We can tell that $$0.11111111... \cdot 9 = 0.999999999...$$ And that $$\frac19 = 0.11111111111...$$  Therefore $$\frac19\cdot9 = 0.999999999...$$  However, we know that $$\frac19\cdot9 = \frac99 = 1$$  Note: I'm taking in account that ... are the other rational digits left.  What am I making wrong? What is misunderstood?  Thanks for the help in clearing this problem.
I'm told by smart people that $$0.999999999\ldots=1$$ and I believe them, but is there a proof that explains why this is?
Using package nomencl How to change the forgotten root password? I forgot my root password...actually I think I know what it is because it is the same password I have for pretty much everything but in the Terminal in tell me "Sorry, try again." Is there a way to reset the password? If so how? Expected value as a function of quantiles? I was wondering where there is a general formula to relate the expected value of a continuous random variable as a function of the quantiles of the same r.v. The expected value of r.v. $X$ is defined as: $E(X) = \int x dF_X(x) $ and quantiles are defined as :  $Q^p_X = \{x : F_X(x) = p \} =F_X^{-1}(p) $ for $p\in(0,1)$.  Is there for instance a function function $G$ such that:  $E(X) = \int_{p\in(0,1)} G(Q^p_X) dp $ The bikeshed problem and Stack Exchange In short, :     If you go before the Board of   Directors and ask for 1.5 billion   dollars to build a nuclear reactor, no   one will review or discuss the details   of the plant. 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JavaFX: Undecorated Window The additive group $\mathbb{G}_a$ over an infinite field $k$ is not a topological group An algebraic group is not necessarily a topological group, since for an algebraic group, the product map $G \times G \to G$ is continuous when $G \times G$ is given the Zariski topology, which is finer than the product topology.   So does this tell you that the additive group $\mathbb{G}_a$ over an infinite field $k$ is not a topological group? The underlying variety of $\mathbb{G}_a \times \mathbb{G}_a$ is $\mathbb{A}_k^1 \times_k \mathbb{A}_k^1 = \mathbb{A}_k^2$, whose Zariski topology is the cofinite topology, where every open set is also open in the product topology (since $\mathbb{A}_k^1$ also has the Zariski topology). How do I add a custom keybind to a button on any website? I use the following command to clear a directory, of files and directories over 30 days old, and move them to an archive directory which I can delete after a few weeks if nobody asks for their files back. The target directory has subdirectories by user name, so will the archive directory.  This is the command I use:  find /path/to/directory/username/ -mtime +30 -exec mv "{}" /path/to/archive/username/ \;   I suggested a modified version of this to answer a question on ask ubuntu, another user edited the code to change the end of line \; for + as it's faster(and more correct?).   However, using + in this way works if the -exec command is ls -lh but not in the actual command that I use. If I try it with + I get an error message:  find: missing argument to '-exec'   I don't understand why it's behaving this way, or what the correct command would be. Please don't just post a command correction, I'd like to understand rather than just follow a suggestion blindly. Linux "top" command: What are us, sy, ni, id, wa, hi, si and st (for CPU usage)? When I issue top in Linux, I get a result similar to this:    One of the lines has CPU usage information represented like this:  Cpu(s): 87.3%us,  1.2%sy,  0.0%ni, 27.6%id,  0.0%wa,  0.0%hi,  0.0%si,  0.0%st   While I know the definitions of each of them (far below), I don't understand what these tasks exactly mean.   hi - what does servicing hardware interrupts mean? si - what does servicing software interrupts mean? st - they say it's the "CPU time in involuntary wait by the virtual CPU while hypervisor is servicing another processor (or) % CPU time stolen from a virtual machine".   But what does it actually mean? Can someone be more clear?  I listed all of us, sy, ni, etc, because it could help others searching for the same. This information is not in the man pages.  us: user cpu time (or) % CPU time spent in user space sy: system cpu time (or) % CPU time spent in kernel space ni: user nice cpu time (or) % CPU time spent on low priority processes id: idle cpu time (or) % CPU time spent idle wa: io wait cpu time (or) % CPU time spent in wait (on disk) hi: hardware irq (or) % CPU time spent servicing/handling hardware interrupts si: software irq (or) % CPU time spent servicing/handling software interrupts st: steal time - - % CPU time in involuntary wait by virtual cpu while hypervisor is servicing another processor (or) % CPU time stolen from a virtual machine Change the location of saved screenshot when screenshot taken by printscreen button in GNOME 3 How do I create a hinged door that opens and closes in Blender? If I knew how to do this, then it would help me also create moving control surfaces on model aircraft, such as the rudder and horizontal stabilizers. My dev team is getting ready to start a new project. The shop has been a "VB shop" since the days of VB3, but the prevailing opinion now is that we're a ".NET shop" and since C# was created specifically for .NET, whereas VB.NET was a retrofit, we've decided to move forward writing C# only. The controversy revolves around the question of whether the Microsoft.VisualBasic namespace has a legitimate place in new development or if it is only for backward compatibility for VB6 (and older) code. A further, and more interesting question is whether the code "under" the Microsoft.VisualBasic namespace is even .NET code of if it is really the old VB runtime carefully packaged in a .NET wrapper, making it in fact a COM interop control (similar to how WinForms wraps the non-.NET Win32 windowing API but exposes only .NET APIs for consumption).  