Is $\lvert a-b\rvert\le\lvert a\rvert+\lvert b\rvert$ always true?
Proof of triangle inequality
I am struggling to convert .dwg to .shp, ideas? Any ideas as to how can I convert dwg to shp?  I tried Kosmo and gvSIG. gvSIG kind of worked but it seems like I lost information.. in addition everything was converted into lines, no polygons. I can manually recreate the polygons, but there must be a better program to do this conversion.  Ideas? What areas of physics depend on the sum $1 + 2 + 3 + 4 + 5 + 6+ 7+\ldots= -1/12$? This youtube video from Numberphile,   shows how the value is derived. In the video, one interviewee claims that "this result is used in many areas of physics". In the video, only string theory is mentioned.  Which areas of physics use or depend on the sum $$1 + 2 + 3 + 4 + 5 + 6+ 7+\ldots= -1/12?$$ Matrices that commute with all matrices Why can't I run two mysqli queries? The second one fails Login required moving to Super User on iPad When moving around the sites on Stack Exchange using Safari on my iPad (not the Stack Exchange App), I am fine when moving to any site other than SuperUser.  When logged in, I can switch sites and stay logged in, but when I switch to Super User I need to log in again. If I choose not to log in and switch to another site, I am logged in there. Is there a problem with the login handling for Super User? If it helps, I log in with a Stack Exchange account, not through Facebook or Google. Update After getting fed up with the problem, I took the advice given in the answer below which was to use Chrome, and the problem still exists. The same goes for Firefox. Have I missed something?  As you can see from the screenshots below, there are no cookie settings to be found. Chrome for iOS settings page  Privacy settings page  Content settings page  Google app settings page Why should the first person pronoun 'I' always be capitalized? How can I include value of sharepoint's version column in a word document? I'm trying to work out a way to display the contents of the version column from SharePoint (i.e. the value that changes every time a file is checked in) as a field (or something similar) inside of a Word document.  Ideally, I'd like to know how to configure SharePoint so I could click something like "Insert > Quick Parts > Document Property > Version", and it would include the version in the document.  The goal is to make it easier for someone to correlate a printed version of a document with the version history of SharePoint.  I have been able to add editable text columns to the Document content-type and have them show up as document property quick parts.  I've also been able to add a calculated column which gets the version as a text string... however this calculated column isn't showing up in Word as a document property.  (Perhaps I'm missing a setting on the calculated column) Recovering user files with a Live CD Q: How many arrangements of a,a,a,b,b,b,c,c,c are there such that  $\hspace{5mm}$ (i). no three consecutive letters are the same?  $\hspace{5mm}$ (ii). no two consecutive letters are the same?  A:(i). 1314. ${\hspace{5mm}}$ (ii). 174.  I thought of using the General Principle of Inclusion and Exclusion along with letting $p_i$ denote a property that.. , and doing so, I will evaluate $E(0)$, which gives us the number of arrangements without any of the properties.   How do I go about doing that? I am trying to use the method stated above in solving this question, but I am unable to generalize the properties $p_i$. The stress tensor can be written as: $$\sigma_{ij}=-p \delta_{ij}+\sigma'_{ij}\label{1}\tag{1}$$ where $\sigma_{ij}'$ is called the extra stress tensor.   From what I understand pressure is pressure is force per unit area, so that the force acting on the surface $d\vec A$ is given by:  $$\vec F=-p d\vec A\label{2}\tag{2}$$ (This has the effect that the force on an infinitesimally thin surface due to a continuous pressure is zero). However, $\sigma_{ij}$ represent the force in the $i$ direction on a surface with normal in the $\hat e_j$ direction. So the force acting on a surface $d \vec A$ must be: $$F_i=\sigma_{ij}dA_j\label{3}\tag{3}$$ Equations (2) and (3) clearly do not agree (even if we look soley at the force in the $d\vec A$ direction they don't agree). So my question is what is the exact meaning of pressure in expression (1) and why do we not have: $$\sigma_{ii}=-p$$ I'm a little confused as to when to use  for my physics class. For example, I'm asked to find the average speed of a race car that travels around a circular track with a radius of $500~\mathrm{m}$ in $50~\mathrm{s}$.  