needed for an Entry level tester as well as what technologies and responsibilities he needs. And for the Mid Level tester and Senior Level as well.  Note that I am working in a company who designs and develops websites. This is an old problem that deserves a bugfix, but it's getting beyond a joke now and I can't seem to work around it.  I keep getting the dreaded failed To download extra data files error in relation to ttf-mscorefonts-installer:    Repeatedly asking it to try again doesn't help, additionally, repeatedly trying-  sudo rm -rf /var/lib/update-notifier/package-data-downloads/partial/* sudo apt-get --purge --reinstall install ttf-mscorefonts-installer   Isn't working either.  I just get at least one 404 error from one of the sourceforge links that stops it working-  Reading package lists... Done Building dependency tree        Reading state information... Done 0 to upgrade, 0 to newly install, 1 reinstalled, 0 to remove and 20 not to upgrade. Need to get 0 B/29.5 kB of archives. After this operation, 0 B of additional disk space will be used. Preconfiguring packages ... (Reading database ... 352049 files and directories currently installed.) Preparing to unpack .../ttf-mscorefonts-installer_3.4+nmu1ubuntu2_all.deb ... mscorefonts-eula license has already been accepted Unpacking ttf-mscorefonts-installer (3.4+nmu1ubuntu2) over (3.4+nmu1ubuntu2) ... Processing triggers for fontconfig (2.11.94-0ubuntu1.1) ... Processing triggers for update-notifier-common (3.168.2) ... ttf-mscorefonts-installer: processing... ttf-mscorefonts-installer: downloading http://downloads.sourceforge.net/corefonts/andale32.exe Get:1 http://downloads.sourceforge.net/corefonts/andale32.exe [198 kB] Fetched 198 kB in 0s (339 kB/s)                                                 W: Can't drop privileges for downloading as file '/var/lib/update-notifier/package-data-downloads/partial/andale32.exe' couldn't be accessed by user '_apt'. - pkgAcquire::Run (13: Permission denied) ttf-mscorefonts-installer: downloading http://downloads.sourceforge.net/corefonts/arial32.exe Get:1 http://downloads.sourceforge.net/corefonts/arial32.exe [554 kB] Fetched 554 kB in 0s (575 kB/s)                                                 W: Can't drop privileges for downloading as file '/var/lib/update-notifier/package-data-downloads/partial/arial32.exe' couldn't be accessed by user '_apt'. - pkgAcquire::Run (13: Permission denied) ttf-mscorefonts-installer: downloading http://downloads.sourceforge.net/corefonts/arialb32.exe Get:1 http://downloads.sourceforge.net/corefonts/arialb32.exe [168 kB] Fetched 168 kB in 0s (306 kB/s)                                                 W: Can't drop privileges for downloading as file '/var/lib/update-notifier/package-data-downloads/partial/arialb32.exe' couldn't be accessed by user '_apt'. - pkgAcquire::Run (13: Permission denied) ttf-mscorefonts-installer: downloading http://downloads.sourceforge.net/corefonts/comic32.exe Err:1 http://downloads.sourceforge.net/corefonts/comic32.exe   404  Not Found W: Can't drop privileges for downloading as file '/var/lib/update-notifier/package-data-downloads/partial/comic32.exe' couldn't be accessed by user '_apt'. - pkgAcquire::Run (13: Permission denied) E: Failed to fetch https://netix.dl.sourceforge.net/project/corefonts/the fonts/final/comic32.exe  404  Not Found  E: Download Failed Setting up ttf-mscorefonts-installer (3.4+nmu1ubuntu2) ...   The specific point at which it fails to download changed - it seems to be a sourceforge reliability problem, but this has now been going on weeks and results in annoying popups as above all the time.  How do we get this fixed and/or how can I work around it for now. Variation of the metric with respect to the metric For a variation of the metric $g^{\mu\nu}$ with respect to $g^{\alpha\beta}$ you might expect the result (at least I did):  \begin{equation} \frac{\delta g^{\mu\nu}}{\delta g^{\alpha\beta}}= \delta^\mu_\alpha\delta^\nu_\beta. \end{equation}  but then to preserve the fact that $g^{\mu\nu}$ is symmetric under interchange of $\mu$ and $\nu$ we should probably symmetrise the right hand side like this:  \begin{equation}\frac{\delta g^{\mu\nu}}{\delta g^{\alpha\beta}}= \delta^\mu_\alpha\delta^\nu_\beta + \delta^\mu_\beta\delta^\nu_\alpha.\end{equation}  Is this reasonable/correct? If not, why not?  It seems that I can derive some weird results if this is right (or maybe I'm just making other mistakes). How do I make a WinForms app go Full Screen I have a WinForms app that I am trying to make full screen (somewhat like what VS does in full screen mode).  