Why does my float of 999999999 become 10000000000?
Is floating point math broken?
When I visit a site I haven't visited (while logged in) for a while, I see:  Welcome back! If you found this question useful, don't forget to vote both the question and the answers up.  That's often intended behavior. But today I visited  and was shown that banner even though the question and all its answers are locked. Voting arrows aren't even shown on any of the posts on that page. I believe that banner should be disabled on pages where there is no post that can be voted on by anyone. Are black hole regarded as baryonic matter in cosmology? Is there a way to show Spotlight indexing status/progress in Yosemite? In previous versions of OS X, you could click the Spotlight icon in the menu bar to show the status of the Spotlight indexing, and it would show an estimate ("6 hours left"), along with a progress bar.  I've updated to Yosemite yesterday, and I noticed that Spotlight is not showing some expected results, i.e. files I know to be there, but it just doesn't find them if I type in their name and file type ("kind:excel vacation").  When I start typing in the Yosemite Spotlight window, it shows a small progress bar under the search box, but there's no estimate.    Is there another way to show the progress or an estimation on how long the indexing is going to take? Proving that $\sum\limits_{n = 0}^{2013} a_n z^n \neq 0$ if $a_0 > a_1 > \dots > a_{2013} > 0$ and $|z| \leq 1$ I'm going to teach a preparation course for the complex analysis qualifying exam from my university (which basically consists of me doing some problems from past exams) and I'm trying to solve some questions from previous exams. One of the questions is the following:           Prove that $\displaystyle{\sum_{n = 0}^{2013} a_n z^n \neq 0}$ if the coefficients  satisfy $a_0 &gt; a_1 &gt; \dots &gt; a_{2013} &gt; 0$ and $|z| \leq 1$.      I tried to approach the problem by using the reverse triangle inequality to try to isolate the leading term, which I thought should be the constant coefficient, as follows:  \begin{array} . \left|  \sum_{n = 0}^{2013} a_n z^n \right| &amp;= \left| a_0 +  \sum_{n = 1}^{2013} a_n z^n \right| \\ &amp;\geq |a_0| - \left|  \sum_{n = 1}^{2013} a_n z^n \right|\\ &amp;\geq |a_0| -  \sum_{n = 1}^{2013} |a_n z^n|\\ &amp;\geq a_0 -  \sum_{n = 1}^{2013} a_n |z^n|\\ &amp;\geq a_0 -  \sum_{n = 1}^{2013} a_0 |z^n|\\ &amp;= a_0\left( 1  -  \sum_{n = 1}^{2013} |z^n| \right) \end{array}  Then for $|z| &lt; 1$, we have that this last expression is equal to  $$ a_0\left( 1  -  |z| \frac{|z|^{2013} - 1}{|z| - 1} \right) $$  and my hope was to prove that this was always positive, nevertheless, after failing to prove it, I plotted the expression inside the parenthesis as a function of $|z|$, and found out that it changes sign in the interval $(0, 1)$.  Question  Can my approach somehow be made to work? And if not, how can I prove that the sum $\displaystyle{\sum_{n = 0}^{2013} a_n z^n \neq 0}$ under the given conditions?  Thank you very much for any help. Unable to start XAMPP using sudo in Desktop Entry I am using Ubuntu 18.04. I have installed XAMPP and created a .desktop file to run it.  [Desktop Entry] Type=Application Name=XAMPP Control Panel Version=7.3.0.0 Exec=sudo -i python /opt/lampp/share/xampp-control-panel/xampp-control-panel.py Encoding=UTF-8 Terminal=false Comment=Start and Stop XAMPP Icon=/home/lee/.local/favicon.ico   But, for some reason it won't run. The "Exec" line runs fine on the CL. I have it set to execute. Any ideas? Is there something like Linux console in Mac OS X? Like "terminal", but without running graphics environment. Can I visit the UK as a tourist before my Student Visa starts? Does a surjective ring homomorphism have to be surjective on the unit groups? What safety precautions should I take when taking photos in the snow? I’m going to Queenstown, NZ in a couple of weeks and want to take my (very new, very precious) Canon 7D with me. I’ve done a little bit of research on how to protect my baby from cold climate (e.g. ) and found that the biggest problem is probably going to be condensation. Some suggestions have been to place the camera in a plastic bag or letting the camera gradually adjust to the new temperature or placing silica gel in the camera bag to absorb moisture. I am leaning toward the latter at the moment because it sounds like it’s the easiest, so I was just wondering if anyone has had any experience in this matter and could share their wisdom.  As an alternative I could take my Canon 350D, as I really wouldn’t care if that got damaged in the snow. However I’m a film student and tend to take just as many videos as photos – hence why I really want to take the 7D. But I would seriously regret it if it got damaged… dilemma!   So as I actually haven’t used a question mark in the body of text, I will specify that the question is: What safety precautions should I take when taking photos in the snow?  