To make this even more confusing, our dev team has a Microsoft Consulting Services consultant telling us Microsoft no longer supports Visual Basic, including the VB runtime underlying the Microsoft.VisualBasic namespace.  What I'm looking for are links -- preferably to unimpeachable Microsoft sources -- to documentation that definitively answers this question one way or the other. I've already tried several search permutations on Google and not gotten any closer to getting to the bottom of this question.  EDIT: Apparently I didn't make my question clear. I'm not asking if VB.NET is true .NET code. I'm trying to determine if whatever is "under" the Microsoft.VisualBasic namespace is .NET code or if it's the old VB6 runtime carefully packaged and exposed as .NET code. Someone already said that 9/10 of the namespace simply wraps code from elsewhere in .NET; what about that other 1/10? What will the universe look like for anyone falling into a black hole? I've heard that, from the perspective of an external observer, something falling into a black hole will eventually look "frozen": light waves will move to the infrared and further into lower frequencies.  But what about that unfortunate individual falling into such a black hole? What will he/she see when looking back at our universe?   For instance, I wonder, will it be the ultimate end of the Universe? Can someone who just crossed events horizon of the black hole still receive messages from our side? How to split a large file into two parts, at a pattern?  Given an example file.txt:  ABC EFG XYZ HIJ KNL   I want to split this file at XYZ such that file1 contains lines up-to XYZ and rest of the lines in file2. Different mechanics of \hyperlink vs. \hyperref I am fiddling around with the hyperref package to build a hypertext structure into my pdf. At first glance, hyperref provides two similar macros to put links between parts of my document: \hyperlink{target}{text} and \hyperref[target]{text}. You might notice their slightly different syntax. What really interests me is their different working mechanics. I will illustrate this by the following example: \documentclass{article}  \usepackage{pdfpages} \usepackage[]{hyperref} \usepackage{mwe}  \begin{document}  \section{Section Heading} \label{sectionheading}  \includepdf[link=true, linkname=pdfpage]{example-image}   Link to section works with \hyperref[sectionheading]{hyperref} and with \hyperlink{sectionheading}{hyperlink} (but with slightly different targets on the page).  Link to pdf works with \hyperlink{pdfpage.1}{hyperlink} but not with \hyperref[pdfpage.1]{hyperref} (and not this way, either: \hyperref[pdfpage]{hyperref}).  \end{document}  To link to the labeled section heading, I may use both commands. While \hyperref directs my pdf viewer directly to the linked section, \hyperlink directs me somewhere slightly different, so I can see more context. To link to the \includepdf of pdfpages however, I may only use \hyperlink. \hyperref does not work at all. I suspect this is because of a subtle difference in their working mechanisms. While checking the aux file, I found a line \newlabel{sectionheading}{{1}{1}{Section Heading}{section.1}{}} which \hyperref seems to use as a target. However, I did not find any similar target for the included pdf. My question: I suspect, I understand the workings of \label and \ref very well. \hyperref seems to work quite similarly with the added clickability. Could you please explain to me how \hyperlink does work differently and how it is implemented? E.g. what mechanics explain the difference when clicked on the link and where and how are the link targets stored in the first place? MSTest Code Coverage How does the Eco-Cooler air conditioner really work? describes a device for developing countries which apparently cools the air by 5 °C without electricity. According to , it works by lowering the pressure to drag in the ambient air. Wouldn't the ambient air be at the same temperature?  Does the constriction compress the air and temporarily increase the pressure and so temperature, which then dissipates heat because it is hotter than surroundings; then after passing the constriction, the pressure returns to almost ambient but the temperature drops to below ambient?  How does the Eco-Cooler air conditioner actually work, if at all? How does gravity work on Serenity? When the good ship Serenity is traveling in deep space, the crew experiences what looks like an Earth-normal (or Earth That Was-normal) level of gravity. Is it ever explained how the ship is able to generate artificial gravity? The ship doesn't spin, so  is out.  is a possibility, but I think the gravity in the ship pulls in a direction that is perpendicular to the direction the ship is usually traveling in, not opposite, like this method would require.   So: how does she pull it off?   Extra credit: how does she pull it off in the episode ? Serenity's engine is totally dead, to the extent where not even life support systems are online. Yet Mal still has to valiantly haul himself around on the floor to replace the compression coil, so whatever creates the artificial gravity on Serenity is clearly still going. How? How to access blocked sites? I am in Pakistan and  is blocked here. I want to take the Lecture videos from YouTube. In Windows, I was using  to bypass the proxy.   But now, using Ubuntu, I don't know how to bypass the proxy. I found some where that i can bypass the proxy by using putty software. Can you guide me how can I bypass proxy by that? I tried, but I was not able to do so. Kindly tell me some easy method to bypass proxy. I don't want to used websites like accesstoblockedsites.com. jQuery/JavaScript to replace broken images