I accidently ran 'sudo chmod -R 775 /' and it completely broke my OS/Shell So I accidentally did sudo chmod -R 775 / when I meant to do sudo chmod -R 775 ./. I quickly realized and hit Ctrl^C, but not in time to save everything. I realize this is a really stupid mistake and all that but I'm aware of that and I would just like to fix my OS now.  Anyway, this completely broke my OS (Ubuntu 12.04). Currently, several functions of the shell, including tab completion prints the error      bash: cannot create temp file for here   And running any bash command that I have tried on any file in my home (/home/$USER) folder crashes the terminal. Several other random things don't work around the OS now.
What if I accidentally run command "chmod -R" on system directories (/, /etc, ...) I accidently ran  sudo chmod 755 -R /   instead of  sudo chmod 755 -R ./   I stopped it after few seconds, but now there is some problems such as  sudo: must be setuid root   How can I revert permissions back?
How do I find out which version and derivative of Ubuntu is right for my hardware in terms of minimal system requirements? For a given hardware configuration, how do I find out if Ubuntu will run on it? What considerations should I take into account when choosing an Ubuntu version and  such as:    with a lighter desktop than the usual Gnome and Unity  with the even lighter LXDE desktop   Obviously Ubuntu does not run on some processor architectures. So how do I go about choosing the right version and derivate. How can I find out the minmal system requirements? How to change geometry for one page without using \newgeometry or \restoregeometry Strange behavior of $\lim_{x\to0}\frac{\sin\left(x\sin\left(\frac1x\right)\right)}{x\sin\left(\frac1x\right)}$ Alright, scratch everything below the line. Let me present one cohesive question not marred by repeated edits.  The limit $\lim_{x\to a}f(x)=L$ exists iff for every $\epsilon&gt;0$ there is a $\delta&gt;0$ such that $|f(x)-L|&lt;\epsilon$ when $0&lt;|x-a|&lt;\delta$.  Thus, $\lim_{x\to0}\sin\left(\frac1x\right)$ does not exist because, being that it oscillates infinitely near $0$, there is no $\epsilon,\delta$.  On the other hand, with the limit$$\lim_{x\to0}\frac{\sin\left(x\sin\left(\frac1x\right)\right)}{x\sin\left(\frac1x\right)}\\\lim_{x\to0}x\sin\left(\frac1x\right)=0\\y=x\sin\left(\frac1x\right)\\\lim_{y\to0}\frac{\sin y}{y}=1\\\lim_{x\to0}\frac{\sin\left(x\sin\left(\frac1x\right)\right)}{x\sin\left(\frac1x\right)}=1$$  this proof can be shown. However, since $\sin\left(\frac1x\right)$ oscillates infinitely, by the same definition of limit we used to show the above, the limit does not exist. How do I resolve this discrepancy? If a derivative of a continuous function has a limit, must it agree with that limit? Suppose we have a continuous function $f : \mathbb{R} \to \mathbb{R}$. Suppose also that for a certain point $c$, $\lim_{x \to c} f'(x)$ exists. Must $f'(c)$ exist as well, and be equal to this limit?  This isn't quite the same as asking if derivatives are always continuous. The well-known function $f(x) = x^2 \sin (1/x)$ is continuous and differentiable everywhere, but its derivative has no limit at $x = 0$. I'm wondering if the derivative of a continuous function can have a discontinuity where its limit does exist. Find all functions $f:\mathbb{N_{0}} \rightarrow \mathbb{N_{0}}$ satisfying the equation $f(f(n))+f(n)=2n+3k,$ for all &amp; $n\in \mathbb{N_{0}}$, where $k$ is a fixed natural number.  A friend of mine suggested me to use recurrence relation. While it is unfortunate that I have problems understanding recurrence relation. Please refer information to understand difference equation, homogeneous equation &amp; auxillary equation.  Thanks in advance! Kindly don't down vote for not showing my attempt. I am seriously not able to understand the question and the process suggested to use. How do I improve boot speed? How to reset evolution settings to defaults? I have not used Evolution for long time now and I would like to reset all the settings and start from scratch. How would I be able to do this? Delete an old Facebook account Two years ago somebody made a fanpage for our company, but that person doesn't work here anymore. We don't have any login or password. We like to see that account be deleted, please. In my native language, we can say:     I have dog   Because I don't want to say a dog (one dog, how many dogs) or the dog (that dog, the listener don't care which dog).  