Cheers. Adding console.log to every function automatically Graph vertex chromatic number in a union of 2 sub-graphs $G_1$ is graph on the set of vertices $\{1,2,3,4,5,6,7,8\}$, $G_1$ vertex chromatic number is 5. $G_2$ is graph on the set of vertices $\{7,8,9,10,11,12,13,14,15,17,18,19,20\}$, $G_2$ vertex chromatic number is 7. We know $G_1$ and $G_2$ have an edge between vertex 7 and vertex 8. (We already used 2 different colors on them both). $G$ is graph on the set of vertices $\{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20\}$, and its set of edges is the union of the edges set of $G_1$ with the edges set of $G_2$. The vertex chromatic number of $G$ is: 5 / 7 / 12 / we can't know without further information Prove the answer. I think I got it, can someone approve? After the union to $G$, we copy the colors of $G_2$ to 7,8,9,10,11,12,13,14,15,16,17,18,19,20, obviously, $G$ vertex chromatic number is 7 and can't be less. We go through the vertices 1,2,3,4,5,6,7,8. We look for a vertex that doesn't connect to a different vertex. (There must be one, because if only one edge was missing in $G_1$, our chromatic number of $G_1$ was 7, but it's 5). Once we find a missing edge, we color both its vertices in the same color. We go through vertices 1-6, and color each vertex that doesn't have a color, with the colors of $G_2$ that we didn't use in $G_1$ (there should be 4-5 of them). How to delete a keyboard layout in Windows 10 I installed Windows 10 on a physically German keyboard, then installed a Window English software keyboard and bought some little stickers to make my keyboard look OK.  However, Windows shows 2 keyboards installed &amp; occasionally toggles back to German.  Note that I am not talking about removing a language (which is all that I can find when I Google).  How do I remove the German keyboard layout? Microscopic interpretation of pressure in liquids Do indexes work with "IN" clause If I have a query like:  Select EmployeeId  From Employee  Where EmployeeTypeId IN (1,2,3)   and I have an index on the EmployeeTypeId field, does SQL server still use that index? Twice today I noticed that my reputation increases with 15 on Stack Overflow, but when I click to see my account, the change is being reverted and none of my recent answers are marked as accepted. Then why does the reputation on the top of the page change ? Use fixed keyboard for a given app I would like to tell my Android that when I'm in a given app it should switch to a given keyboard. My use case is that I want to use Hacker keyboard with Connectbot. How do I move Ubuntu dock to bottom on Ubuntu 17.10 and later? Evaluating the product $\prod\limits_{k=1}^{n}\cos\left(\frac{k\pi}{n}\right)$ Recently, I ran across a product that seems interesting.  Does anyone know how to get to the closed form:  $$\prod_{k=1}^{n}\cos\left(\frac{k\pi}{n}\right)=-\frac{\sin(\frac{n\pi}{2})}{2^{n-1}}$$  I tried using the identity $\cos(x)=\frac{\sin(2x)}{2\sin(x)}$ in order to make it "telescope" in some fashion, but to no avail. But, then again, I may very well have overlooked something.  This gives the correct solution if $n$ is odd, but of course evaluates to $0$ if $n$ is even.   So, I tried taking that into account, but must have approached it wrong.   How can this be shown? Thanks everyone. How to log source file name and line number in Python My internet connection used to be a direct LAN connection to my provider. Back then, everything would load fine on both Windows and Ubuntu (dual boot). However, a while ago they started needing me to dial (PPPoE) using a username and password. Gateway, subnet mask, IP, DNS servers all stayed the same. But since then, I haven't been able to browse certain websites on Ubuntu, even though there have been no such issues on Windows. Some example websites are -  (although share.ovi.com loads fine, and nokia.com loads fine),  (works on Chrome(ium) and Opera but not on Firefox (both 3.6 and 4)) Mozilla  and other random websites.  Some of the websites that don't load show timeout messages and for some websites (like the moz addons one), the browser will keep trying to load without an end (I've left it like that even for hours but not noticed anything different happen).  I have tried changing the DNS servers to public ones. I have even tried booting from a Fedora LiveCD and then changing the DNS to those (and even to the ones of OpenDNS), but the exact same thing happens. What could be inherently wrong with some config within Linux itself that is causing this problem?  Does anyone know why this is happening and how it can be fixed?  Note: This question has been  on SU, but not gotten any responses.  Update: Just saw  that someone else was having similar problem and solved it by putting a NetworkManager.conf file in /etc/NetworkManager. What needs to be in that file?