What is the meaning of this sentence? I ain't worried 'bout nothin'
Correct interpretation of a "double-negative" in American Pop Culture (i.e. "I ain't afraid of no ghost!")
Need help with a question regarding the Big Oh In class we are currently covering upper/lower bounds, big Oh and omega and the like. I am pretty good on the "typical" functions one would do, but at a complete loss at "general" statements. This ons function, for example:  $$\forall f\in\mathcal{F}: \lfloor \sqrt{\lfloor f(n)\rfloor }\rfloor \in O(\sqrt{f(n)}).$$  the domain F by the same is all natural numbers that return a real positive number when inputted. My first instinct with something like this is to remove the floors, the general strategy I though to solve this is remove the outer floor, then get rid of the square root, and then the inner floor. But I have no idea how to go about this or if this is even the right way to do it.  Help please? Thanks in advance. Why does my Mac's list of "Open with" applications start listing the apps twice and sometimes three times? I stumbled upon this "relation" (is the name correct?):  $$ \lim_{m \to \infty} \lim_{n \to \infty} \cos^{2n}(m! \pi x) = \begin{cases} 1,&amp;x\text{ is rational}\\ 0,&amp;x\text{ is irrational}\end{cases} $$  How is it called and why is it so? I'm really not asking for a proof since I fear it would be too complicated for me to understand, but rather for an "intuition". Find all $n \in \mathbb{N}$ such that $\phi(n) = 4294967296=2^{32}$.  I managed to find that $16106127360$, $8589934592$, $10737418240$ and $12884901888$ are solutions for the equation, but I do not know how to find all of them. Commandline shortcut for current directory similar to ~ for home directory? When i use the cp or move command in a terminal window, i'm currently with bash in a certain folder like this.  NES@server:~/Desktop/dir1$   And now i wanna copy a file from here ~/anotherdir/dir2 into the current chosen folder in bash (dir1) i would use the command  cp ~/anotherdir/dir2/file ~/Desktop/dir1   does a shortcut string exist to refer to the current chosen directory? So that in this example i don't have to provide the full path to the target dir, but the command knows it should use the current chosen directory in bash? i.e. as ~ stands for the home directory? How to re-index the values of an array in PHP? How to have a figure with caption in multicol environment? I am having the following problem with adding a figure inside the multicol environment:  \documentclass[10pt, twoside]{book} \usepackage{graphicx} \usepackage{subfig}  \begin{document}   \begin{multicols}{2}  a test file for picture inclusion along with the captions and labeling \begin{figure}  \centering  \includegraphics[width=5cma]{Cauchy_sequence_illustration-png}\\  \caption{Lets see}\label{pinki} \end{figure} \end{multicols}  \begin{figure}  \centering   \includegraphics[width=5cm]{Cauchy_sequence_illustration-png}\\  \caption{Lets see}\label{pinki} \end{figure}    \end{document}    After this while I am pressing Ctrl + Shift + X (usually I compile like this in DVI format and then clicking "dvi--->pdf" I convert it into PDF document.) the picture in multicol environment is not shown in YAP Viewer but the second one (which is outside of multicol environment) is shown along with the caption.  Kindly help me how to handle this problem. Please note that I am using the figure in .ps format. And I am not allowed to use any other format according to the instruction. “between” vs. “among” Today I was cut off in the middle of the following sentence:     Between Cook, Strauss, and Pietersen—   My friend said I was wrong. He said that for more than two entities, among/amongst are used, and that between is only for two entities.   I vaguely remember some rule like this, but I asked him to hear the whole sentence, which was:     Between Cook, Strauss, and Pietersen, they’ve notched up 56 centuries in Test cricket.   Should I have used among here? Seems correct to me to use between, but my friend was certain.   Another friend pointed out the following sentence:     I’m still choosing between Harvard, Yale, and MIT.    Certainly among doesn’t seem to fit here, and she, to me, was correct in using between. In the Prisoner of Azkaban, Harry and Lupin could practice the patronus on the boggart, but when Harry was in the final task in the Goblet of Fire, he tried to use the patronus on the boggart, it didn't work and he then moved on to use ridikkilus.  Why could he use a patronus against the boggart, but then not in another? I need to remove the annoying new "locking" screen that shows a giant clock: I can't remove it with just moving the mouse (as with any other desktop environment), the animation is slow, and it isn't asking me for a password!  I managed to disable it, just to discover that now I can't lock my screen on purpose, so I can't go away from the computer.  Just to clarify, I want to:   After some time the screen could go black, but if I move the mouse or press any key then I can use it directly (like a normal screensaver). If I press super-L then it is locked, and I must type the password to unlock (like a normal lock screen).   I found several "solutions", but none seems to work: How do I switch sides in the Civil War? Conjugate subgroup strictly contained in the initial subgroup? Let $G$ be a group, $H\subseteq G$ a subgroup and $a\in G$ an element of the group. Is it possible that $aHa^{-1} \subset H$, but $aHa^{-1} \neq H$?   If $H$ has finite index or finite order, this is not possible. Direction of angular velocity Angular velocity is the rate of angular displacement about an axis. Its direction is determined by right hand rule.  According to right hand rule, if you hold the axis with your right hand and rotate the fingers in the direction of motion of the rotating body then thumb will point the direction of the angular velocity.  The direction of angular velocity is above or below the plane. But what does it mean? I mean in linear velocity the direction of velocity is in the direction of motion of body but what does it mean that body is moving in one direction while the direction of its angular velocity is in another direction? How to check the tasks that are running at different run levels in debian? Let $f: M \to N$ be a mono in $\mathsf{Mon}$. I want to prove that the underlying function $U(f): U(M) \to U(N)$ is injective.   How can this be done ? Thanks in advance. Oracle 11g: increasing buffer cache with AMM On a 2-node RAC we have enabled Automatic Memory Management. The advisor views indicate that increasing the buffer cache by 4 GB will half the physical reads, and we have 4 GB to give.   How must we do this? By increasing memory_target and letting Oracle grab more memory for the buffer cache? Or by explicitly setting a value for db_cache_size (which now is zero)? I have 3 old computers lying around right now running a P2 at 800 MHz(?), Intel Mobile 1.6 GHz, AMD Athlon XP 2000+ at 1.66 GHz, and (might not use this) P4 at 2.7 GHz, all with 512 MB Ram, and am considering clustering them together for fun/knowledge. They would be running an undecided version of linux, preferably ubuntu based.   The issue is what I want to use it for: general computing and occasional video encoding. By general computing I mean day to day tasks. However I'm not sure if every program started by a single X session is going to exist on the same machine, defeating the purpose of such a system. Will programs be split up or exist on one machine?  Second, assuming this is running 100baseT ethernet (not sure if the PCI slot itself could handle Gigabit), would the speed of having a program exist over the network be an issue? It seems that the constant asking of various things in RAM would be quite slow.  And before you say "buy another computer!", that's not the point of this question. I'm asking would it be usable, not necessarily practical. And yes I know, this is going to be extreamly power consuming. Prove that : $$\sum_{k=0}^{\infty} \frac{(-1)^{k}}{(2k+1)^3}=\frac{\pi^3}{32}.$$    I think this is known (see ), I appreciate any hint or link for the solution (or the full solution). I'm having a bit of a trouble with the below question     Given $G$ is an undirected graph, the degree of a vertex $v$, denoted by $\mathrm{deg}(v)$, in graph $G$ is the number of neighbors of $v$.   Prove that the number of vertices of odd degree in any graph $G$ is even. Why is learning modern algebraic geometry so complicated?