Why is there no method to comment in JSON?
Can comments be used in JSON?
We are conducting a test on a rare disease. A positive result means that, according to the test, the subject is infected. The following characteristics are known about the test and the disease: If a person is infected, the person has a $95\%$ chance of testing positive. When a healthy person is tested, the test has a $99\%$ chance of giving a negative result. A mere $0.1\%$ of the population is infected with the disease. If a person is tested positive for the disease. What is the probability that the person actually has the disease? I don't understand how to write the conditional probabilities if someone can explain to me than I should know how to solve it, but I'm not sure how to convert the text into the mathematics language. A word to describe "work that is ready to be done" QGIS color polygon according to points I have two layers. Layer 1 contains points (x,y) and layer 2 contains one polygon. All points in layer 1 are positioned within the polygon of layer 2. The points in layer 1 contain an attribute with information on the topography/elevation at the specific point. Can I color the polygon in layer 2 based on attributes from the points in layer 1 in order to create an elevation map? Mis-aligned shapefiles in QGIS? Problem 20-9 in Lee's Introduction to Smooth Manifolds (2nd Ed.) asks to prove that for a Lie group $G$, and for $X, Y\in \text{Lie}(G)=\mathfrak g$, there is $\epsilon&gt;0$ and a smooth map $Z:(-\epsilon, \epsilon)\to \mathfrak g$ such that   $$(\exp tX)(\exp tY) = \exp\left(t(X+Y) + \frac{1}{2}t^2[X, Y] + t^3 Z(t)\right)$$   What we want to show is that the first and second term in the Taylor expansion of $\exp^{-1}\left((\exp tX)(\exp tY)\right)$ are $t(X+Y)$ and $\frac{1}{2}t^2[X, Y]$ respectively.  Calculating the first term is easy since we just need to differentiate $\exp^{-1}((\exp tX)(\exp tY))$ with respect to $t$ at $t=0$ once, and this gives the desired result.  But for the second term we need to take the second derivative at which I am stuck. I have two different machines (home and work) running Ubuntu 18.04. Last night vim froze at home. I was in insert mode and typing and went to save (esc :w) and nothing happened. The status bar still reads -- INSERT --, the cursor is still blinking where it was. I was stuck. I couldn't find a way out. I couldn't type (nothing happened when I type), I couldn't move around (the up and down arrows did nothing). It was stuck in insert mode with the cursor blinking where it was.   I was definitely multitasking and probably hit some other keys in there, but I don't know what keys. It was late, though, so I closed the terminal window and tried again (I was entering a git commit message). It happened again partway through my typing so I switched to git commit -m "don't need an editor for this" instead. And then I shut down my computer and stopped working.  I figured I was just tired, but then it happened to me today at work on a different laptop altogether. Again I was multitasking and can't swear I didn't type any bizarro key sequence but if I did it was accidental. And other tabs in the same terminal aren't frozen.   I'm used to getting trapped in visual mode in vim. That's a trick I've learned. But stuck in insert mode? Any ideas on what I might've done and how to get out of it?   Per a comment suggestion I tried looking at .viminfo but the only .viminfo I see is owned exclusively by root and only appears to show things I would have edited with sudo:   # Input Line History (newest to oldest):  # Debug Line History (newest to oldest):  # Registers:  # File marks: '0  1  0  /etc/neomuttrc |4,48,1,0,1531789956,"/etc/neomuttrc" '1  1  66  /etc/apt/sources.list.d/signal-bionic.list |4,49,1,66,1530816565,"/etc/apt/sources.list.d/signal-bionic.list" '2  51  0  /etc/apt/sources.list |4,50,51,0,1530816531,"/etc/apt/sources.list"  # Jumplist (newest first): -'  1  0  /etc/neomuttrc |4,39,1,0,1531789956,"/etc/neomuttrc" -'  1  66  /etc/apt/sources.list.d/signal-bionic.list |4,39,1,66,1530816565,"/etc/apt/sources.list.d/signal-bionic.list" -'  1  66  /etc/apt/sources.list.d/signal-bionic.list |4,39,1,66,1530816565,"/etc/apt/sources.list.d/signal-bionic.list" -'  51  0  /etc/apt/sources.list |4,39,51,0,1530816531,"/etc/apt/sources.list" -'  51  0  /etc/apt/sources.list |4,39,51,0,1530816531,"/etc/apt/sources.list" -'  51  0  /etc/apt/sources.list |4,39,51,0,1530816531,"/etc/apt/sources.list" -'  51  0  /etc/apt/sources.list |4,39,51,0,1530816531,"/etc/apt/sources.list" -'  1  0  /etc/apt/sources.list |4,39,1,0,1530816447,"/etc/apt/sources.list" -'  1  0  /etc/apt/sources.list |4,39,1,0,1530816447,"/etc/apt/sources.list" -'  1  0  /etc/apt/sources.list |4,39,1,0,1530816447,"/etc/apt/sources.list" -'  1  0  /etc/apt/sources.list |4,39,1,0,1530816447,"/etc/apt/sources.list"  # History of marks within files (newest to oldest):  &gt; /etc/neomuttrc     *   1531789952  0     "   1   0  &gt; /etc/apt/sources.list.d/signal-bionic.list     *   1530816564  0     "   1   66     ^   1   67     .   