Type this in the console of your browser:  9999999999999999==10000000000000000  It says they are equal, why?
Is this defined by the language? Is there a defined maximum? Is it different in different browsers?
Auto Package download for TeXLive I use MiKTeX on Windows and quite satisfied with it. Recently I started switching all my tasks toward open-source alternatives, and in the course I would love to use Linux. In Linux TeXLive is available as alternative to MiKTeX. The thing I really like about MiKTeX, is its ability to install packages automatically. Can I do the same in TeXLive too? Is there a way I can enable such or install some plugins for it?  I am using Fedora 18, if that's needed. Proof that a sum of Bernoulli rvs has Binomial distribution Let $\{X_n, n \geq 1\}$ be iid Bernoulli random variables with $\Pr(X_1 = 1) = p = 1 - \Pr(X_1 = 0)$ and let $S_n = \sum\limits_{i=1}^n X_i$ be the number of successes in $n$ trials. Show $S_n$ has a binomial distribution by the following methods:  1.) Prove for $n\geq0,$ $1\leq{k}\leq{n+1}$  $$\Pr(S_{n+1} = k) = p\Pr(S_n = k - 1) + q\Pr(S_n = k)\text{ where }q = 1-p.$$  2.) Solve the recursion using generating functions.  For the first method, I think I need to use convolution of $n + 1$ Bernoulli rvs, but I cannot immediately see the progression. For the second method, I don't exactly understand how to proceed either. This is problem 1.2 from Resnick's Adventures in Stochastic Processes. How should you deal with (deliberate) selective deafness? Why does the CRT formula yield a solution of a congruence system? I'm trying to create a command, which calls on an environment, which defines a custom column definition with one argument using \newcolumntype, and defines a second command, containing parameters for a table column.  Then, still within the first command, I begin the tabular environment and call the custom column, with the second command as its argument. I always get an undefined control sequence error, though. Any thoughts on why that might be?  I'm sure that was clear as mud, but I've cut it down to a minimal example, which follows:  \documentclass{article} \usepackage{array} \usepackage[table,dvipsnames]{xcolor} \usepackage{colortbl}  \newenvironment{tablecolor}{     \newcommand{\tlight}{\columncolor{SkyBlue!30}\color{black}}     \newcolumntype{C}[1]{&gt;{##1}c} }{}  \newcommand{\tablegoals}{ \begin{tablecolor} \begin{tabular}{l|C{\tlight}} Goal 7  &amp; \\ \end{tabular} \end{tablecolor} }  \begin{document}     \tablegoals \end{document}     Here's my second attempt. Different approach, same undefined control sequence error with \columncolor.  \documentclass{article} \usepackage{array} \usepackage[table,dvipsnames]{xcolor} \usepackage{colortbl} \usepackage{ifthen}  \newenvironment{tablecolor}{     \newcolumntype{C}[1]{&gt;{         \ifthenelse{\equal{dark}{##1}}{             \columncolor{Cyan}\color{white}             }{             \columncolor{SkyBlue!30}\color{black}         }     }c} }{ }  \newcommand{\tablegoals}[1]{     \begin{tablecolor}         \begin{tabular}{l|C{dark}}             Goal 7  &amp;   #1         \end{tabular}     \end{tablecolor} }  \begin{document}     \tablegoals{Check mark} \end{document} TV identification: Short-lived TV show about a time traveller with a super-computer disguised as a credit-card It might have only been a pilot or a made for TV movie, but I remember a male time traveller who was for some reason in 90s US from a semi-distant future. He had in his possession a super-computer disguised as a regular credit card, which could hack things and I think spoke to him in a female voice.   Note: Not Quantum Leap - the time traveller and "credit card computer" might be keywords that people would hit upon, but 'Ziggy' the computer in QL was non-speaking, operated by a hologram and did not resemble a credit card - this one had its own voice and was disguised as a CC. How to add horizontal cylinder at end of cube What's the difference between a shunt resistor and a four-terminal resistor? I want to know if the four-terminal resistor and the shunt resistor are the same.   Is there another use for the four-terminal resistor except measuring current? I'm making a Java application with an application-logic-thread and a database-access-thread. Both of them persist for the entire lifetime of the application and both need to be running at the same time (one talks to the server, one talks to the user; when the app is fully started, I need both of them to work).  However, on startup, I need to make sure that initially the app thread waits until the db thread is ready (currently determined by polling a custom method dbthread.isReady()). I wouldn't mind if app thread blocks until the db thread was ready.  Thread.join() doesn't look like a solution - the db thread only exits at app shutdown.  while (!dbthread.isReady()) {} kind of works, but the empty loop consumes a lot of processor cycles.  Any other ideas? Thanks. How do I set a user environment variable? (permanently, not session) This is irritating me. I seen several suggestions (all using different files and syntax) and none of them worked.  