Can you help me to prove that $$|x-y|\leq |x|+|y|$$ I get a proff of this equality, but it's very short and I don't know if it's correct.
I understand intuitively that this is true, but I'm embarrassed to say I'm having a hard time constructing a rigorous proof that $|a+b| \leq |a|+|b|$. Any help would be appreciated :)
Purpose of else and finally in exception handling This question is about cosmology and general relativity. I understand the difference between the universe and the observable universe. What I am not really clear about is what is meant when I read that the universe is infinite.   Does it have infinite mass or is it dishomogeneous?  How can the universe transition from being finite near the big bang and infinite 14 billion years later? Or would an infinite universe not necessarily have a big bang at all? I am running 14.04 and have a HP Deskjet 2545 wireless printer which is supported by Ubuntu. I have run HpLIP, the latest version and installed the printer.  The printer is recognised by Ubuntu, printer and network, but LibreOffice do not see the printer. Only a Generic printer.  I don't know what to do anymore and would like to get some good advice How can I make 3D Text in Russian? I've seen a similar question on BSE about entering foreign languages into 3D Text, but it doesn't help. I've tried using two different fonts (both of which support Russian). I've tried enabling International Fonts in Blender's User Preferences, but it doesn't work as well. It either types English text with Greek letters or displays empty vertical rectangles.   If anyone has been able to add text in any foreign language, please let me know.  I actually found out that it can be easily done through Text Editor, which would be probably the best way for me since I would prefer to paste my text. Can anyone perhaps guide me through? Reading InputStream as UTF-8 Are there any age limits (formal, informal, or guidelines) that schools use when deciding to accept someone into a PhD program? I'm most curious about the upper age limits. For example, will most schools accept someone in their 40's? How about their 50's? Labelled spanning trees of $K_n-e$ Let $e$ be an edge of $K_n$- the complete graph on $n$ vertices. Prove that the number of labelled spanning trees of $K_n-e$ is $(n-2)n^{n-3}$.  I think the answer lies in using some modified form of Prüfer's sequence but I can't quite nail it. Compute the period of a decimal number a priori Route SSH to host through interface Is it possible to route all outgoing requests for SSH (port 22) to mydynamicdns.afraid.org via wlan0 instead of eth0 when both are connected?  Since my IP is dynamic, I would like to use a name instead of IP. GPU Rendering causing strange lines When I render using my r9 390 graphics card, weird lines are appearing over the render. This problem has just started happening recently, as a few days ago I was rendering the same scene without the lines appearing. I don't believe I've changed any settings in Blender and the below scene is from a new file, so render settings should be default.   Rendering using my CPU is fine:   The only thing I can think that has changed is I recently updated my card to the latest drivers. Playing games with it is still fine and the card is quite new so I wouldn't think it's a problem with the card itself. How to preserve the same parskip in minipage Ought we only form beliefs based on sufficient empirical evidence? In , John Loftus often makes statements like:  Faith, as I argue, is an irrational leap over the probabilities. Probabilities about such a matter are all that matter. We should think exclusively in terms of them. (19) If God created us as reasonable people, then the correct religious faith should have sufficient evidence for it, since that’s what reasonable people require. (22) Because science is the only game in town. It works. It produces the goods. There isn’t a better alternative. (119)  Loftus' attitude seems representative among many atheists; while I'm aware that there are other views, it is this kind of view which leads to the title of this question: Ought we only form beliefs based on sufficient empirical evidence? Here are some sub-questions which may help guide answers:  How can we get an ought from an is, given that evidence only describes what is? Reformulating the title as a hypothetical imperative doesn't seem to help, because the scientific method doesn't seem to ever make a hypothetical imperative binding. And yet, surely those who would agree with the quoted text would find certain hypothetical imperatives binding?  