I installed the 64-bit version of Ubuntu 14.04 for the first time, and I think it is heavier than the 32-bit version. While it was installing it got stuck. I tried four times to install.   Is it true that Ubuntu does not get very many updates? Does installing less software and updates help to keep the system running smoothly and fast?  My system has these specs:   Intel-E5700 processor ASUS P5G41T-MLX3 motherboard 4 GB RAM   I know it is old and slow. My question is this:   Do I have to change it to 32-bit for my PC to work faster?
What is the difference between 32-bit and 64-bit Ubuntu? I've heard the 64-bit platform performs better and can detect more than 4GB of RAM. Also, while some apps haven't ported to 64-bit yet, ia32-libs lets a 64-bit machine run them.  If so, why not promote 64-bit over 32-bit?
For which $n$ is the sum: $$\sum_{k=0}^{n}10^k$$ a prime number? Are they finite? how to count dates entries monthwise from a resultset Find all $x$ such that $$x^6=(x+1)^6.$$   So far, I have found the real solution $x= -\frac{1}{2}$, and the complex solution $x = -\sqrt[3]{-1}$.  Are there more, and if so what/how would be the most efficient find all the solutions to this problem? I am struggling to find the rest of the solutions. Good refactoring support for C++ The Visual Studio refactoring support  for C# is quite good nowadays (though not half as good as some Java IDE's I've seen already) but I'm really missing C++ support.  I have seen  and am currently trying it out, but maybe one of you guys know a better tool or plugin?  I've been working with  now for a week or two and got totally addicted. Thanks for the tip, I'll try to convince my boss to get me a license at work too.  I've been bughunting for a few days since Visual Assist X kept messing up my Visual Studio after a few specific refactorings, It took me (and customer support) a week to hunt down but let's say for now that Visual Assist X is not a good combination with . I know there are some command-line applications like pdflatex that can help me to compile a LaTex document from C#.Net (using the System.Diagnostics.Process class) .   I wanna know that what's the best command-line tool for compiling a TeX document ? Proof Verification : Prove -(-a)=a using only ordered field axioms I need to prove for all real numbers $a$, $-(-a) = a$ using only the following axioms:     Thanks to many members of the Mathematics Stackexchange Community, I have the following proof worked out:  Theorem: The Additive Inverse Identity is Unique  $ ( \forall a,b,c \in \mathbb{R} )(a+b=0) \land (a+c=0) \\ ( \forall a,b,c \in \mathbb{R} )(a+b=a+c) \\ ( \forall a,b,c \in \mathbb{R} )(b=c) \\ \text{QED} \\ $  Theorem $\textbf{a} \cdot \textbf{0 = 0}$  $ \begin{align} a \cdot 0 &amp;= a \cdot 0 \\ a \cdot (0 + 0) &amp;= a \cdot 0 \\ a \cdot 0 + a \cdot 0 &amp;= a \cdot 0 \\ a \cdot 0 + a \cdot 0 + (-a) \cdot 0 &amp;= a \cdot 0 + (-a) \cdot 0 \\ a \cdot 0 &amp;= 0 \\ &amp;\text{QED} \\ \end{align} $  Theorem: $-\textbf{1} \cdot \textbf{(a) = (}-\textbf{a)}$  $ \begin{align} a \cdot 0 &amp;= 0 \\ a \cdot \left[ 1 + (-1) \right] &amp;= a + (-a) \\ 1 \cdot a + (-1) \cdot a &amp;= a + (-a) \\ -1 \cdot (a) &amp;= (-a) \\ &amp;\text{QED} \\ \end{align} $  Theorem: $-\textbf{(}-\textbf{a) = a}$  $ \begin{align} 0 &amp;= 0 \\ -a \cdot 0 &amp;= 0 \\ -a \cdot \left[ 1 + (-1) \right] &amp;= 0 \\ -a \cdot 1 + -a \cdot (-1) &amp;= 0 \\ -a + \left[ -(-a) \right] &amp;= 0 \\ -(-a) &amp;= a \\ \text{QED} \\ \end{align} $  Does everything look alright? Have I missed anything?  Also--why is it necessary to show that the additive inverse is unique?  Many thanks in advance. Why is the gap between the translation and the last line of the gloss so wide in my interlinear gloss? How to calculate the division and remainder of a big number manually Let $x = 2017^{2017}$. How can I manually determine:   The remainder of the division of $x$ by $31$ The least significant digit of $x$ If you draw two circles that are exactly the same in all aspects (location, size, etc...) except they have different colors, then the "border" of the underlying circle is showing through.  \documentclass[10pt]{book} \usepackage{xcolor} \usepackage{tikz}  \begin{document}  \begin{tikzpicture}     \fill (0,0) circle (0.1);     \fill[color=red] (0,0) circle (0.1);     \fill[color=red] (0.5,0) circle (0.1); \end{tikzpicture} \end{document}   Notice the first circle has a black "edge" around it that looks different than the 2nd circle which doesn't.   The problem is due to the fact that one is anti-aliasing both circles and the edge colors are being blended.   Is there a way to fix this but still have anti-aliasing? (basically render all the objects I need then anti-alias them properly afterwards?)  (I realize TikZ probably can't do anything about this but one doesn't know unless they ask) How do I show that a two-qubit state is an entangled state? The Bell state $|\Phi^{+}\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle )$ is an entangled state. But why is that the case? How do I mathematically prove that? $AB-BA$ is a nilpotent matrix if it commutes with $A$ I saw this in a  and am putting it here for posterity.  Problem: Let $A$ and $B$ by square matrices and set $C=AB-BA$. If $AC=CA$, prove $C$ is nilpotent. How do I find out the user name and password for an existing account? MY site was created and maintained from a developer I cannot contact, and I need to know the username/password the developer used to access the site.  How can I achieve this? Convert a string to an enum in C# What's the best way to convert a string to an enumeration value in C#? I have an HTML select tag containing the values of an enumeration. When the page is posted, I want to pick up the value (which will be in the form of a string) and convert it to the corresponding enumeration value. In an ideal world, I could do something like this: StatusEnum MyStatus = StatusEnum.Parse(&quot;Active&quot;);  but that isn't a valid code. $\sum_{n=1}^\infty \log \frac{n+1}{n}$  $\sum_{n=1}^\infty \log \frac{n+1}{n}$ =  $\displaystyle\lim_{n \to{+}\infty}(\log2 - \log1)+(\log3-\log2)+...+(\log(n+1)-\log n)$=$\displaystyle\lim_{n \to{+}\infty}\log(n+1)\to \infty$. So, the series diverges.  Is my procedure correct? What is the name of the default font in math mode? I draw figures in Inkscape. When I label elements within the figures with variable names that I have used in the underlying TeX document, I would like them to look exactly the same as in the document. (e.g. l does not look the same as $l$)  What is the name of the math mode font so I can select it correctly in the Inkscape font list?  If the exact font should not be available, what is a similar looking font that is present on most systems? What is the difference between Set and SetDelayed? I have  experience where empty spaces cause unwanted effects. It is not easy to trace the cause of these unwanted effects. In order to eliminate any doubt, I often overuse % as follows.   \usepackage% [% left=3cm, right=3cm% ]% {geometry}   or  \newcommand{\mycommand}% {% This is my command.% }   I got an extreme example that will break what Leo Liu said     In fact, only spaces which would be   output have to be removed by comment.   The following code does not produce output, but we cannot remove the % and leave a blank line between two elements of a list below.  \newpsstyle{gridstyle} { gridwidth=0.4pt, % griddots=0 }   Shortly speaking, where are the necessary places to be appended with % to remove unwanted spaces? I'm trying to determine which battery to use for my application. I'll be using a class 1 or class 2 Bluetooth (not low energy) module, which requires about ~50/60mA of RX/TX current. In addition, there is a microcontroller and some low power analog IC's. I require a continuous stream of data from the device for 1-10 minutes.  Are coin cells completely out of the question? I'm talking about CR2450 Lithium-ions. I don't really mind if they don't last long, but will they work? Because in my application, size is key, and battery life is a trade off that I'm willing to make. Can someone point me to a paper, or show here, why symmetric matrices have orthogonal eigenvectors? In particular, I'd like to see proof that for a symmetric matrix $A$ there exists decomposition $A = Q\Lambda Q^{-1} = Q\Lambda Q^{T}$ where $\Lambda$ is diagonal. What is the difference between "information on", "information of", "information about" "Information on something", "information of something", "information about something" — these three usages all sound having the same meaning for me. Are there any differences?