Let $f:[1,\infty)\to\mathbb R$ be uniformly continuous.   Prove $\exists$ $M &gt; 0$ s.t $$\frac{\big|f(x)\big|}{x} \leq M, \hspace{11pt} \forall x\in[1,\infty)$$
Assuming $f:\mathbb R\to\mathbb R $ be an uniform continuous function, how to prove $$\exists a,b\in \mathbb R^+ \quad \text{such that}\quad |f(x)|\le a|x|+b.$$
What do the E and R prefixes stand for in the names of Intel 32-bit and 64-bit registers? More options when flagging for migration I think there should be more Stack Exchange networks available when flagging a question to be migrated. For example I'd think that the following question:    ...would be a better fit on unix.stackexchange.com instead of Stack Overflow. But without the option to mark it so, I feel hesitant to mark it. How to get all possible combinations of a list’s elements? If you have a conducting hollow sphere with a uniform charge on its surface, then will the electric field at every point inside the shell be 0. The reason the electric field is 0 at the center is clear from the symmetry of the sphere, but for a point at a certain distance from the center, shouldn't a net electric field exist?  I saw a similar question on the site but it was vaguely explained. Why should you not use Number as a constructor? I've got a project where I'm looking to tweak the standard lead conversion process.   Triggers and lead conversion has always been funky in past projects so I was hoping to start the design off by reviewing the order of execution, but after a long google search I'm coming up empty handed.   Anyone out there know the specific trigger order for lead conversion?    Edit: I'm not asking about trigger execution order for any object, but all the objects created in the lead conversion process.  I'd think it would be something like this:        Lead Before Update Triggers (isConverted = false, convertedAccountId = null, convertContactId = null, convertedOpportunityId = null)         Account Before Insert Triggers (not fired if merged with existing account)   Account After Insert Triggers (not fired if merged with existing account)   Contact Before Insert Triggers (not fired if merged with existing contact)   Contact After Insert Triggers (not fired if merged with existing contact)   Opportunity Before Insert Triggers (not fired if no opportunity) (OpportunityContactRoles null)   Opportunity After Insert Triggers (not fired if no opportunity) (OpportunityContactRoles = convertedContactId)   Lead After Update Triggers (isConverted = true, convertedAccountId = XXX, convertedContactId = XXX, convertedOpportunityId = XXX) Recently I found a claim saying that  $$  \int_0^\infty \left( \frac{\sin ax}{x}\right)\left( \frac{\sin bx}{x}\right) \mathrm{d}x= \pi \min(a,b)/2  $$ from what I can see this seems to be true. I already know that $\int_{0}^\infty \operatorname{sinc}xy\,\mathrm{d}y = \pi/2$, and so independant of $y$. My suspicion is that this is closely related to the integral above.   Can someone give me some suggestions for evaluating the integral above? Also are there any generalizations for the integral? Eg $$ \int_{0}^{\infty} \left( \prod_{k=1}^N \frac{\sin (a_k \cdot x)}{x} \right) \,\mathrm{d}x $$ Where $a_k, \cdots, a_N$ are arbitrary positive constants. It seems related to the , but there are some subtle differences. find command: -or option doesn't work I want to execute a command for an each file that matches a pattern. But the command that seems to be right, doesn't work for me, I have no idea why.  $ find . -type f -name '*.c' -or -name '*.h' -or -name '*.cpp' -exec ls {} \; $ ls script.sh  test.c  test.h Do I have to worry about copyright issues for code posted on Stack Overflow? I was wondering about the copyright of code snippets from answers. Let's say you ask a question and the solution consists of ten lines of code, which are given in an answer. Are there any restrictions about the use of that code?   It seems that the content of this page is under the . So does one have to attribute the author if code is used in an open source project? Can it be legally used in closed source projects at all?  I guess ten lines of code are not really problematic, but is there a critical number of lines? Why do shadows from the sun join each other when near enough? I was laying on my bed, reading a book when the sun shone through the windows on my left. I happened to look at the wall on my right and noticed this very strange effect. The shadow of my elbow, when near the pages of the book, joined up with the shadow of the book even though I wasn't physically touching it.   I have posted :The video seems to be the wrong way up, but you still get the idea of what is happening.  What is causing this? Some sort of optical illusion where the light gets bent?  Coincidentally, I have been wondering about a similar effect recently where if you focus your eye on a nearby object, say, your finger, objects behind it in the distance seem to get curved/distorted around the edge of your finger. It seems awfully related...  EDIT: I could see the bulge with my bare eyes to the same extent as in the video! The room was well light and the wall was indeed quite bright. future or present with when I have an URL structure like the following:     sitename.com/cellphone/nokia/galaxy-5678-nokia-cellphone-from-abc/   For more example:     sitename.com/cellphone/motorolla/new-motorolla-gta800-cellphone-from-zxy/   The directory structure is like the cellphone is the main directory of the module and the words like Motorolla and Nokia are subdirectories which are categories and then comes the title of the cellphone.  Here the word cellphone and Nokia in the first link and cellphone and Motorolla in the second link are repeated.  