Prove that there exists a monotone nondecreasing function $f:[0,1] \rightarrow \mathbb{R}$ discontinuous in rationals of $[0,1]$   I tried to test functions of the type  $$ f(x)=\begin{cases} \frac{1}{q} &amp; \text{if } x=\frac{p}{q} \mid p,q \in \mathbb{Z}^+ \,\,\, \text{and} \,\,\, \gcd(p,q)=1  \\ x &amp; \text{if } x \not\in \mathbb{Q} \end{cases}$$ which is discontinuous in all rationals, but is not monotone.
I have really no idea about this:  Problem: Show that there exists a function $f:[0,1]\rightarrow\mathbb{R}$ such that:  $f$ is discontinuous in all $x\in \mathbb Q$. $f$ is increasing in $[0,1]$. $f$ is integrable.   EDIT: Sorry, it is not discontinuous in all $x\in \mathbb R \setminus \mathbb Q$, just in $\mathbb Q$.
Where do I get the key for the first house? How do I remove a property from a JavaScript object? There is already a similar post, that has an answer to my question, but it is quite short and I don't get it... So I am trying to show that  \begin{align} \{e_K |~ K \subset G~ conjugacy~ class \} \end{align} is a basis for $Z(\mathbb{Z}[G])$. Serre even writes "one immediately checks that the $e_K$ form a basis", but even reading the other post  I don't see that...  My approach to this is:  Be $x \in Z(\mathbb{Z}[G])$, which is equivalent to: $x = gxg^{-1}$ for all $g \in G$. Writing  $x = \sum\limits_{h \in G} \lambda_h h$, we get $x = \sum\limits_{h \in G} \lambda_h ghg^{-1}$. I don't really know how to go on at this point. I mean, I know that when $a,b \in K$ (same conjugacy class) you get $\sum\limits_{s \in K} \mu_s s = \mu\sum\limits_{s \in K} s$, since \begin{align} a = hbh^{-1} \Rightarrow \mu_a = \mu_b ~\forall a,b\in K \end{align} So all elements in the same conjugacy class have the same scalar.  But from here I don't really know how I can generate the $x = \sum\limits_{h \in G} \lambda_h ghg^{-1}$ with the $e_K$ ...  I would be really thankful, if someone could give me quite a basic proof that even I understand... I am using Ubuntu 12.04.  My /etc/network/interfaces file consists of:    # The loopback network interface   auto lo   iface lo inet loopback     # The primary network interface   auto eth0  iface eth0 inet static   address 192.168.1.58   gateway 192.168.1.1 network 192.168.1.0   broadcast 192.168.1.255 dns-nameservers 66.212.63.228 66.212.48.10     I ran the command: /etc/init.d/networking restart  Which responded with:   *Running /etc/init.d/networking restart is deprecated because it may not enable again some interfaces   *Reconfiguring network interfaces...   RTNETLINK answers: File exists   Failed to bring up eth0   [ OK ]     Next I ran ping google.com and received:    ping: unknown host google.com   I am not sure if my interfaces refreshed. How do I properly configure my network with my static DNS addresses? Read a file backwards line by line using fseek pgfplots fillbetween with multiple curves I have a TikZ picture like this:  \begin{tikzpicture}   \begin{axis}[     axis lines=middle,     xmin=-0.5,xmax=3.5,ymin=-0.5,ymax=3.5   ]   \addplot[very thick,blue, samples=300, domain=0:3, name path=A] {sqrt(x)};    \addplot[very thick,yellow!70!red, samples=300, domain=0:3, name path=B] {9-3*x};    \addplot[very thick,red!90!teal, samples=300, domain=0:3, name path=C] {3};    \addplot[very thick,green!70!magenta, samples=300, domain=0:3, name path=D] coordinates{(1/9,-6) (1/9,6)};   \end{axis} \end{tikzpicture}     I’d like to fill the area enclosed by these four curves.  Similar questions have been answered using pgfplots’s fillbetween package, but it only seems to support filling between two curves. What are my options? Around 3 months ago, I submitted a paper to a Math journal for peer-review through an online submission system. The same day I received in my e-mail an acknowledgement saying that the paper had been received.  The problem is that the status of the paper on the online submission system is still "Manuscript submitted".  I think this means that the paper has not even been assigned to an editor yet (once this happens, the editor will probably start looking for reviewers), but as far as I know submissions are assigned to editors within a few weeks (I once submitted a paper to another journal and when an editor had been assigned, the status on the online system changed to "Editor handles" or something like that).  I know that publishing is a long and complicated process and I'm not trying to rush anybody, but sometimes manuscripts are lost in the system. In fact, this has once happened to me, so I just want to make sure that the paper was not lost in the system.  Should I send an e-mail asking for the status of the paper?  