p.s. after 3 years later, I have to say, why I ask this question, is I still cannot grasp how to use the right 'article word'. sometimes, a noun will use an article, sometimes, a noun could not(or omit) the article word before it. there aren't a formula for this. So, I have to remember all the time! I feel so frustrate In  thread, the question was to find a $f: \mathbb{R} \to \mathbb{R}$ such that  $$f(f(x)) = f(x) + x$$  (which was revealed in the comments to be solved by $f(x) = \varphi x$ where $\varphi$ is the  $\frac{1+\sqrt{5}}{2}$).    Having read about  shortly before though, I came up with this train of thought:  $$f(f(x)) = f(x) + x$$ $$\Leftrightarrow f^2 = f^1 + f^0$$ $$f^2 - f - f^0 = 0$$  where $f^n$ denotes the $n$'th iterate of $f$.  Now I solved the resulting quadratic equation much as I did with plain numbers  $$f = \frac{1}{2} \pm \sqrt{\frac{1}{4} + 1}$$ $$f = \frac{1 \pm \sqrt{1+4}}{2} = \frac{1 \pm \sqrt{5}}{2}\cdot f^0$$  And finally the solution $$f(x) = \frac{1 \pm \sqrt{5}}{2} x .$$  Now my question is: *Is it somehow allowed to work with functions in that way?** I know that in the above, there are denotational ambiguities as $1$ is actually treated as $f^0 = id$ ... But since the result is correct, there seems to be some correct thing in this approach.  So can I actually solve certain functional equations like this? And if true, how would the correct notation of the above be? I am a physics Master's student.  I have good grades, with CGPA above 9(/10)(However, all courses in my university are graded on a curve so the actual marks are significantly lower than 90%). This has been my marks throughout my undergraduate and graduate courses and I was happy because this was above average. Also, my summer projects in UG were usually computational and any difficulty I had in theoretical aspects I attributed it to my inexperience in advanced Physics.   However, recently I have started to work on pure theoretical project and while reading for the project I realized that I consistently miss some details from each topic. I understand the general idea, can re-derive most of the equations(with some effort) however when I discuss things with my professor or when I read further topics I realize that I have missed certain key-details. This is exactly similar to the case of me missing a few key questions in my exams and getting that 9 grade point instead of 10(or at-least I think so). I was not worried about this before but now I realize that there is some flaw in the way I study (but I do not know what).   Since I want to apply for Physics PhD I realized that I will need to have solid concepts and it would be best to correct my mistakes but I do not know how or even what could be the reason for my imperfect understanding.  Any direct suggestion would help or even certain general guidelines on what I can do.    Things I've tried recently -   1) I've started to written down almost everything I read. This is slightly laborious but is certainly helping. It also helps me to gloss over the things I read previously when I come back the next day.  2) I completely avoid smartphone when I'm library/study room so that I won't get distracted. Not sure if it helps me solve the above problem but certainly helps me study better in general.  3) I've tried to read the topics from several sources. The books I am reading is somewhat like a collection of research papers and hence does not have a exercises. So I though reading from various sources might help get better ideas but it's not really helping because most other sources are too high level as an introductory text. But this will probably help me in cases where it's practical to do this.  4) Somewhat similar to point (1)- I am trying reread, whenever I can, what I've done until that point. But not sure how much this will help me in filling the gaps. When $f(x+1)-f(x)=f'(x)$, what are the solutions for $f(x)$? The question is:     When $f(x+1)-f(x)=f'(x)$, what are the solutions for $f(x)$?   