I am currently learning about fractions, and there is something that I am finding it hard to make sense of. When a fraction it added to the right of the decimal point, the number becomes slightly bigger right? So for example if I add enough fractions to the 0.99999999, will this number eventually become equal to 1?  So will this number eventually become equal to 1 (if I added enough 9): 0.9999999999999999999999999999999999999999999999999999999999999999999999...9
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?
How can I repair a buried 120v cable splice to make it meet code? I have an electrical question. I have a cable feeding an outdoor yard light. It was cut, I spliced it, soldered it and wrapped it with tape. Is there a way to splice and bury it safely to code? If not, I'll need to dig a 30 foot trench to replace the whole length.  Was about 8 inches below ground, surfaced over the years and probably hit with the weed trimmer.   It is outdoor cable inside copper tubing. Years ago when I bought the wire I knew outdoor was gray. The box said outdoor but it is white like indoor wire.   It was spliced about 20 years ago but am fixing up house and like to hide the ugly splice. Finding the distribution of $\|X-\mu \|_\Sigma^2$ with $X \sim N(\mu,\Sigma)$ Let $\Sigma$ be positive definite and symmetric and let $\| x \|_\Sigma := \sqrt{x^t\Sigma^{-1}x}$ be the Mahalanobis norm. Let further $X \sim N(\mu,\Sigma)$ be a $p-$variat normally distributed random vector. Find the distribution of $\| X-\mu \|_\Sigma^2$.   I do not kow how I could do that. Could you help me? Why are my sprinkles beneath the frosting I am a beginner to Blender and watching .  At 8:46 is when my problem occurs, because my sprinkles are appearing beneath the icing. Non-numerical citation mark like [Str91] [Samar] [Tro77] What is recordSetVar and where is it used? I was looking at some code and in the 'apex:page' tag, an attribute called recordSetVar was mentioned. I'm new to VisualForce so could someone please tell me when and why is it used? Windows installer for Ubuntu 14.04 LTS onwards Is there any Windows installer (wubi) for Ubuntu 14.04 LTS?  When I mount the .iso file with Daemon Tools and run wubi.exe, it just asks me if I want to reboot (I think that's useful only when the .iso  is burned on CD), so is there no "real" installation? Types in MySQL: BigInt(20) vs Int(20) Whenever I startup from the LinuxLive USB, and try to install Ubuntu 12.04, it only gives me two options instead of the usual 3 or 4. My options are "Replace Windows 7 with Ubuntu" and "Something Else". Whenever I go into "Something else", it looks extremely confusing. How do I install it side-by-side while using the "Something else" section? These are my partitions.   /dev/sda /dev/sda1 ntfs (104Mb, System Required Partition) /dev/sda2 ntfs (1000097Mb, Windows 7 Partition)   Or should I try reinstalling my installer on a CD rather than USB and maybe then it will have the "Install alongside" function? How to remove some pages from the navigation bullets in Beamer? I'm making a beamer presentation using the miniframes outer theme, with navigation bullets, and the subsection=false option, meaning the bullets are all on a single row. The problem I have is that, if one section has too many pages, the bullets overflow to the next section:  Section 1 Section 2 oooooooooooooooooooo   I tend to have many frames, some of them just asking a question, leading to the next detailed frame. I don't really need those frames to be represented by navigation bullets, and removing them would fix the problem. Any idea how to do that?  I could cheat by using overlays to have the question and the answer on the same frame, but that would be a mess...  Code example to answer percusse's question: this should give you one circle per frame, not one per subsection. If you add many frames in one subsection, the circles will overflow over the next section.  \documentclass[compress]{beamer} \useoutertheme[subsection=false]{miniframes} \begin{document} \section{S1} \subsection{SS1} \frame{1} \frame{2} \frame{3} \subsection{SS2} \frame{1} \frame{2} \frame{3} ... \end{document} I am familiar with the set-theoretical definition of functions.   A function $f : A \rightarrow B$ from a set $A$ to a set $B$ is a subset $f \subseteq A \times B$ of the Cartesian product $A \times B$ such that the following conditions hold:   $\forall a \in A : \exists b \in B : (a,b) \in f$ $\forall a \in A : \forall b, b' \in B : (a,b), (a,b') \in f \rightarrow b=b'$   Is there a purely set-theoretical definition of the function evaluation $f(a)$ for every $a \in A$? I get as far as defining  $f(a) = \{ b \in B : (a,b) \in f \}$ but that defines rather the set of values of a multi-valued function. a command to list all packagas installed on the system and their installed files, how? I'd like to do something like this:  &gt;&gt; foo = @() functionCall1() functionCall2()   So that when I said:  &gt;&gt; foo()   It would execute functionCall1() and then execute functionCall2().  (I feel that I need something like the )  EDIT:  functionCall1 and functionCall2 are not necessarily functions that return values. update-initramfs missing /lib/modules/4.4.0-13-generic What should be created first in a video game? Creating label in QGIS? I am using QGIS 2.18.16 on Windows 10.    What I want is a label to appear within the boundaries of a polygon.    I select a layer, then select command Layer>Labelling, and I get:    From here, I can change "No Labels" to "Show labels for this layer".  But I can't actually create label text.  I find a clue in a prior question:    “Labelling polygon using QGIS?”    The answer was:  The layer you are trying to label must have at least one attribute field populated with data. You can then turn on labelling in Layer Properties and select which attribute field to use for your labels.  I can enter command Layer>Open Attribute Table, and what I get is:    If I need something in the attribute table in order to apply a label, how do I accomplish that? Let $p$ be prime and $(\frac{-3}p)=1$. Prove that $p$ is of the form $p=a^2+3b^2$ Let $p$ be prime and $(\frac{-3}p)=1$, where $(\frac{-3}p)$ is Legendre symbol. Prove that $p$ is of the form $p=a^2+3b^2$.   My progress:  $(\frac{-3}p)=1 \Rightarrow$ $(\frac{-3}p)=(\frac{-1}p)(\frac{3}p)=(-1)^{\frac{p-1}2}(-1)^{\lfloor\frac{p+1}6\rfloor}=1 \Rightarrow$ $\frac{p-1}2+\lfloor\frac{p+1}6\rfloor=2k$  I'm stuck here. This is probably not the way to prove that.  Also tried this way:  $(\frac{-3}p)=1$, thus $-3\equiv x^2\pmod{p} \Rightarrow$ $p|x^2+3 \Rightarrow$ $x^2+3=p\cdot k$ stuck here too.  Any help would be appreciated. Activating 'missing' standard GRASS utilities in QGIS Processing toolbox Android OS without Google Services? I have a Sony Xperia Z with version 4.1.2 running.  My question is about removing all of the Google baggage from the phone.  I have no Google account tied to my phone and would really like to get rid of all traces of Google from my phone for a few reasons:   Battery performance: Google services ranks in the top 3 of what uses up my battery Privacy: I try to minimize what Google siphons from my phone with the exception of Google maps Less Dependency: I don't want to be dependent on one company for all my needs.   So are there any Android versions out there that are minimalistic and do not invade your privacy? Seasonal Loan Amortization Hi I can compute a Basic Loan Amortization Schedule, But now I'm trying to Calculate a Seasonal Loan Amortization Schedule . So for example A loan starts at January And Will go on for 3 years, with Monthly Payments. Interest is at 3% Annually and is compounded Annually. During the months of September, October, November, December It'll only accumulate Interest But no payments and principal. Principal is 100000. How Do I calculate Payments and interest. Render result is completely blank A scene I made is not rendering, at all. This grey screen stays the same and nothing changes.  Here are my settings:  [