PS: I think that, at the time of submitting the paper, I didn't choose any specific editor to submit the paper to. Numbering side-by-side equations or inline equations Compact way to assign values by slicing list in Python How do I remove login credentials (emails or OpenIDs) from my account?     For more information, see "" in the . How do I test a private function or a class that has private methods, fields or inner classes? How do I unit test (using xUnit) a class that has internal private methods, fields or nested classes? Or a function that is made private by having  (static in C/C++) or is in a private () namespace?  It seems bad to change the access modifier for a method or function just to be able to run a test. Note: If you're looking for a simple explanation as to why comments aren't required on downvotes, see .   I used to get "upset" (though that is too strong a term) when I got downvoted without comment. If my answer isn't good enough then I'd like to know why. Not only does it improve the answer for the OP but it improves my knowledge too.  Where the down-vote has been explained I've found it useful &amp; it has improved my answer, or forced me to delete the answer if it was totally wrong.  So is there any way we can encourage people to leave a comment? Perhaps they don't lose rep if they explain their down-vote?  I must admit though that I haven't always explained my down-vote either so you could call me a hypocrite. I've also grown a thicker skin over the months of using SO (it seems to have come with the higher rep score ;-)), so I'm less bothered about this now. Could not load file or assembly 'System.Web.Mvc' My new ASP.NET MVC Web Application works on my development workstation, but does not run on my web server...    Server Error in '/' Application.    Configuration Error  Description: An error occurred during the processing of a configuration file required to service this request. Please review the specific error details below and modify your configuration file appropriately.     Parser Error Message: Could not load file or assembly 'System.Web.Mvc, Version=1.0.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35' or one of its dependencies. The system cannot find the file specified.    Source Error:    Line 44:         &lt;add assembly="System.Web.Abstractions, Version=3.5.0.0, Culture=neutral, PublicKeyToken=31BF3856AD364E35"/&gt; Line 45:         &lt;add assembly="System.Web.Routing, Version=3.5.0.0, Culture=neutral, PublicKeyToken=31BF3856AD364E35"/&gt; Line 46:         &lt;add assembly="System.Web.Mvc, Version=1.0.0.0, Culture=neutral, PublicKeyToken=31BF3856AD364E35"/&gt; Line 47:         &lt;add assembly="System.Data.DataSetExtensions, Version=3.5.0.0, Culture=neutral, PublicKeyToken=B77A5C561934E089"/&gt; Line 48:         &lt;add assembly="System.Xml.Linq, Version=3.5.0.0, Culture=neutral, PublicKeyToken=B77A5C561934E089"/&gt;   Source File: C:\inetpub\www.example.org\web.config    Line: 46    Assembly Load Trace: The following information can be helpful to determine why the assembly 'System.Web.Mvc, Version=1.0.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35' could not be loaded.     WRN: Assembly binding logging is turned OFF. To enable assembly bind failure logging, set the registry value [HKLM\Software\Microsoft\Fusion!EnableLog] (DWORD) to 1. Note: There is some performance penalty associated with assembly bind failure logging. To turn this feature off, remove the registry value [HKLM\Software\Microsoft\Fusion!EnableLog].     Version Information: Microsoft .NET Framework Version:2.0.50727.3053; ASP.NET Version:2.0.50727.3053    Do I need to install the AspNetMVCBeta-setup.msi on the server?  Or is there a different installer for servers? Intel Corporation Device [8086:0d4f] is not supported on Ubuntu 18.04.3 I am currently unable to install ubuntu server 18.04.03 LTS on the latest intel NUC10i7FNH.  Ubuntu always states both network adapters as unclaimed. The previous version (NUC8i7BEH) has the same network controller I219-V and worked like a charm.  *-network:0 UNCLAIMED      description:  Network controller      product: Intel Corporation      vendor: Intel Corporation      physical id: 14.3      ...   Without network it is not even possible to follow most suggestions how to get it enabled, because it is impossible to fetch new packages from internet.  Here are some more information as requested:  The output from: modprobe -v e1000e &amp;&amp; dmesg | grep e10   [ 3447.889394] e1000e: Intel(R) PRO/1000 Network Driver - 3.2.6-k [ 3447.889395] e1000e: Copyright(c) 1999 - 2015 Intel Corporation.   