The most obvious solution is a linear function of the form $f(x)=ax+b$. Is this the only solution?  Edit  I should add that $f:\mathbb R\to\mathbb R$ to the question. What's the relationship between initial eigenvalues and sums of squared loadings in factor analysis? On the one hand I read in a comment  that:     You can't speak of "eigenvalues" after rotation, even orthogonal   rotation. Perhaps you mean sum of squared loadings for a principal   component, after rotation. When rotation is oblique, this sum of   squares tells nothing about the amount of variance explained, because   components aren't orthogonal anymore. So, you shouldn't report any   percentage of variance explained.   On the other hand, I sometimes read in books people saying things like:     The eigenvalues associated with each factor represent the variance   explained by that particular factor; SPSS also displays the eigenvalue   in terms of the percentage of variance explained (so factor 1 explains   31.696% of total variance). The first few factors explain relatively large amounts of variance (especially factor 1), whereas subsequent   factors explain only small amounts of variance. SPSS then extracts all   factors with eigenvalues greater than 1, which leaves us with four   factors. The eigenvalues associated with these factors are again   displayed (and the percentage of variance explained) in the columns   labelled Extraction Sums of Squared Loadings.   That text is from Field (2013) Discovering statistics using IBM SPSS, and this diagram accompanies it.    I'm wondering     Who is correct about whether it's possible to speak of eigenvalues after rotation? Would it matter if it was an oblique or orthogonal rotation?   Why are the "initial eigenvalues" different from the "extraction sums of squared loadings"? Which is a better measure of total variation explained by the factors (or principal components or whatever method is used)? Should I say that the first four factors explain 50.317% of variation, or 40.477%? I am trying to solve a 2 part question, the first part is to expand $\sqrt{1-x}$ up to and including the term $x^2$ which I did.  This gives me $1-(0.5)x-(0.125)x^2 + ...$  However, the 2nd part of the question says that by taking $x=(1/64)$ in the expansion of part (i) -> which refers to the one above, deduce that $\sqrt 7 = 10837/4096$. How do i do this part?  EDIT (After Hint Given By SimpliFire):  $$ \sqrt{1-\frac1{64}}=\frac{\sqrt{63}}8=\frac38\sqrt7 $$ $$ =\frac83\sqrt{1-\frac1{64}}\;=\sqrt7 $$ $$ =\frac83\left(1-\frac12\left(\frac1{64}\right)-\frac18\left(\frac1{64}\right)^2\right)\; $$ $$ =\frac83\left(1-\frac1{128}-\frac1{32768}\right)\; $$ $$ =\frac83\left(\frac{32768}{32768}-\frac{256}{32768}-\frac1{32768}\right)\; $$ $$ =\frac83\left(\frac{32511}{32768}\right)\; $$ $$ =\frac{260088}{98304} $$ $$ \frac{10837}{4096}\;\approx\sqrt7 $$  I'm not sure if I can present it like this, if it is okay i will post it as my answer :X Publicity badges might be taking internal links into account? Cannot change lock screen background on Ubuntu 18.04 How can I achieve the correct garden tap orientation when threading it in? I'm installing an external tap using a wall plate like this one:    And a tap like this one:    This might be a stupid question, but if I screw the tap into the wall plate it will end up at a certain angle. I can install the wall plate with that angle and the tap will end up with the correct orientation (i.e. pointing down). But what if I want to put another tap in later that has its thread cut slightly differently? How do I prevent it ending up upside-down or whatever? Are all the threads cut exactly the same in these taps?  This seems like a stupid design. Can a java file have more than one class? Is it supposed to be a HTML or an HTML I've seen many people who say:     This is a HTML page.   Yet I've also seen many people who say:     This is an HTML page.   Are both usages equally correct?  Or, which is the grammatically correct one?       Possible Duplicates: Hide UIToolbar UIBarButtonItems