The minimum value of $ f(x) = | x - 1 | + | x - 2 | + | x - 3 | $ is?
Maximum and minimum of of $f(x)=|x-1|+|x-2|+|x-3|$
After the last update of TeXLive 2018 (pretest) I get an error with csquotes' macro MakeAutoQuote:  \setcounter{errorcontextlines}{100} \listfiles \documentclass[fontsize=11pt,paper=a4,pagesize,ngerman]{scrartcl} \usepackage[utf8]{inputenc} \usepackage{babel} \usepackage[T1]{fontenc} \usepackage{csquotes} \MakeAutoQuote{»}{«}  \begin{document} ABC \end{document}   The error:  ! Package csquotes Error: Invalid argument.   My versions:  inputenc.sty    2018/04/06 v1.3b Input encoding file babel.sty    2018/02/14 3.18 The Babel package csquotes.sty    2018/02/11 v5.2c context-sensitive quotations (JAW)   I use pdfLaTeX. What is wrong here? How to run BitTorrent Sync? I am in Ubuntu 12.04 (precise) 64bit and downloaded the btsync executable from  but running it doesn't seem to have any effect. Double-clicking the executable does nothing, and running ./btsync in the terminal also exits immediately without any output.  Has anyone successfully ran this under Ubuntu, and if so, is there any special configuration changes that need to be made to make it work? Can you use an external 301 redirect for a blog post hosted on wordpress.com? If the Standard Normal PDF is $$f(x) = \frac{1}{\sqrt{2\pi}} e^{-x^2/2}$$  and the CDF is  $$F(x) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^x e^{-x^2/2}\mathrm{d}x\,,$$  how does this turn into an error function of $z$? What is the difference between $* and $@? Consider the following code:  foo () {     echo $* }  bar () {     echo $@ }  foo 1 2 3 4 bar 1 2 3 4   It outputs:     1 2 3 4       1 2 3 4   I am using Ksh88, but I am interested in other common shells as well. If you happen to know any particularity for specific shells, please do mention them.  I found the follwing in the Ksh man page on Solaris:     The meaning of $* and  $@  is   identical  when  not  quoted  or  when  used  as a parameter   assignment value or as a file name. However, when used as  a   command argument, $* is equivalent to ``$1d$2d...'', where d   is the first character of the IFS variable,  whereas  $@  is   equivalent  to  $1 $2 ....   I tried modifying the IFS variable, but it doesn't modify the output. Maybe I'm doing something wrong? Orientation on $\mathbb{CP}^2$ How to fix "W: Duplicate sources.list entry"? On the meta home page I noticed the  is listed as doing something, but cannot figure out what it is.  There is nothing on the  or its , but the recent activity is listed with the same timestamp. Where M is a matrix calculate a formula for M^n Let $$M = \begin{bmatrix} -7 &amp; 8 \\ -8 &amp; -7 \end{bmatrix}.$$ Find formulas for the entries of $M^n$ where $n$ is a positive integer.  (Your formulas should not contain complex numbers.)  Your answer should be in the form of a matrix.  I diagonalized to the form $M = P D P^{-1}$  and $M^n = P D^n P^{-1}$ where $P$ is my matrix of eigenvectors and $D$ is my matrix of eigenvalues.  My final answer after diagonalization was $$M^n = \begin{bmatrix} .5((-7+8i)^n+(-7-8i)^n) &amp; (i/2)(-(-7+8i)^n+(-7-8i)^n) \\ (.5/i)(-(-7+8i)^n+(-7-8i)^n) &amp; .5((-7+8i)^n+(-7-8i)^n) \end{bmatrix}$$  I can't seem to find an answer not in terms of complex numbers.  Can someone show me what I'm missing? Use of pizza stone in gas oven I have a new gas kitchen stove.  The oven seems to burn so easily. I have a thermometer in there and it is registering the temp that I have the oven set on.  I have seen where people have used a pizza stone to even out the heat.  I want to know if you place a rectangle pizza stone directly on the bottom of the oven or should it be placed on a rack on the lowest setting?  I would appreciate replies from anyone who has used this and if it had helped the problem when calling SCP in PuTTY on my Win7 box, it doesn't let me use C:/, but I also have no idea where on my local machine it will look for files by default. None of program directory or user directory worked. For example, I saved file.txt next to PuTTY.exe, and also in C:\Users\Me but calling SCP file.txt file.txt in PuTTY failed both times with      cp: cannot stat 'file.txt'   So, how do I transfer a file to my server using PuTTY?  EDIT: Also, calling SCP file.txt myserver:file.txt gives a similar error: file.txt: No such file or directory Prove that $\mathbb{N}^k$ is countable for every $k \in \mathbb{N}$.  I am told that we can go about this inductively.   Let $P(n)$ be the statement: “$\mathbb{N}^n$ is countable” $\forall n \in \mathbb{N}$.  Base Case: $\mathbb{N}^1 = \mathbb{N}$ is countable by definition, so $\checkmark$  Inductive Step: $\mathbb{N}^{k+1}$ $“=”$ $\mathbb{N}^k \times \mathbb{N}$  We know that $(A,B)$ countable $\implies$ $A \times B$ is countable. I am stuck on the part where I have to prove the rest, but I know that, for example, $(1,2,7) \in \mathbb{N}^3 \notin \mathbb{N}^2 \times \mathbb{N}$ but instead $((1,2),7) \in \mathbb{N}^2 \times \mathbb{N}$. So how would I go about proving the statement. How to properly render smoke on a transparent background? When rendering volumes with Film > Transparent enabled, the alpha appears to be the wrong type (premultiplied/straight). In the 3D view it works as expected:    This is a known .  Is there any way to work around this? Negative Mass and gravitation Selecting pixels in raster using polygon selection tool? I want to reclassify landcover image manually with respect to online imagery. I am looking for a software/plugin/script to manually select raster pixels using polygon selection tool and could be able to enter new value.  I have Arcgis with spatial analyst license. What is vertex and edge shading? The Lie algebra of $SL_n(\mathbb C)$ are the matrices where the trace is $0$. But what is the Lie algebra of $SL_n(\mathbb H)$ where $\mathbb H$ is the quaternions? How can I edit/create new launcher items in Unity by hand? Ellipse formula from points Question: Best way to derive an ellipse formula when given bunch of points (say 60 points which when connected draws an ellipse)?  Background: Using R Momocs library function  which returns confidence ellipse coordinates. Would be nice to abstract those points into a formula.  You can see my ellipse points in the image below;    Any suggestions much appreciated, Thanks A sequence includes $a_p=\sqrt2$, $a_q=\sqrt3$, $a_r=\sqrt5$ for some $1\leq p<q<r$. Can these be terms of an arithmetic progression? harmonic?