Lattice of congruences of a lattice is distributive
Lattices are congruence-distributive
Disable sleep on laptop lid close in tty1 I'm using Ubuntu Desktop 15.10 on a laptop and it runs an Apache server with SSH as well. When using a GUI, I have the power options set to not sleep at all even when the laptop lid is closed, but recently I stopped the X-System and am now using TTY1 instead to save resources. However, in TTY1, if I close the laptop lid, the computer goes to sleep and prevents the SSH and Apache server from working. Any way to prevent this easily? The realistic answer I bet is to use Ubuntu Server instead (unless I'm mistaken and Ubuntu Server will also sleep on lid close) but I don't exactly want to switch yet unless there's an easy way to switch to it like you can switch from ubuntu-desktop to lubuntu-desktop? Any advice is welcome to prevent the computer from sleeping Does being denied entry to a country affect future travel to other countries? I was denied entry to India due to a visa technicality. I was advised by organisation I was travelling with to get tourist visa when I actually needed miscellaneous visa. Will this affect future travel to other countries if I have been refused once by a country, or if I want to re-enter India? Getting text from last marker to EOF in POSIX.2 $ df -kh Filesystem      Size  Used Avail Use% Mounted on udev            7,8G     0  7,8G   0% /dev tmpfs           1,6G   19M  1,6G   2% /run /dev/sda2       622G  227G  364G  39% / tmpfs           7,8G  1,1G  6,7G  14% /dev/shm tmpfs           5,0M  4,0K  5,0M   1% /run/lock tmpfs           7,8G     0  7,8G   0% /sys/fs/cgroup /dev/loop1      143M  143M     0 100% /snap/inkscape/2527 /dev/loop3       79M   79M     0 100% /snap/core/1441 /dev/loop0       79M   79M     0 100% /snap/core/1577 /dev/loop4       79M   79M     0 100% /snap/core/1512 /dev/loop2       62M   62M     0 100% /snap/pencilsheep/5 tmpfs           1,6G   92K  1,6G   1% /run/user/1000   What are these /dev/loop device files? My RAM is always full. Is this related? Call to a member function prepare() on a non-object PHP Help Some time ago, when I installed Ubuntu, I chose a rather stupid username for my account that I do not want to use anymore. How do I change this (including the name of my home directory, and the name in the terminal) without losing settings for applications? How do I keep permissions and my keys for various authentification (e.g. email, SSH, GPG and more)? What settings could possibly get lost if I changed my username? Prove that if a number $n > 1$ is not prime, then it has a prime factor $\le \sqrt{n}$. I'm using listings and I want to extend a language with additional keywords for highlightning. I know there is an option morekeywords available, but that only works for a particular lstset declaration and I don't want to have to copy-paste all keywords into all listings. I've tried declaring the keywords as part of a command but that doesn't work (probably because the command is not expanded and I don't know how to fix that).  So is there any way of declaring a new language by copying an existing one and just adding more keywords? I am quite proficient with the keyboard and try to only use the mouse when necessary. Given that context I was very familiar with the shortcut keys in MS Outlook 2003 and never needed to use the mouse to use that product. Now my company has recently upgraded to MS Outlook 2010 and I am finding it impossible to operate it without having to use the mouse. In particular replying to meeting requests with the old shortcut keys no longer seems possible.   I have held down the ALT key and sometimes it shows some shortcuts on the ribbon but this seems to be limited to ALT+H which tends to alternate between designating "Accept" and "Tentative" without any keys for the other options. Also as this appears to switch between "Accept" and "Tentative" one can't even use this consistently without first having to check what it means for each particular instance.  Any help with this would be greatly appreciated! Sum of a Hyper-geometric series. (NBHM 2011) How to find the sum of the following series $$\frac{1}{5} - \frac{1\cdot 4}{5\cdot 10} + \frac{1\cdot 4\cdot 7}{5\cdot 10\cdot 15} - \dots\,.?$$  I have no idea. I have written the general term and tested its convergence by Gauss' test for convergence, but they are neither the question nor the answer. Why is this sequence of functions not uniformly convergent? For the following sequence of functions and its limit function, we can see that $f_n(x)$ is clearly pointwise convergent  $$f_n(x) = x^n\text{ }\forall x\in[0,1]\text{ and }\forall n\in\mathbb N^*\\ f(x) = \begin{cases}0&amp;\text{if } x\in[0,1)\\1&amp;\text{if } x=1\end{cases}$$  However, I was wondering why this is not uniformly convergent. The condition for uniform convergence is:  $$|f_n(x) - f(x)| &lt; \epsilon,\ \ \ \forall x \text{ when } n &gt; N$$  Now most sources present an argument along the lines of: assume that $f_n(x)$ is uniformly convergent and that $0 &lt; x &lt; 1$, this means that $x^n&lt;\epsilon$ whenever $n&gt;N$. Specifically, this would mean $x^{N+1}&lt;\epsilon$ for some fixed $N$. But if we now pick $x$ such that $1 &gt; x &gt; ε^{\frac{1}{N+1}}$, then this would lead to a contradiction, therefore $f_n(x)$ is not uniformly convergent.  However, I was wondering why couldn't we take $n$ to infinity. If $0 &lt; x &lt; 1$, then $\lim_{n\rightarrow \infty} |f_n(x) - f(x)| = 0$ (which is less than $\epsilon$). Now since $|f_n(x) - f(x)|$ will always be $0$ if $n &gt; \infty$, then wouldn't this be uniformly convergent? How to simplify the summation kk! without using induction? My system freezes completely at random, frequent intervals. I started to have the same problem in Ubuntu 14.04 but after recent upgrade to 16.04 there is no improvement, in fact it seems worse.  When it happens, it's impossible to do anything. I've tried everything in this thread:  but nothing works, I have to hard reset. I have read all the system logs and journalctl but there is never any information that could help diagnose the problem.  This is a dual-boot system with Windows 10 and there's no problem there, so it's not defective hardware.  My laptop has an Intel Bay Trail processor (Pentium N3540) sort() and reverse() functions do not work Should I activate the additional driver: Processor microcode firmware for Intel CPUs for intel-microcode I have recently noticed that there is an additional driver called Unknown: Unknown here which was not there before:    I have already read , and understand why it is there, but my question is, should I activate it? Will this make a difference? Or should I just leave it as it is as it sounds rather useful?    OS Information:  Description:    Ubuntu 15.04 Release:    15.04 Are there integral solutions to the equation $x^2+y^2-z^2=1$? Ubuntu 16.04 Jan 3 2018 update causing screen/access issues How to Sort Multi-dimensional Array by Value? Though I never quite understood what those numbers were and they were quite ugly, they were the only reason I ever visited the reviews page.   Can we have similar functionality back on the top bar please? What is Deviance? (specifically in CART/rpart) What is "Deviance," how is it calculated, and what are its uses in different fields in statistics?  In particular, I'm personally interested in its uses in CART (and its implementation in rpart in R).   I'm asking this since the  seems somewhat lacking and your insights will be most welcomed.