Currently I am setting FormBorderStyle to None and WindowState to Maximized which gives me a little more space, but it doesn't cover over the taskbar if it is visible.  What do I need to do to use that space as well?  For bonus points, is there something I can do to make my MenuStrip autohide to give up that space as well? Converting HTML to plain text in PHP for e-mail What happens when a photon hits a beamsplitter? Yesterday I read that we can affect the path and the 'form' (particle or wave) of a photon after the fact ().  Part of what is puzzling me is the beam-splitter. Are the individual photons actually being split into two new photons of lesser energy?  This  implies that you cannot split a photon but it seems that beam splitters do exactly that. Unable to lock the administration directory (/var/lib/dpkg/), are you root? I get this error in Lubuntu 12.04 when I try to update in terminal:  $ apt-get update E: Could not open lock file /var/lib/apt/lists/lock - open (13: Permission denied) E: Unable to lock directory /var/lib/apt/lists/ E: Could not open lock file /var/lib/dpkg/lock - open (13: Permission denied) E: Unable to lock the administration directory (/var/lib/dpkg/), are you root? After a very long time will we see more stars (due to the fact that more light is get to us) or less stars (as the universe expends and light have to pass larger distance)? In general, can stellar objects go outside of the scope of the observable universe or is it only growing with time? Calculations are always better than just discussion. Does it have any connection to dark matter? Prove that matrix can be square of matrix with real entries Prove that matrix   \begin{bmatrix}1&amp;0&amp;0\\0&amp;-1&amp;0\\0&amp;0&amp;-1\end{bmatrix}  can be square of matrix with all real entries.  I have found one such matrix to be   \begin{bmatrix}1&amp;0&amp;0\\0&amp;1&amp;-1\\0&amp;2&amp;-1\end{bmatrix} but is there an elegant way to do it without any trial and error? For symmetric stable distributions, why is $\alpha \le 2$? "Contact us"... and then what? So I had a dispute with the moderators at a specific SE site. As a result, I got suspended there. As per SE guidelines, I pressed the "Contact us" button and wrote to the higher powers to appeal.  That was 5-6 weeks ago. There was zero feedback, neither positive, nor negative, not even "it's in progress, please wait".  So what is this "contact us" thing supposed to do? Is it a placebo to make me feel better while being routed to dev/null?  What is the normal time it takes to process a "contact us" message?  Notes:   As far as I remember, I did not contact the team before. I'm a longtime user of multiple SE sites and never had any problems except for that one site. I'm pretty sure my form was submitted. I didn't make screenshots or anything, because I did not think I would need them in a post like this. I didn't expect a super-fast reply either, so I wasn't wondering after a week or two. Orange squares appearing on render? I'm trying to render a scene in Blender, and as of yesterday (it was not doing this when I was working on it 2-3 days ago), I am seeing orange squares dancing around the rendered image. Google tells me that these are render tiles (I think), but what are they, why are they there, and how do I get rid of them? Execute Java from command line "Planar" graphs on Möbius strips When saving a .qgs file in QGIS, another appears. Is this a backup? When saving a project file (.qgs), which when executed is automatically loaded with qgis.bat, there's another .qgs file which appears in the same directory of the original project file, although this one is not loaded with the qgis.bat file:    This is just out of curiosity but is the latter designed to be a backup of the original .qgs file? How do I disable the guest session? I entered the USA on a three month visa waiver program from Australia. I am about to return to  Australia and would like to come back again to the USA. How long do I have to wait until I can re-enter the USA for another 3 months? What is the name of the first decade in a century? 80s: the "Eighties"   90s: the "Nineties"   00s: the ???   For that matter, what is the second decade called? The "tens" just doesn't sound right. Can I have a hint on how to construct a ring $A$ such that there are $a, b \in A$ for which $ab = 1$ but $ba \neq 1$, please? It seems that square matrices over a field are out of question because of the determinants, and that implies that no faithful finite-dimensional representation must exist, and my imagination seems to have given up on me :)