I have an entire function $f $, whose restriction to $\mathbb C \setminus \{0\}$ is defined by $$f (z)=\frac {\sin z-z} {z^3}.$$ I must show that it has infinite zeros. Clearly it has order $1$; I think that I should use Hadamard factorization theorem, but I can't see clearly how to proceed. I'd like just a hint to start with, thank you in advance
Show that $\sin(z) = z$ has infinitely many solutions in complex numbers. Little Picard theorem should help, but using big Picard theorem is undesirable. Thanks a lot!
What should I do if I have two libraries that provide functions with equivalent names? Fixed point, union of $\aleph_0, \aleph_{\aleph_0},\aleph_{\aleph_{\aleph_0}}\dots$ [see Noah's comment on notation] An alternative software to Live Writer? What is the difference between "Have you seen this?" and "Did you see this?" What's the difference between these two phrases? The sum $\sum_{k=1}^nk(k!)$ can be easily calculated by noting $k(k!)=(k+1)!-k!$. Is there a way to calculate the sum nicely using a combinatorial argument. Is it possible to notice it is $(n+1)!-1$ combinatorially? How to determine when Settings change on iOS What is the difference between confidence intervals and hypothesis testing? I have read about   with some commentators suggesting that hypothesis testing should not be used. Some commentators suggest that confidence intervals should be used instead.    What is the difference between confidence intervals and hypothesis testing? Explanation with reference and examples would be appreciated. What should we do with old, very popular closed questions? Motivated by the deletion of     On one hand, I disagree with these closures, because:  These questions were (and still are) very popular They have some good information in them (or at least the first one does) and it feels like bad sportsmanship to remove good information from the internet, particularly when it was contributed by your fellow users  Number 2 in particular bothers me. A lot. On the other hand, I do agree that:  The community of 10k users should be able to decide which closed questions they wish to delete on their own without me intervening These questions should definitely remain closed, because they either have an absurd # of answers, or are duplicates (though some duplicates ). Which means they are eligible for deletion … forever. These questions wouldn't survive more than 10 minutes if asked today on Stack Overflow, so in some ways they are artifacts from the past, like dinosaurs in an era of mammals.  There is some related discussion in:   While I normally favor code solutions here, I am not sure I like the idea that once a question gets 400 upvotes it should become extremely difficult to delete. It feels like mob rule. Official policy on the blog: I was confused, trying to copy some files from one PC to another. I have it figured out, but the syntax is still confusing to me. This works:  scp ~/Desktop/Volenteer.png jay@server.ip:~j0h/b   which puts Volenteer.png in the folder /home/j0h/b.  However, this doesn't work:  scp ~Desktop/Volenteer.png     jay@server.ip:~j0h/b   This also fails, giving an exit status 1 file not found:  scp ~/Desktop/Volenteer.png     jay@server.ip:~/j0h/b   As does this:  scp ~Desktop/Volenteer.png     jay@server.ip:~j0h/b   So clearly, there is some difference between ~ and ~/ That difference is the presence of /   $~/ bash: /home/j0h/: Is a directory $ ~ bash: /home/j0h: Is a directory   So why in scp, does the ~ resolve to ~/ ? That is a guess, I cant verify that's what is happening.  But it seems inconsistent, and therefore confusing.  Is this a bug in scp? or is there something about tilde I am missing? How did Thanos know about the power of "The Snap"? In the scene on Titan with Doctor Strange in Avengers: Infinity War, Thanos said,     With all six Infinity Stones, I will simply snap my fingers and it would all cease to exist.   Then again, in the very first scene with Thor and Loki, when Maw gave Thanos the Space Stone, he said that no one has ever worn two Infinity Stones together.   So how come Thanos knew about the power of the Snap? Because as Wong puts it to Tony, the Big Bang hurled the six Infinity Stones across the universe.   So if no one had collected all the six stones before Thanos, then how did he know about the ability to "Snap"? Install a single specific package from future distribution I'm currently using precise. I need to upgrade a certain package (namely  and it's dependencies) to a newer version, which is currently found in raring (alfa at the time of writing this). How to do it ?  What will happen if I just add to my sources.list:  deb http://archive.ubuntu.com/ubuntu raring main   Will the next apt-get update / apt-get upgrade, upgrade most of my system to raring then ? How do you attach a debugger to a Web service? I am using a Web service. Can anybody tell me how to debug through it? Based on the question , I got curious. Is there a guide or resource that describes how the price of a ticket is determined?  When you search you often see curious effects like cheaper tickets for a flight from A to B with a layover compared to a direct flight. This seems counter-intuitive from an outsider's perspective since you fly twice. Also one way tickets more expensive than 2 ways.  It can be a short set of rules. Something that helps someone to get started with finding good prices. I know these can be very complex and they probably change over time and over airline interests but there is probably a simplified set of rules that can be enunciated. Why was a moved question deleted? Moderator to whom deletion is attributed claims they didn't do it A  appears to have been deleted, and deletion is attributed to a moderator,  deleted by Sathyajith Bhat♦ 12 hours ago , however,  (however, they did previously (unsuccessfully) tried migrating it to another site in the network where they're also a moderator, but migration was rejected by another moderator, it was then on hold on webapps, and then the hold was removed, which was supposed to have been the end of it).  Can someone explain what's going on here?  And restore the question that clearly wasn't meant to have been deleted, was a HNQ, and has 75 votes on the question, plus 74 votes on the top answer, and 56 on second answer; and 19 on third?  There's a lot of links to this question, too, and now they're all broken, making SE look like a community hostile to a popular question ontopic for the site it was on. Move the Add Favorite / Ignored Tags boxes to the top It seems that most people who use the ignored tags feature end up with a fairly long list of those tags.  Although , it is sometimes necessary to add new ignored tags manually (typically when adding some-tag*).  It would be a lot easier if the add box was above the long list of ignored tags rather than below. I suppose the same would apply to the favorites tags for consistency's sake. Pdf of the square of a standard normal random variable Elementary argument for conservation laws from symmetries *without* using the Lagrangian formalism It is well known from Noether's Theorem how from continuous symmetries in the Lagrangian one gets a conserved charge which corresponds to linear momentum, angular momentum for translational and rotational symmetries and others.  Is there any elementary argument for why linear or angular momentum specifically (and not other conserved quantities) are conserved which does not require knowledge of Lagrangians? By elementary I mean, "if this is not so, then this unreasonable thing occurs".   Of course, we can say "if we want our laws to be the same at a different point in space then linear conservation must be conserved", but can we derive mathematically the expression for the conserved quantity without using the Lagrangian?  I want to explain to a friend why they are conserved but he doesn't have the background to understand the Lagrangian formalism. Since I installed TeXLive 2016 I cannot build documents with the standalone document class any more using LuaLaTeX (PDFLaTeX works fine). For example:  \documentclass{standalone} \begin{document} hi \end{document}   Gives me:  ! Undefined control sequence. \sa@placebox -&gt;\newpage \global \pdfpagewidth                                                =\wd \sa@box \global \pdfpageh...  l.4 \end{document}   How to fix that? Which Ubuntu repositories are totally safe and free from malware? There are two vectors called $\vec{a}$ and $\vec{b}$. Vector $\vec{c}$ is the bisector and it can be given as  $$\vec{c} = |b|\vec{a} + |a|\vec{b}$$  How to prove that? I have used the dot product method. But there I can't find the angle between them. Then I tried to do this by using unit vectors. Then I got an answer like in the given picture. . Can you help me to get the correct answer