Would I need to apply the rules of significant figures to this step of the problem? $$ C = 2\pi (1000~\mathrm{m}) = 6283.19 $$  Or do I just need to apply significant figures at this step? $$ \text{Average speed} = \frac{6283.19~\mathrm{m}}{50~\mathrm{s}} = 125.664~\mathrm{m}/\mathrm{s} $$  Should I round $125.664~\mathrm{m}/\mathrm{s}$  to  $130~\mathrm{m}/\mathrm{s}$ since the number with the least amount of significant figures is two? How and why do accelerating charges radiate electromagnetic radiation? Let's consider it case by case:  Case 1: Charged particle is at rest. It has an electric field around it. No problem. That is its property.  Case 2: Charged particle started moving (it's accelerating). We were told that it starts radiating EM radiation. Why? What happened to it? What made it do this?  Follow up question: Suppose a charged particle is placed in uniform electric field. It accelerates because of electric force it experiences. Then work done by the electric field should not be equal to change in its kinetic energy, right? It should be equal to change in K.E + energy it has radiated in the form of EM Waves. But then, why don't we take energy radiated into consideration when solving problems? (I'm tutoring grade 12 students. I never encountered a problem in which energy radiated is considered.) I have seen many softwares such as Update Manager and Synaptic Package Manager, they wait if some other program is using the /var/lib/dpkg/lock and is locked. How can we do this through the Terminal? I saw apt-get's manual but didn't find anything useful. Is there any difference in equals and == for String variables? if ('text'.equals(str))   or   if ('text' == str)   Is there any difference? If yes, then what is it?   Added, after answered.  String q = 'teXt'; system.debug('teXt'.equals(q)); // true system.debug('teXt' == q);      // true system.debug('text'.equals(q)); // false system.debug('text' == q);      // true I searched it a while and found some articles regarding Xperia Mini X10 also on XDA but I couldn't understand them easily. So I want help from you geeks who can give me the lighted way with simple steps to root my phone.    I want a step by step guide about to root this model. I'm a not much familiar with this technology so please guide me through some detailed answer. I've set my Units (in scene properties) to Metric, and the Scene Scale to 0.01 hoping to get the Blender dimensions it mm's. While the (normal) scale is 1 for x,y,z, the standard cube has the dimensions 2x2x2 cm. When I export this to an STL and open it in a slicing program (Netfabb, Slic3r or Cura) they all give the dimensions: 2x2x2 mm. While exporting, the scale is 1.  What am I doing wrong? I hope you can help me.  Thanks! Increasing extent of Raster? How to align prices in columns when both 2 digit and 4 digit variations of a price exist? How does one prove that if $n \mid (a^{n}-b^{n}) \ \Longrightarrow$ $ \displaystyle n \mid \frac{a^{n}-b^{n}}{a-b}$ where $a,b, n \in \mathbb{N}$.  What i thought of is to consider $$(a-b)^{n} \equiv a^{n} + (-1)^{n}b^{n} \ (\text{mod} \ n)$$ and if we suppose that $n$ is odd then we have, $$(a-b)^{n} \equiv a^{n} -b^{n} \ (\text{mod} \ n)$$ and since $n \mid (a^{n} - b^{n})$ we have $$(a-b)^{n} \equiv 0 \ (\text{mod} \ n) $$  I think i am far away from the conclusion of the problem, but this is what i could work on regarding the problem. Counter with 4 flip flops jk synchronous from 3 to 13! I have to create a counter with 4 flip flops jk synchronous. The counter shall count in this order: 3 to 13 and then to 3 to 13 and so on..  I have to use logisim simulator.   Ok. So i think its solved. I realized that the circuit needs to start at 0 ou 1 and stabilize after the 13 and then it goes to 3. Thanks for your help.  Hope this will help for somebody else too.  Thank you all for your help!