Problem with File permissons
What if I accidentally run command "chmod -R" on system directories (/, /etc, ...)
Let $X_n$ be iid random variables with $P(X_n=(-1)^kk)=\dfrac{C}{k^2\log k}$ for all $k\geq 2$. Here $C$ is just a constant so that the sum of probabilities is $1$. Find constant $\mu$ such that $S_n/n\to \mu$ in probability where $S_n=\sum_{k=1}^nX_k$.   Here $E(X_n)=\infty$. I'm a bit lost after this. In general how does one find constants like this? How to prove this limit exists: $a_{n+2}=\sqrt{a_{n+1}}+\sqrt{a_{n}}$ Question: Consider a sequence $\{a_{n}\}$ such that $a_{1},a_{2}&gt;0$, and for all $n \in \mathbb{N}$ we have:  $$a_{n+2}=\sqrt{a_{n+1}}+\sqrt{a_{n}}$$  Prove that :  $\displaystyle\lim_{n\to\infty}a_{n}$ exists and find this limit.  My work: If this limit exists, let $\displaystyle\lim_{n\to\infty}a_{n}=x&gt;0$; then we have $$x=\sqrt{x}+\sqrt{x}\Longrightarrow x=4$$ But I can't see how to prove the limit of $\{a_{n}\}$ exists. Thank you for you help! Draw ellipses with different coloring for their intersection in tikz? How do I color intersection of two ellipses in different color. For instances, the ellipses should themselves be colored as yellow and their intersection as red. My code for drawing ellipses is given below  \draw (-4,0) ellipse (8 and 3); \draw (8,0) ellipse (8 and 3);   UPDATE: In the comments to individual answers, I have requested to show it for three ellipses. How to expand primary partition when WUBI is used to install? I have installed Ubunut 12.04 using WUBI. The "Installation size" options I chosen was 18GB i.e the amount of space you want to "give up" for WUBI. That is the space wubi's Ubuntu install is able to use. Wubi creates a disk image (loopmounted device) on your host system in/on which Ubuntu is installed. Now, I am running out of memory in primary partition.   Could anyone help me out to extend/stretch the partition size? Require minimum reputation on the target site for migration The  prohibited the development or use of cloaking technology by the Federation. This treaty was a peace treaty and use of cloaking technology in one's own space couldn't disturb peace. Plus, the Romulans already had cloaking technology, so banning it was unfair for the Federation. So, why was this ban introduced?  Another thing: There were many things to ban, but why cloaking technology? Is it okay to have a multi-language deck? I want to buy a few booster pack from a local shop that only gets them in French. Is it generally acceptable to show up to a tournament with cards in different languages? Vertical spacing in floats I am using a float inside the text. As I found out, using \intextsep I could set space above and below the float and the texts. But when I am using \setlength{\intextsep}{5mm}, the space below the float is more than the one above it. Why they are not equal?  % Preview source code  %% LyX 2.0.0beta1 created this file.  For more info, see http://www.lyx.org/. %% Do not edit unless you really know what you are doing. \documentclass[english]{report} \usepackage[T1]{fontenc} \usepackage[latin9]{inputenc} \setcounter{secnumdepth}{3} \setcounter{tocdepth}{3} \usepackage{graphicx}  \makeatletter  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% LyX specific LaTeX commands. %% A simple dot to overcome graphicx limitations \newcommand{\lyxdot}{.}   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% User specified LaTeX commands. \usepackage{setspace} \setlength{\intextsep}{5mm} \setlength{\belowcaptionskip}{0mm}  \setstretch{2}  \makeatother  \usepackage{babel}  \begin{document} Text Text Text Text Text Text Text Text Text Text Text Text  \begin{figure}[h] \begin{centering} \includegraphics[scale=0.5]{\lyxdot \lyxdot /Pictures/fedora} \par\end{centering}  \caption{}  \end{figure} Text Text Text Text Text Text Text Text Text Text Text Text \end{document} How do I skip specific tests when building an rpm? I am building an RPM of git version 2.13.0. The build has gone ok but one of the tests are failing:  Config variable ${LIB_HTTPD_SVN} is not defined Config variable ${LIB_HTTPD_SVN_PATH} is not defined   I cannot find any info about these variables so I was going to just skip the tests. How can I do that? I have a program which produces useful information on stdout but also reads from stdin. I want to redirect its standard output to a file without providing anything on standard input. So far, so good: I can do:  program &gt; output   and don't do anything in the tty.  However, the problem is I want to do this in the background. If I do:  program &gt; output &amp;   the program will get suspended ("suspended (tty input)").  If I do:  program &lt; /dev/null &gt; output &amp;   the program terminates immediately because it reaches EOF.  It seems that what I need is to pipe into program something which does not do anything for an indefinite amount of time and does not read stdin. The following approaches work:  while true; do sleep 100; done | program &gt; output &amp; mkfifo fifo &amp;&amp; cat fifo | program &gt; output &amp; tail -f /dev/null | program &gt; output &amp;   However, this is all very ugly. There has to be an elegant way, using standard Unix utilities, to "do nothing, indefinitely" (to paraphrase man true). How could I achieve this? (My main criteria for elegance here: no temporary files; no busy-waiting or periodic wakeups; no exotic utilities; as short as possible.) Prove that in a triangle $$r^2+r_1^2+r_2^2+r_3^2=16R^2-(a^2+b^2+c^2)$$ where the symbols have their usual meanings. I am looking for a smaller or elegant proof using trigonometry. A geometric proof would be super cool. I did prove it but it took me ages to do the calculation. Thanks. Parentheses vs. double commas vs. dashes to provide additional detail When do you use commas and when do you use parentheses to provide more detail about something?  