Is it any kind of keyword stuffing? will it be penalized by Google? For $p,q$ prime and $p \neq q$ show that $C_p \times C_q \cong C_{pq}$ Here are my thoughts so far:    $C_p = \langle x \mid x^p =e\rangle$ $C_q = \langle y \mid y^q =e\rangle$ $C_p \times C_q$ has elements of the form $(x^a,y^b)$ There are $p$ possible values for $x^a$ and $q$ possible values for $y^b$. So there are $pq$ possible elements in $C_p \times C_q$. $C_{pq} = \langle z\mid z^{pq} = e\rangle$ and there are $pq$ elements in this group. For an isomorphism from $C_p \times C_q$ to $C_{pq}$ we send $(e,e)$ to $e$ to ensure that the identities are mapped to each other. However, I'm not sure how to define an isomorphism for the other elements. siunitx uses math mode for symbols - workaround needed when using different fonts for math and text This is a follow up question from . The original problem has been solved using siunitx instead of dcolumn. However, the problem is that I am using mathpazo with osf as my main body font and eulervm as my math font. With siunitx used to decimal align tables this results in []() symbols being drawn in the math font, but the digits being drawn in the text font, as the following MWE example illustrates.  Is it possible to draw the symbols in the normal text font or redefine the mathfont for S columns completely?  \documentclass{scrartcl} \usepackage{booktabs} \usepackage[osf]{mathpazo} \usepackage[euler-digits]{eulervm}  % For Tables created by estout \newcommand{\sym}[1]{\ensuremath{^{#1}}} % for symbols in Table \usepackage{siunitx} \sisetup{ detect-mode,            group-digits            = false ,           input-signs             = ,           input-symbols           = ()[]-+ ,           input-open-uncertainty  = ,           input-close-uncertainty = ,           table-align-text-post   = false          } \begin{document} \begin{tabular*}{\textwidth}{     l @{\extracolsep\fill} *{2}{S[table-format=4.4]} @{}} \toprule \multicolumn{1}{@{}l}{\emph{Age}}  \\[0.5ex] 18--24 &amp;   [-1360.228]\sym{*}  &amp;  -1371.941\sym{*}  \\        &amp;       (6.915)         &amp;    (-7.953)        \\ 25--34 &amp;     -219.216          &amp;   -240.271         \\        &amp;     (514.894)         &amp;   (515.348)        \\ 35--44 &amp;     -310.715          &amp;   -311.438         \\        &amp;     (485.780)         &amp;   (486.013)        \\ 55$+$  &amp;       -5.135          &amp;     [2.656]        \\        &amp;      (53.267)         &amp;   (533.875)        \\ \bottomrule \end{tabular*} \end{document}   Edit: Thanks to David the problem has been solved including a fix for amsmath and extending to XeTeX. On a side note, the command for * generated by estoutshould now be simply plain text:  \newcommand{\sym}{#1} % for symbols in Table  \newcommand{\sym}[1]{\rlap{$#1$}} % Thanks to David Carlise again. We all use mathematical induction to prove results, but is there a proof of mathematical induction itself? I just realized something interesting. At schools and universities you get taught mathematical induction. Usually you jump right into using it to prove something like   $$1+2+3+\cdots+n = \frac{n(n+1)}{2}$$  However.  I just realized that at no point is mathematical induction proved itself? What's the mathematical induction's proof? Is mathematical induction proved using mathematical induction itself? (That would be mind blowing.) Getting error message when trying to start a virtual machine I have been using VMWare on Windows for a long time. But after a long wait, I moved to VirtualBox on Ubuntu 11.10. I installed Ubuntu, 32 Bit, installed all available updates and installed Virtual Box. When I try to create a new Windows installation inside VirtualBox, I got the following error messages.  VirtualBox - Error  Failed to open a session for the virtual machine Windows XP. The virtual machine '**Windows XP**' has terminated unexpectedly during startup with exit code 1. Details  Result Code: NS_ERROR_FAILURE (0x80004005) Component: Machine Interface: IMachine {5eaa9319-62fc-4b0a-843c-0cb1940f8a91}   2nd error dialogue  Virtualbox - Error in suplibOsinit Kernal driver not installed (rc--1908) Please install the virtualbox-dkmbs package and execute 'modprobe vboxdrv' as root.    I have already tried reinstalling VirtualBox. Google result seem to indicate the the problem happens due to Kernel updates.   Is there anyway I can get this working? I need this for malware analysis and if VirtualBox is going to crash on me all the time, then I won't be able to use Ubuntu for work.  Output to dpkg -l | grep virtual   server rc  virtualbox                             4.1.2-dfsg-1ubuntu1                     x86 virtualization solution - base binaries rc  virtualbox-qt                          4.1.2-dfsg-1ubuntu1                     x86 virtualization solution - Qt based user interface  cute 'modprobe vboxdrv' as root.&lt;p&gt; I'm one of those exceptions that deviates from the norm: I run CyanogenMod without any Google apps.   Is it possible to download the Stack Exchange Android app .apk directly? Number of publications needed to get into a computer science PhD program? I've looked at the resumes of the type of candidates that get into computer science PhD programs at the top few universities (e.g. Stanford, MIT etc.) and a lot of them seem to have multiple publications (2-4) done during their undergraduate years. Is this representative of the entire pool? Or is this just a self-selected group that puts their resumes online.  I currently have one first-author workshop paper (5 pages), and I wonder how this might affect my chances at entry into these top universities. Simple as the title states: Can you use only Java commands to take a screenshot and save it?  Or, do I need to use an OS specific program to take the screenshot and then grab it off the clipboard? What sort of cheat sheets for a new DM lead to a better flowing 5e game of Dungeons and Dragons? The question is, what elements on a DM screen are essential? I'm new at playing and DMing, altough a lot of experience watching games, just got a group to play with now. Started with the starter set in 5E and the Lost Mine of Phandelver adventure, however I've noticed the game can come to a stop when checking the rules or how to do something, while getting the books and stuff like that. So I thought to make a DM screen with some cheat sheets, of the most usual things new players, and new DM's have doubts on, and how to make the game flow well without long rule-checking breaks. What are the essential things to have on that screen? So far this is what I found  but not sure if it has all I need or so much stuff that'll also make the game stop a lot while cheking it out.