The output from: sudo lspci -knn  00:1f.6 Ethernet controller [0200]: Intel Corporation Device [8086:0d4f]     Subsystem: Intel Corporation Device [8086:2081] 01:00.0 PCI bridge [0604]: Intel Corporation JHL7540 Thunderbolt 3 Bridge [Titan Ridge 2C 2018] [8086:15e7] (rev 06)    For me this looks somehow, as the kernal driver would not be in use :-/  Here are a few more information i got from playiung around with 19.10 desktop version.  [    0.000000] Linux version 5.3.0-29-generic (buildd@lcy01-amd64-024) (gcc version 9.2.1 20191008 (Ubuntu 9.2.1-9ubuntu2)) #31-Ubuntu SMP Fri Jan 17 17:27:26 UTC 2020 (Ubuntu 5.3.0-29.31-generic 5.3.13)   output from lshw:    *-network:0        Beschreibung: Kabellose Verbindung        Produkt: Intel Corporation        Hersteller: Intel Corporation        Physische ID: 14.3        Bus-Informationen: pci@0000:00:14.3        Logischer Name: wlp0s20f3        Version: 00        Seriennummer: c8:09:a8:9c:cd:e0        Breite: 64 bits        Takt: 33MHz        Fähigkeiten: pm msi pciexpress msix bus_master cap_list ethernet physical wireless        Konfiguration: broadcast=yes driver=iwlwifi driverversion=5.3.0-29-generic firmware=48.4fa0041f.0 ip=192.168.178.109 latency=0 link=yes multicast=yes wireless=IEEE 802.11        Ressourcen: iomemory:600-5ff irq:16 memory:6023114000-6023117fff   The output from: modprobe -v e1000e &amp;&amp; dmesg | grep e10  [    2.357430] e1000e: Intel(R) PRO/1000 Network Driver - 3.2.6-k [    2.357430] e1000e: Copyright(c) 1999 - 2015 Intel Corporation. [    2.357616] e1000e 0000:00:1f.6: Interrupt Throttling Rate (ints/sec) set to dynamic conservative mode [    2.562796] e1000e 0000:00:1f.6 0000:00:1f.6 (uninitialized): registered PHC clock [    2.634139] e1000e 0000:00:1f.6 eth0: (PCI Express:2.5GT/s:Width x1) 1c:69:7a:60:44:f0 [    2.634140] e1000e 0000:00:1f.6 eth0: Intel(R) PRO/1000 Network Connection [    2.634258] e1000e 0000:00:1f.6 eth0: MAC: 13, PHY: 12, PBA No: FFFFFF-0FF [    2.634991] e1000e 0000:00:1f.6 eno1: renamed from eth0 [    5.103285] checking generic (4000000000 e10000) vs hw (4000000000 10000000) [   15.806697] e1000e: eno1 NIC Link is Up 1000 Mbps Full Duplex, Flow Control: None    output from lspci:  00:1f.6 Ethernet controller [0200]: Intel Corporation Ethernet Connection (10) I219-V [8086:0d4f]     DeviceName:  LAN     Subsystem: Intel Corporation Ethernet Connection (10) I219-V [8086:2081]     Kernel driver in use: e1000e     Kernel modules: e1000e What is the precise definition of a rigid shape? If a measure only assumes values 0 or 1, is it a Dirac's delta? Having problems with listings and UTF-8. Can it be fixed? I'm having some problems with listings and UTF-8 in my document. Maybe someone can help me? Some characters work, like é and ó, but á and others appear at the beginning of words...  \documentclass[12pt,a4paper]{scrbook} \KOMAoptions{twoside=false,open=any,chapterprefix=on,parskip=full,fontsize=14pt}  \usepackage[portuguese]{babel} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{listingsutf8}  \usepackage{inconsolata} \lstset{     language=bash, %% Troque para PHP, C, Java, etc... bash é o padrão     basicstyle=\ttfamily\small,     numberstyle=\footnotesize,     numbers=left,     backgroundcolor=\color{gray!10},     frame=single,     tabsize=2,     rulecolor=\color{black!30},     title=\lstname,     escapeinside={\%*}{*)},     breaklines=true,     breakatwhitespace=true,     framextopmargin=2pt,     framexbottommargin=2pt,     extendedchars=false,     inputencoding=utf8 }  \begin{document} \begin{lstlisting} &lt;?php  echo 'Olá mundo!'; print 'Olá mundo!'; \end{lstlisting}  \end{document} \end{lstlisting} The "proper" way to test if a service is running in a script My problem:  I'm writing a bash script and in it I'd like to check if a given service is running.  I know how to do this manually, with $ service [service_name] status.  But (especially since the move to systemd) that prints a whole bunch of text that's a little messy to parse. I assumed there's a command made for scripts with simple output or a return value I can check.  But Googling around only yields a ton of "Oh, just ps aux | grep -v grep | grep [service_name]" results. That can't be the best practice, is it? What if another instance of that command is running, but not one started by the SysV init script?  Or should I just shut up and get my hands dirty with a little pgrep? I am using a cloned hard drive in attempts to restore some old files.   The cloned drive has 2 users, one with an encrypted home drive, one without. Both are administrators. When I couldn't get into the main user (with the encrypted home directory), I logged in as the 2nd user and changed the password.   It seems that I somehow broke the relationship between the encryption passphrase and the user. I'm pretty sure I have the passphrase. Is there a way to get to the data? Number of planks required to stop the bullet