Given that the scientific method includes &quot;basic arithmetical truths and also certain truths about formal provability&quot;,  seems to apply: a given axiomatic formulation of the scientific method will be unable to imply certain (virtually all, it turns out) truths. To say that science is complete—there are no other methods of knowing things—seems to imply that science is inconsistent. Is this 'seems' an illusion?  Does the scientific method require that we make observations prior to forming hypotheses? It could be argued that probabilistically, trying to come up with hypotheses before making a 'sufficient' number of observations will result in a failed hypothesis too much of the time. Is there evidence to support this which can probabilistically rule out all other kinds of hypothesis-forming?  Must we accept any unfalsifiable claims? The answer seems to be 'yes', given e.g. the example of crystal structure discussed by Michael Polanyi in  (43-48, 1984 paperback). A set of geometries seemed to well-describe many crystals found in nature, and even if some crystals aren't well-described, that doesn't falsify the instances in which it does. This opens up the question of which unfalsifiable claims we ought to accept.  If we model human reasoning as , we can ask what is meant by 'sufficient' by what the 'probabilities' are, prior to any observations: what  ought we start with? I am tempted to say &quot;the most effective one&quot;, but that presupposes a purpose; are we given an objective purpose?   I am left with the suspicion that one ought to only follow the scientific method to the extent that one only wants to predict one's future observations—this smells like a tautology. It seems to beg the question to say that the most important area of 'truth' is objective reality, a question which cannot be answered with the scientific method. A 'yes' answer to the main question would seem to fall prey to something like  of .  I was tempted to phrase my question as:  Is science the only source of truth?  I believe this is a bad question, for a few reasons:  We care about whether a method can reliably arrive at truth/knowledge. The terms 'truth' and 'knowledge' would possibly stir a debate about , which may not be a prerequisite for the answer to my question. My question makes explicit that we are talking about what one ought to do, which is not explicit in the above formulation. Running a 32-bit application in Debian Wheezy 64 bits: Missing libraries I want to play the game Aquaria in a Debian Wheezy 64 bits. The installation went ok, but when trying to play the game I get these errors:  ALSA lib conf.c:3314:(snd_config_hooks_call) Cannot open shared library libasound_module_conf_pulse.so ALSA lib control.c:951:(snd_ctl_open_noupdate) Invalid CTL hw:0 AL lib: alsa.c:1000: control open (0): No such file or directory Message: SDL_GL_LoadLibrary Error: Failed loading libGL.so.1   I have added 32 bit compatibility with dpkg --add-architecture i386 and I think that the required libraries are present in the system since typing locate libasound_module_conf_pulse.so yields:  /usr/lib/x86_64-linux-gnu/alsa-lib/libasound_module_conf_pulse.so  and locate libGL.so.1:  /etc/alternatives/glx--libGL.so.1-x86_64-linux-gnu /usr/lib/mesa-diverted/i386-linux-gnu/libGL.so.1 /usr/lib/mesa-diverted/i386-linux-gnu/libGL.so.1.2 /usr/lib/mesa-diverted/x86_64-linux-gnu/libGL.so.1 /usr/lib/mesa-diverted/x86_64-linux-gnu/libGL.so.1.2 /usr/lib/x86_64-linux-gnu/libGL.so.1 /usr/lib/x86_64-linux-gnu/fglrx/fglrx-libGL.so.1.2 /usr/lib/x86_64-linux-gnu/fglrx/libGL.so.1   However, it seems that Debian is ignoring them. What can I do to play Aquaria?  EDIT 1: ldd aquaria  linux-gate.so.1 =&gt;  (0xf77e1000) libSDL-1.2.so.0 =&gt; /opt/Aquaria/./libSDL-1.2.so.0 (0xf7748000) libopenal.so.1 =&gt; /opt/Aquaria/./libopenal.so.1 (0xf76fa000) libstdc++.so.6 =&gt; /opt/Aquaria/./libstdc++.so.6 (0xf760d000) libm.so.6 =&gt; /lib/i386-linux-gnu/i686/cmov/libm.so.6 (0xf75c3000) libgcc_s.so.1 =&gt; /opt/Aquaria/./libgcc_s.so.1 (0xf75b8000) libc.so.6 =&gt; /lib/i386-linux-gnu/i686/cmov/libc.so.6 (0xf7455000) libdl.so.2 =&gt; /lib/i386-linux-gnu/i686/cmov/libdl.so.2 (0xf7451000) libpthread.so.0 =&gt; /lib/i386-linux-gnu/i686/cmov/libpthread.so.0 (0xf7437000) librt.so.1 =&gt; /lib/i386-linux-gnu/i686/cmov/librt.so.1 (0xf742e000) /lib/ld-linux.so.2 (0xf77e2000) Do I need to activate the firewall? I only use Ubuntu for a home desktop use? I have a TikZ picture with a node containing a minipage with an itemize environment; each item is a hyperref to other sections of the document.   