Italicizing Variables in SI unit commands
How to use siunitx with non numerical values?
Given $f(x) = x + |x|$ for what values of $x$ is $f$ differentiable Problem : Given $f(x) = x + |x|$ for what values of $x$ is $f$ differentiable?   For the sake of generality, let's assume that it is unknown to us that $|x|$ is not differentiable at $x = 0$  Attempted Solution :  Using the definition of differentiability, a function is differentiable over an interval $I$ $\text{iff}$  $$f'(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}, \ \ \forall x\in I$$  Now implicitly this definition of differentiability requires $$\lim_{h\to 0^+} \frac{f(x+h)-f(x)}{h} = \lim_{h\to 0^-} \frac{f(x+h)-f(x)}{h}$$  Therefore $f$ will be differentiable only when  $$\lim_{h\to 0^+} \frac{(x + h + |x+h|)-(x + |x|)}{h} = \lim_{h\to 0^-} \frac{(x - h + |x-h|)-(x + |x|)}{h}$$  But it is unclear what to do next as $x$ is just arbitrary $$ \begin{equation} \begin{aligned} |x+h| &amp;= \begin{cases}x+h &amp; \text{if} &amp; x \geq -h\\ -x-h &amp; \text{if} &amp; x &lt; -h \end{cases} \\ &amp;= \begin{cases}x+h &amp; \text{if} &amp; x \geq 0\\ -x-h &amp; \text{if} &amp; x &lt; 0 \end{cases} \end{aligned} \end{equation}$$    A Wrong Solution :  We could take the derivative of $f$, (and evaluate the domain of the derivative $f'(x)$ to values for which it is defined), using the rules of differentiation, but we would get a wrong answer.  $$f'(x) = \frac{|x| + x}{|x|}$$ $$\implies f'(x) = \begin{cases} 2 &amp; \text{if} &amp; x \geq 0 \\ 0 &amp; \text{if} &amp; x &lt; 0 \end{cases}$$  This implies the derivative $f'(0)$ exists, when it does not as per the definition of differentiability. Why is that so?    Questions:   How can a solution be found using the definition of differentiablity? Why does taking the derivative of $f$, $f'(x)$ and evaluating it's domain, not give the correct values of $x$ for which $f$ is differentiable? Financial requirements to sponsor relatives visiting the Schengen area [Germany]? MacOS 10.14 Mojave public beta public Wi-Fi problem I can not connect to a single public Wi-Fi hotspot that does not require a password but instead shows a pop-up window pointed to captive.apple.com  The pop-up opens blank with the error "The web page couldn't be loaded"  Any idea on how to fix this? Inadvertent use of = instead of == It seems that   if (x=y) { .... }   instead of  if (x==y) { ... }    is a root of many evils.  Why don't all compilers mark it as error instead of a configurable warning?  I'm interested in finding out cases where the construct if (x=y) is useful. How to prevent iTerm2 from creating overlaps and broken lines after pasting multiline chunks of text? If I paste multiline chunks of text into iTerm2, I always a get mess of output. It seems limited to only some programs running interactively (such as Bash, IRB - Python / VIM work flawlessly). Using Apple's native Terminal, I can paste whatever I want wherever I want - it works. For example, this sample text ():  echo Lorem ipsum dolor sit amet, consectetur adipiscing elit. Donec a diam lectus. echo Sed sit amet ipsum mauris. Maecenas congue ligula ac quam viverra nec consectetur ante hendrerit. echo Donec et mollis dolor. Praesent et diam eget libero egestas mattis sit amet vitae augue. echo Nam tincidunt congue enim, ut porta lorem lacinia consectetur. Donec ut libero sed arcu vehicula ultricies a non tortor. echo Lorem ipsum dolor sit amet, consectetur adipiscing elit. Aenean ut gravida lorem. Ut turpis felis, pulvinar a semper sed, adipiscing id dolor. echo Pellentesque auctor nisi id magna consequat sagittis. Curabitur dapibus enim sit amet elit pharetra tincidunt feugiat nisl imperdiet. echo Ut convallis libero in urna ultrices accumsan. Donec sed odio eros. Donec viverra mi quis quam pulvinar at malesuada arcu rhoncus. [snip]   pasted into IRB produces this in iTerm2:    while it produces this in native Terminal:    I am running the latest versions of OSX and iTerm2. What's going wrong here? I have a BA degree in Biochemistry.  I worked at a research lab for 5 yrs before I quit my job to be a stay at home.  Now I want to change my career and get into the field of QA.  I don't have much knowledge as to what the best way is to get into this field.  I cant afford to take online courses, so I want to self teach it to me.  Any suggestions and help would be greatly appreciated. Determine if Type is a pointer in a template function Recently I have updated my postgresql version. I have also upgraded pgAdmin from 3 to 4. But I was unable to load shapefile. I didn't find any plugin called shapefile loader. How can I get the shapefile loader plugin in pgAdmin 4? How do I get permissions to edit system configuration files? What is the smallest viable reproducing population, such as in a human population. By viable I mean a population which keeps genetic defects low (enough).  A very strongly related question: what is the expected number of generations a given population can survive? Brownian motion - Hölder continuity I have just dropped a half full latté on my company laptop and am not sure what to do.  Is there a way I can make sure that my laptop is usable again?  