For example:   The suspect, Tom Wilson, is now being charged with murder. The suspect (Tom Wilson) is now being charged with murder. John Smith, a member of the jury, agreed with the verdict. John Smith (a member of the jury) agreed with the verdict. The first example, the one about the fox, is the more valid one. The first example (the one about the fox) is the more valid one.   I realize that the first example, the one that uses parentheses, is probably more valid in this case (if anyone has a better example, please include it), but when, if ever, would you favor parentheses?  Update: I realize that dashes are sometimes used for similar situations, so I'd appreciate information on these as well.  For example:   The children—who are wearing shoes—will go on the trip The children, who are wearing shoes, will go on the trip The children (who are wearing shoes) will go on the trip How fast does the sequence $y_t$ defined by $y_{t+1}=y_t(1-y_t)$ decay to zero? The question is in the title; I'm looking for the exact decay rate. Naturally, assume the starting point $y_0$ belongs to $(0,1)$.   This is motivated by one of the answers to . Can't do reviews after failing 1 audit Rolling back a completely changed question was originally asked August 9, and received answers. A month later, the OP  the question, invalidating the existing answers. I rolled it back, and left a comment to say that a new question should be opened, but the OP changed it back saying "There is no rule about it, so you can't edit my post."  There is also a bounty on this question, making things more interesting.  What are the guidelines on completely changing a question or rolling back changed questions? Was I out-of-line rolling back the question?  I have no desire to get into an edit war, so I'm not going to touch the question again. If a moderator wants to get involved, great. .       The  has no sign of the user sharth The  also does not have any sign of related activity   I would like to know why the user's name is associated with the question. At least why their display name shows up as having modified the question timeline activity.  Possible reason that I can think of is that, .  Is this the reason?  Is there a way (for normal users), to look for such details, other than looking at the user activity and the question's revision history. Variation of the metric with respect to the metric For a variation of the metric $g^{\mu\nu}$ with respect to $g^{\alpha\beta}$ you might expect the result (at least I did):  \begin{equation} \frac{\delta g^{\mu\nu}}{\delta g^{\alpha\beta}}= \delta^\mu_\alpha\delta^\nu_\beta. \end{equation}  but then to preserve the fact that $g^{\mu\nu}$ is symmetric under interchange of $\mu$ and $\nu$ we should probably symmetrise the right hand side like this:  \begin{equation}\frac{\delta g^{\mu\nu}}{\delta g^{\alpha\beta}}= \delta^\mu_\alpha\delta^\nu_\beta + \delta^\mu_\beta\delta^\nu_\alpha.\end{equation}  Is this reasonable/correct? If not, why not?  It seems that I can derive some weird results if this is right (or maybe I'm just making other mistakes). Find duplicate files Is it possible to find duplicate files on my disk which are bit to bit identical but have different file-names? Ball $X^*$ is weak-star metrizable iff X is separable in Conway's book. This is a Theorem in Conway's book     I don't understand in the third paragraph why there are open sets $\{U_n:n\geq1\}$ in $(ball X^*,wk^*)$ such that $0\in U_n$ and $\bigcap^{\infty}_{n=1}U_n=\{0\}$. By the definition of the relative weak-star topology on ball $X^*$, for each $n$, there exists a finite set $F_n$ contained in $X$ such that $$\{x^*\in\text{ball }X^*:|\langle x,x^*\rangle|&lt;1 \text{ for all }x\in F_n\}\subseteq U_n.$$  Can someone explain this for me？ Thank you so much!! I have a simple question answer to which would help me more deeply understand the concept of (non)commutative structures. Let's take for example (our teacher's definition of) a ring:  Let $R\neq \emptyset$ be a set, let $\oplus:A\times A \to A$ and $\bullet :A\times A \to A$ be binary operations. Moreover, let $(R, \oplus)$ be a commutative group, $(R, \bullet)$ be a monoid and following property holds for all $a, b, c\in R$: $$a\bullet(b\oplus c) = (a\bullet b)\oplus(a \bullet c)$$ $$(b\oplus c)\bullet a = (b\bullet a)\oplus(c \bullet a)$$ Then ordered triple $\mathbf R = (R, \oplus, \bullet \mathbf)$ is called a (unitary) ring.  Moreover, we call ring $\mathbf R$ commutative iff $(R, \bullet)$ is a commutative monoid. Commutativity of a ring is always a matter of its multiplicative operation because the additive operation is always assumed to be commutative.  Could anyone explain me the bold part? Why do we even in non-commutative rings (and fields etc.) assume the addition to be always commutative? Is there some serious reason? Would it make any trouble? Or studying of structures with non-commutative addition just doesn't give us anything new so we can take addition as commutative simply because of our comfort?