When scaling the image (for example with \begin{tikzpicture}[scale=.7, transform shape] I've a strange behavior: links in itemize are not in the right place: they present a somewhat vertical offset, as if they don't scale as the rest of image.   Here the MWE:  \documentclass[a4paper]{article} \usepackage{tikz} \usepackage[pdftex]{hyperref} \begin{document}  Here something interesting\label{text:interesting-one} \newpage  Here something interesting, too\label{text:interesting-two} \newpage  and here there are very very interesting stuff\label{text:interesting-three} \newpage  \newpage Now the problem: links rectangles have some offset, making links unusable in case of long itemize  \begin{figure}[htb] \begin{tikzpicture}[scale=.7, transform shape] \node at (0,0) (mynode) { \begin{minipage}{4cm} \begin{itemize} \item \hyperref[text:interesting-one]{First link} \item \hyperref[text:interesting-two]{Second link} \item \hyperref[text:interesting-three]{Third link} \item \hyperref[text:interesting-one]{First link again} \item \hyperref[text:interesting-two]{Second link again} \item \hyperref[text:interesting-three]{Third link again} \end{itemize} \end{minipage} }; \end{tikzpicture} \end{figure} \end{document}   And here a snapshot of the problem    Note: This is evident using the default settings of hyperref package, which draws the red rectangle around links, but it took me some time to found it when only the text is coloured, i.e. when using \usepackage[linkcolor=blue,colorlinks=true]{hyperref} When I entered the -al attribute with the  command, I got the following:  anupam@JAZZ:~/blog$ ls -al total 76 drwxrwxr-x 13 anupam anupam 4096 Aug 28 21:45 . drwxr-xr-x 34 anupam anupam 4096 Aug 28 20:52 .. drwxrwxr-x  8 anupam anupam 4096 Aug 28 12:19 app drwxr-xr-x  2 anupam anupam 4096 Aug 28 12:19 bin drwxrwxr-x  5 anupam anupam 4096 Aug 28 12:19 config -rw-rw-r--  1 anupam anupam  154 Aug 28 12:19 config.ru drwxrwxr-x  3 anupam anupam 4096 Aug 28 12:37 db -rw-rw-r--  1 anupam anupam 1339 Aug 28 12:19 Gemfile -rw-rw-r--  1 anupam anupam 2871 Aug 28 12:19 Gemfile.lock drwxrwxr-x  7 anupam anupam 4096 Aug 28 21:45 .git -rw-rw-r--  1 anupam anupam  466 Aug 28 12:19 .gitignore drwxrwxr-x  4 anupam anupam 4096 Aug 28 12:19 lib drwxrwxr-x  2 anupam anupam 4096 Aug 28 12:29 log drwxrwxr-x  2 anupam anupam 4096 Aug 28 12:19 public -rw-rw-r--  1 anupam anupam  249 Aug 28 12:19 Rakefile -rw-rw-r--  1 anupam anupam  478 Aug 28 12:19 README.rdoc drwxrwxr-x  8 anupam anupam 4096 Aug 28 12:19 test drwxrwxr-x  6 anupam anupam 4096 Aug 28 12:33 tmp drwxrwxr-x  3 anupam anupam 4096 Aug 28 12:19 vendor   What does each column mean, and what does the total 76 signify here? If $\lambda_{max} = n$, then $n\times n$ positive, reciprocal matrix A is consistent At the end of . the author states that  Suppose we have $n \times n$ matrix $A$ having only positive elements and satisfying the property $a_{ij}=1/a_{ji}$ (a matrix satisfying this property is called a reciprocal matrix).  If its largest eigenvalue $\lambda_{max}$ is equal to $n$, then the matrix $A$ satisfies the property (consistency property) $a_{ij} a_{jk} = a_{ik}$ where $i,j,k=1,2,...,n$.  I'm not convinced this theorem is true. Could anyone help? Can a magus with a high BAB cast two spells or attack and cast, with their full attack action? Suppose you are a level 10 Magus or something similar. (Something with a decent BAB progression and spellcasting abilities) When you hit +6/+1, can you cast a spell, then attack, vice-versa, or simply case two spells? Everywhere I look I can't get a clear answer. Which X-Men movies should I watch before Deadpool? I want to watch Deadpool, but I have heard the character has appeared in X-Men series too. My question is, if I watch X-Men before Deadpool, will it enhance my interest in the Deadpool character? Just looking for the difference between   2&gt;&amp;- 2&gt;/dev/null |&amp; &amp;&gt;/dev/null &gt;/dev/null 2&gt;&amp;1   and their portability with non-Bourne shells like tcsh, mksh, etc.