What steps must I go through to improve it's chances of survival? A sine integral $\int_0^{\infty} \left(\frac{\sin x }{x }\right)^n\,\mathrm{d}x$ The following question comes from   post $$\int_0^{\infty} \left(\frac{\sin x }{x }\right)^n\,\mathrm{d}x$$ but now I'd be curious to know how to deal with it by methods of complex analysis. Some suggestions, hints? Thanks!!!  Sis. Many of the people have asked almost the same question.  I'm trying to render a big mesh + fur/grass file with a few characters on the screen.  when I hit render, after a number of processing, copying data to gpu etc... i get following error.  Mem: 2960.07M, Peak:2960.07M | CUDA error: Out of memory in cuMemAlloc(&amp;device_pointer, size).  I'm using Geforce GTX 690 which contains 4GB memory.   Can somebody tell me how can i get GPU rendering, while 2960M is far less then 4196M of memory.   I know somebody would suggest me to use CPU.. but i'm curios why not GPU?   I've already compressed texture, etc   Edited  I don't think any other application is using any of my 1GB remaining memory. everything is closed but blender is there, also the GPU utilities are showing 2000/2000 MB are free on one card and 1900/2000MB is free on 2nd card.    i'm using GTX 690. with two GPUs of 2GB each. If somebody thinks that one GPU should have memory matching to the cuda memory/or Peak memory then I'm doubtful. Because in preferences Blender does know that I have 2GPUs where I can select either first GPU or second GPU or even both.   When I render some of smaller objects/scenes both of my GPU renders simultaneously with two blocks.  I'm running following specs  Xeon E5-1660 0 24GB - 1600mhz GTX690 Why no file-name in Inode information? I know that symlinks have a separated inode from the original file and that they only point for the inode containing the data. My question is, where is the hardlink name stored if there's no field in the inode structure refering to "name". I know that this could be a a relatively easy question, but as all hardlinks have the same inode number i assume that no inode is created when creating a hard link. First let me explain what I mean by "transitive" Suppose that the price of product A and the price of product B has a correlation of .5 Suppose also that the price of product B and product C has a correlation of .5  One might thing that if correlation(A,B) = .5 and correlation(B,C) = .5 then correlation(A,C) > 0, but with an intuitive example we can see why this is not the case:  Suppose that A is a fruit salad made of papaya and banana, suppose also that B is a fruit salad made of banana and strawberry and, finally, suppose that C is strawberries and cream. Clearly, when the price of banana goes up, both the price of A and B will go up; when the price of strawberry goes up the price of B and C will go up; but since A and C have no ingredients in common, their price isn't correlated.  My question is which statistical concept captures this intuitive idea. Is it the concept of dimensions?  What do I mean by transitive? Let me define the binary operator X corr? Y as 1 if correlation(X,Y) != 0 and 0 otherwise, so:   A corr? B = 1, B corr? C = 1, but  A corr? C could be = 0   If corr? was transitive, then A corr? C = 1 What is the bug about: Keyword gets duplicated even when the query is not modified.  Impact: As far as i can tell - cosmetic.  How to replicate: Go to:  and keep pressing Search button. With each search there will be a duplicate python keyword appended to search box.  Best guess for what is causing it: I think you have somewhere a piece of code that appends tag as a keyword without checking if it is already present. My reasoning comes from this url:  not having the same issue - the tag is not present in it. Variables in batch file not being set when inside IF? I have two examples of very simple batch files:  Assigning a value to a variable:  @echo off set FOO=1 echo FOO: %FOO% pause echo on   Which, as expected, results in:  FOO: 1  Press any key to continue . . .   However, if I place the same two lines inside an IF NOT DEFINED block:  @echo off IF NOT DEFINED BAR (     set FOO=1     echo FOO: %FOO% ) pause echo on   This unexpectedly results in:  FOO:  Press any key to continue . . .   This shouldn't have anything to do with the IF, clearly the block is being executed.  If I define BAR above the if, only the text from the PAUSE command is displayed, as expected.    What gives?    Follow up question: Is there any way to enable delayed expansion without setlocal?   If I were to call this simple example batch file from inside another, the example sets FOO, but only LOCALLY.   For example:   testcaller.bat   @call test.bat  @echo FOO: %FOO%  @pause    test.bat   @setlocal EnableDelayedExpansion  @IF NOT DEFINED BAR (      @set FOO=1      @echo FOO: !FOO!  )    This displays:   FOO: 1  FOO:  Press any key to continue . . .    In this case, it appears that I have to enable delayed expansion in the CALLER, which may be a hassle. Normality of dependent variable = normality of residuals? How to test whether a file uses CRLF or LF without modifying it? I need to periodically run a command that ensures that some text files are kept in Linux mode. Unfortunately dos2unix always modifies the file, which would mess file's and folder's timestamps and cause unnecessary writes.   The script I write is in Bash, so  I'd prefer answers based on Bash.