$\lim_{x \to 0}\frac{\sin x}{x}$ intuition
How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?
Error when updating texlive 2015 When I want to update packages of texlive 2015 I get this error? what is the problem?  tlmgr update --list  The locale codeset (cp720) isn't one that perl can decode, stopped at   C:\texlive \2015\tlpkg\tlperl\lib/Encode/Locale.pm line 123. Compilation  failed in require at C:\texlive\2015\tlpkg\tlperl\lib/LWP/UserAgent. pm  line 1001. I tried to write out the aura if statement but I am getting stuck if someone can explain it to me in detail. thank you  &lt;aura:if isTrue=&quot;{!lessthan(v.Tl.time, v.Tl.End_Date_Time1__c)}&quot;&gt;                            &lt;/aura:if&gt; Splitting lines with points while maintaining other dissolved lines? I am on ArcGIS Desktop 10.2. I have a line feature class of a stream network. I also have a point feature class along the main stream (line) where a catchment enters that stream. I have dissolved my whole streams layer into one line feature and want to split this feature at the points.    However, when I use the  tool, the lines that don't have a point splitting them are still being split at the intersection of two streams.    Why did this line not stay as one feature with the other lines on that side of the splitting node and how can I prevent this from happening? Handle either a list or single integer as an argument Unable to acheive desired effect with ID mask I'm trying to make the render have an effect where the stars (which are exploded fragments) have a glowing glare-like effect and the other objects (i.e. film reel and cubes) are their natural colors.  However, despite having made the star objects all a pass index of 1 and the rest 0 by default, everything seems to render a green glowing effect that's supposed to be only for the objects with a pass index of 1.  To illustrate:  This is the render of the image naturally (I rendered at very low quality but it's just for demonstration purposes):    And this is with the composite nodes:    So in essence I want the objects in the the first render I showed to keep those colors, but the stars to have the colors of the green glowing effect.  As you can see from the 2nd picture everything has the green effect.  My node setup is pretty big so I will provide a link to download the  so you can see the nodes more clearly. Setting a custom RGB background color in beamer I believe I've correctly followed the manual in defining a custom background color in the example below.     But as the example shows, the background color is black rather than an extremely pale beige.    Could anybody advise what I'm doing wrong please?  \documentclass{beamer} \definecolor{MyBackground}{RGB}{1.0000    0.9451    0.6549} \setbeamercolor{background canvas}{bg=MyBackground} \begin{document} \begin{frame} Hullo world \end{frame} \end{document} Get Age of a person in MySQL Until I went to army, I (had been / used to be / was ) a introverted person. - which one is right? Until I went into the army, I (had been / used to be / was ) an introverted person. And after I I finished army service, I became more confident.   I think all of these are possible.  As for had been, I'm referring to the state of me being introverted before the accident that happened in the past. So, I think I can use had been.  And at the same time I feel I can use used to be and was.. If I don't want to emphasize the time gap between two accident, I feel I don't need to use past perfect. So I think this problem depends on how I'm going to say something.   which one is preferable? and what is the difference? My webcam just came on "out of the blue" What are the rules for splitting words at the end of a line? What are the rules in English language to split words at the end of a line?   Where exactly must the hyphen split the word? I am developing firefox extension and wanted to count total number of text box of webpage so how to count text box? Vanishing of Taylor series coefficient How do I center floated elements? Testing convergence of series $\sum_{n=3}^\infty\frac{1}{n (\ln(n))^p(\ln\ln(n))^q}$ Degrees of freedom for standard deviation of sample would someone please explain why the degrees of freedom for a random sample is n-1 instead of n ?   I'm looking for an explanation that is intuitive and easily understood by a high school student. OpenCV argc and argv confusion Subject vs. Object marking for whoever? I know similar questions have been asked before, but I'm having trouble reconciling the following sentence, received in an email:     Can we ask whomever is your contact there to email us a job so we can check backward compatibility?   I could understand using objective case if the sentence were "can we ask (him) to email...", but I get tripped up considering "whomever" to be the subject of "(he) is your contact there". How does order-preserving encryption work? Order-preserving encryption (OPE) is, apparently, a method of encrypting data so that it's possible to make efficient inequality comparisons on the encrypted items without decrypting them.  I've been coming across this term in various places (including ) lately, but I have no idea how such encryption schemes are supposed to work.  Any obvious methods I can think of to allow such comparisons on encrypted data would result in catastrophic security failure.  Certainly, I assume that OPE must involve some kind of security tradeoff compared to traditional encryption, but given that it seems to be actively  and , it seems that it must be possible to implement in a way that retains at least some level of useful security.  I just don't see how.  Given that  didn't turn up any convenient Wikipedia articles or other popular summaries of OPE, I figured I'd try asking for one here before diving into the academic literature.  (At worst, I may try to answer my own question later, if nobody else beats me to it.)  So, to summarize, my question is: How does order-preserving encryption work, and what security properties does it provide? Let $G$ be a finite group and $F$ a field with $\mathrm{char}(F)=0$ or coprime to $|G|$. Let $V$ be a $FG$-module in a way that every $ FG$-homomorphism $ f : V \to V $ is given by $f(x)= \lambda x $. Then $V$ is irreducible.   I already managed to proof this by contradiction, using Maschke's Theorem. We can  write $V$ as $U\oplus W$ and get a $FG$-homomorphism $\pi:U\oplus W \to U\oplus W$, $\pi (u+w)=u$, then $\pi(u+w)=\lambda (u+w)=u $ then either $U$ or $W$ are trivial and thus $V$ is irreducible.  My question is if this statements still holds if the characterictic of $F$ divides the order of $G$, since I only used this fact in my proof to use Maschke's theorem. Why is python ordering my dictionary like so?