1   66     +   1   66  &gt; /etc/apt/sources.list     *   1530816454  0     "   51  0   It seems odd that I wouldn't have an unprivileged .viminfo but I did sudo udpatedb and locate .viminfo and still didn't surface more than the one root-owned file. Finding parenthesis via regular expression I need to use a different version of circuitikz. How can I do that? Real Analysis, Folland Problem 1.3.15 Measures Given a measure $\mu$ on $(X,M)$, define $\mu_0$ on $M$ by $$\mu_0(E) = \sup\{\mu(F): F\subset E \ \text{and} \ \mu(F) &lt; \infty\}$$ a.) $\mu_0$ is a semifinite measure. It is called the semifinite part of $\mu$. b.) If $\mu$ is semifinite, then $\mu = \mu_0$ (Use Exercise 14) c.) There is a measure $\nu$ on $M$ (in general, not unique) which assumes only the values of $0$ and $\infty$ such that $\mu = \mu_0 + \nu$.  The proof of Exercise 14 can be found  For a.) I believe we need to show that $\mu_0(E) = \infty$. Perhaps we can do this by proof of contradiction, similarly to what the proof in the link above does (actually it seems identical). For b.) I am not sure how we can show $\mu = \mu_0$ I think maybe we have to show by construction that $\mu \leq \mu_0$ and $\mu \geq \mu_0$ For c.) I haven't any idea for. Any suggestions is greatly appreciated. I'm using a 5 V / 2 A voltage regulator () without a heatsink. I'm testing the circuit with a microcontroller (PIC18FXXXX), a few LEDs and a 1 mA piezzo buzzer. The input voltage is aprox. 24 VDC. After running for a minute, the voltage regulator starts to overheat, meaning it burns my finger if I keep it there for more than a second. Within a few minutes it starts to smell like it's burnt. Is this a normal behavior for this regulator? What could cause it to heat that much?    Other components used in this circuit:  L1:   R2:   F1: Show that the Sorgenfrey line does not have a countable basis. Geometry with Trigonometry From the given figure, prove that      $$\cot\ \theta=\cot\ A+\cot\ B+\cot\ C$$     I could not even start to the first point. Please help me to solve this.  Thanks in advance What is likely to happen when you plug two ends of a network cable to a single switch/router? Will this create problems on the network, or just be ignored? Being an early adopter and using 11.04 daily builds I sometimes meet a situation when some packages require earlier versions of other packages than those I have installed. Usually newer (but refused) versions of needed packages provide all the functionality of their older versions.  If I use dpkg -i --force-depends-version to install dependent packages everything works fine, I've never seen a problem.  Instead of manually downloading and installing every package, can I just make the system pretend there is a specific package version installed when there is a newer? Or is there a --force-depends-version key equivalent for apt-get? How can I test within a document, whether or not the initial  \documentclass[a4paper,11pt,twoside,fleqn,draft]{report}   includes the "draft" option? My naive attempt  \newif\ifmydraft \mydraftfalse \DeclareOption{draft}{\mydrafttrue}   does not work, and breaks a later \usepackage command. How to avoid becoming stressed while playing endurance games? Although I am asking for Super Hexagon, I've noticed there is a multitude of games (rhythm games in particular) where the more stressed I am, the worse I play and/or are more likely to make a mistake. Often then the games are designed in such a way to induce stress, such as various ways of telling me how far I am, which also is telling me just how much it would suck if I were to fail right now.  This leads to a stress cycle, where I am noticing I am stressed, and I am aware of this being a bad thing, which makes me more stressed, over and around until I eventually fail.  This often means that I probably could've done &lt;some new level I just unlocked&gt; just fine, except I saw that it was new, got stressed about it and started the stress cycle.  So how can I:   Avoid getting stressed while playing Defuse the stress cycle once it has inevitably started   One thought I had for this is simply taking deep breaths, but particularly in Super Hexagon, there is no way to pause and taking deep breaths is distracting enough to make me fail. given that $f$ is an analytic function with real part $u$ is a polynomial in the variable of $x,y$, $z=x+iy$, we need to show $f$ is a polynomial in $z$, I am kind of puzzled to see the problem, first I would like to say:any hint please Showing this metric space is complete Let $X=(0,1]$ and $d(x,y)=\left|\frac{1}{x}-\frac{1}{y}\right|$. I've proven $(X,d)$ is a metric space but I don't know how to show its completeness. How can I do that? SQL Join Differences What's difference between inner join and outer join (left join,right join), and which has the best performance of them?  Thanks! scanf() misbehaving