How do I set an environment variable for a specific user? I am on debian squeeze. What is the exact syntax I should put in the file to make ABC = "123"? What is the method to make files in a USB Flash Drive undeletable? Does these method work with USB 3.0 interface?  (I have surveyed some Flash Drive manufacturers, and I only see undeletable files for USB 2.0 drives, and not 3.0 drives. One manufacturer claimed that USB 3.0 cannot do undeletable file, so I am curious whether the claim is correct...) Let H={e,(12)(34)} and K ={e, (12)(34), (13)(24), (14)(23)} be subgroups of $ S_4$ where e is identity element. Then which of following is true   H and K are normal subgroups of $S_4$ H is normal in K and K is normal in$ A_4$ H is normal in $A_4$, but not normal in $ S_4$ K is normal in $S_4$ but H is not   How should this question be approached, checking left and right cosets of these subgroup is very time consuming. Checking gh$ g^{-1}$ $\in $ H for every g in $ S_4$ is also time consuming. Is there a specific reason for having a very short window for passengers to get to the boarding gate before closing it? I am not a frequent traveler but it's been like this with all the flights I have been on. Here is the most recent example:  Below is my boarding pass    As you can see Gate Closes at 20:20  Here is the departures board at 18:32, clearly it says that they will announce the boarding gate at 20:10  ?!    I was hoping they will do that earlier but at 19:41 it's still the same    In fact they announced it at 20:11 but since I was freaking out and had to leg it to the gate I didn't have the time to take a photo.  You might think 9 minutes is enough, well below are the times required to reach the gates from the closest place to them     And that's for a healthy young person, no way my grandmother could be able to be at the gates within 9 minutes.  Is there a specific reason? it's not like they allocate the gate dynamically! The staff must have known about the gate hours ago as I don't expect the pilot to drive the airplane from the garage to the gate within 9 minutes? Suppose $f$ is a differentiable function over $\mathbb{R}$ satisfying $f(0) = 0$. Show that if $f'$ is strictly increasing, then $\frac{f(x)}{x}$ is increasing over $(0,\infty)$.   Attempt:  Since $f'$ is increasing we know that $f'' &gt; 0$ for all $x$. Now let $g(x) = \frac{f(x)}{x}$ and thus $f(x) = xg(x)$. Then we wish to show that $g'(x) &gt; 0$ on $(0,\infty)$ and so since $f'(x) = xg'(x)+g(x)$ and $f''(x) = xg''(x)+2g'(x) &gt; 0$, we have $g''(x) &gt; \frac{-2g'(x)}{x}$. I am not sure how to use this though to prove the statement. What happens when I run the command cat /proc/cpuinfo? What happens when I write cat /proc/cpuinfo. Is that a named pipe (or something else) to the OS which reads the CPU info on the fly and generate that text each time I call it? Does equality of characteristic polynomials guarantee equivalence of matrices? I have a qualifying exam coming up in a couple days and I am just trying to understand some pathological examples I have in my notes. I will list a similar problem which I know the solution to and then the question.  True or False:   let $A,B \in \mathbb{Q}^{n \times n }$  Suppose $xI-A$ and $xI-B$ are equivalent then $\det(xI-A) = \det(xI-B)$.     I wrote in my notes this is true because any two matrices are equivalent in $\mathbb{Q[x]}^{n \times n}$ if and only if they have the same invariant factors.  Since the characteristic polynomial is a product of the invariant factors it follows that $\det(xI-A) = \det(xI-B)$.        True or False:   let $A,B \in \mathbb{Q}^{n \times n }$. If $\det(xI-A) = \det(xI-B)$ (in $\mathbb{Q}[x]$) then $xI-A$ and $xI-B$ are equivalent  in $\mathbb{Q}[x]^{n \times n}$   I think this is false because of the fact that equality of determinants is not strong enough to guarantee all invariant factors are equal but I do not have an example. Join CSV file to shapefile I wanted to join a CSV file to a shapefile.  When I identified a field to facilitate the join, e.g.,   map &lt;- spChFIDs(map, as.character(map$ID))   it returned     Error in spChFIDs(SP, x) : lengths differ   Can anyone advise? In the example  $\cup^{i=1}_{\infty}F_i$   How do you get the i=1 directly below the union symbol and the infinity directly above? Take most recent (or concatenate) edit comments when editing during grace period Recently, I edited  to update a link to a better resource. I clicked "Save" without entering a description of the edit (edit #1).  Then I realised that the question was asked by a new user who may not be able to easily identify the change that was made. So I edited it again, this time only to add a detailed edit description (edit #2).  Since edit #2 was made during the grace period (within 5 minutes of edit #1), the system has merged them into a single edit, but only the edit comment from edit #1 was recorded in the revision history, whereas edit #2's comment was simply discarded/ignored.  I'd suggest that either the most recent (non-default) edit comment is taken or that the comments are concatenated to provide a more useful edit history How do I to properly handle spaces in PHP Shell_exec?