Let $A$ and $B$ be two observers and suppose they meet when both their clock are  zero.  Suppose that  $B$ moves with constant  velocity $v$ in relation to $A$  then we have  $$t=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}  t'$$  where $t$ is the time for observer $A$ and $t'$ the time for observer $B$.For simplicity  suppose that $\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}=0.5$ then when the clock of $B$ is $t'=1$ the clock of $A$ is $t=2$.   From the point of view the observer is moving with velocity $-v$ and so by symmetry  $$ t'=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}} t$$  So when the clock of observer $A$ is $t=2$ the clock of $B$ is $t'=4$   That is if the clock of $A$ run faster than $B$, the clock of $B$ run faster than the clock of $B$ by symmetry.  Isn't this a contradiction ?
Suppose we have two twins travelling away from each other, each twin moving at some speed $v$:    Twin $A$ observes twin $B$’s time to be dilated so his clock runs faster than twin $B$’s clock. But twin $B$ observes twin $A$’s time to be dilated so his clock runs faster than twin $A$’s clock. Each twin thinks their clock is running faster. How can this be? Isn’t this a paradox?
Getting all the combinations in an array Show that $\langle 2,x \rangle$ is not a principal ideal in $\mathbb Z [x]$ I've got an iPhone app with icon file Icon.png.  This icon shows up properly when the app is on the phone itself, but it doesn't show up in the applications pane in iTunes.  What do I need to do to get it to show up properly? Temporal Table that doesn't use system time We want to implement temporal tables in SQL Server 2016. We are creating a Datawarehouse and developing Type 2 Slowly changing Dimension Tables.  For the BeginDate, we want it to be dependent on transaction date and not the current getdate time. We are reprocessing a history of transactions. Example below, customer has gym or bank status, and goes from inactive, to active, or pending, dependent on transaction date.  We currently have this.  CREATE TABLE dbo.Department (     CustomerId int primary key,     MembershipStatus int,     TransactionDate datetime  );   We we would like to create a table like this.  CREATE TABLE dbo.DepartmentHistory (     CustomerId int primary key,     MembershipStatus int,     TransactionDate datetime,     BeginDatetime datetime,     EndDatettime datetime  );   Example usage would be:   first Customer Transaction on 3/5/2018 as Pending P        +------------+--------+-----------+---------+     | CustomerId | Status | BeginDate | EndDate |     +------------+--------+-----------+---------+     | 1          | P      | 3/5/2018  | NULL    |     +------------+--------+-----------+---------+    second transaction is 4/21/2018 is Active A        +------------+--------+-----------+-----------+     | CustomerId | Status | BeginDate | EndDate   |     +------------+--------+-----------+-----------+     | 1          | P      | 3/5/2018  | 4/21/2018 |     | 1          | A      | 4/21/2018 | NULL      |     +------------+--------+-----------+-----------+ Formula for expected value of continuous random variable without using density How to effectively use the man pages? I am looking forward to mastering linux. I have been repeatedly told to refer to man pages when you are in doubt.   Though I am very comfortable with the commandline, I find it very difficult to quickly and efficiently use man to find help with commands. Hence I end up googling up how to get things done. It is even more painful when the system I am using does not have internet access and I have to walk back to my office to get help from the internet.  How does one master man pages? What are the most common tricks that can be used to quickly get whatever you want from the man page? What are the most commonly used keyboard shortcuts? I have seen people apply a filter to imported data before plotting with pgfplots, see . Is there a way to extend the approach presented there to apply multiple filters? In the MWE below I made the naive modifications to the solution given there, but it seems that only the last filter is applied: the unwanted y=1 data points are plotted too.  \documentclass{article} \usepackage{filecontents} \usepackage{pgfplots}  \begin{filecontents}{foo.txt}   x y z f   0 0 0 0   0 0 1 1   0 1 0 2   0 1 1 3   1 0 0 4   1 0 1 5   1 1 0 6   1 1 1 7   \end{filecontents}  \pgfplotsset{   discard if not/.style 2 args={   x filter/.code={   \edef\tempa{\thisrow{#1}}   \edef\tempb{#2}   \ifx\tempa\tempb   \else     \def\pgfmathresult{nan}   \fi   }}   }  \begin{document} \begin{figure}   \centering   \begin{tikzpicture}   \begin{axis}   \addplot table[x=x, y=f,                  discard if not={y}{0},                  discard if not={z}{0},                 ] {foo.txt};   \end{axis}   \end{tikzpicture}   \caption{$f(x)$ given $y=0$ and $z=0$.}   \end{figure} \end{document} Calling a Java method with no name Is there a maximum possible acceleration? First, this is about beta sites that might not even exist later, but imagine they will for the sake of this question. Taking the latest 10 questions on , I see 3 questions related to Mac OS X:    From my point of view, all 3 could also fit on , the 1st one could also be on SO, the 2nd and 3rd could also be on SU. How we will deal with this type of situation? When should we close a question as &quot;Belongs on [...]&quot;? I already see identical questions asked on 2 or 3 different sites (by the same or different users). Is there anything planned to link these questions or something like that? I mean something else than the already existing &quot;Linked&quot; feature. Something to include answers from site X in site Y or something like this. If you use sudo su - or sudo -s you will get the full root certification  "likewise a root user ".  Is this user an official user or is it from canonical?  ~$ sudo su - [sudo] password for username:  root@lp:~# id uid=0(root) gid=0(root) groups=0(root) root@lp:~# pwd /root root@lp:~# Does opacity:0 have exactly the same effect as visibility:hidden If so, does it effectively deprecate the visibility property?  (I realize that Internet Explorer does not yet support this CSS2 property.) Difference between $(this) and event.target? Repeating something with (1/n)th chance of success n times Is there anything that can be said about how many attempts it will take to correctly guess a random number out of 1000 numbers? If the number wouldn't change the probability would just increase every guess, giving in the end a probability of 1.  If the number changes every guess tough, you just have a 1/1000th chance everytime. Can it be calculated how many attempts it would probably take, on average?  (I'm sorry, i'm not very skilled in probability maths) How do the comment replies (aka &quot;pinging users&quot;) work?  Who can I send an @reply to? How do I respond to a specific user when entering my comment? Will they be notified? What do people mean when they talk about &quot;pinging&quot; another user?  Related: bash dynamic (variable) variable names Aligning equations within multline I have this really long equation and I have used multline to break it up. I also want to align the broken bits of the equation to the left. When I use  align, for some reasons it aligns to the right when I want it to be on the left. How can I align to the left?  \begin{multline} \begin{align} \mathcal{H}_{q1} \mathcal{H}_{q2} \mathcal{H}_{q3}...\mathcal{H}_{qn}0=\frac{1}{2}H_{q1}\{\mathcal{H}_{q2}\mathcal{H}_{q3}...\mathcal{H}_{qn}0\}+\frac{1}{2} h_{q1} \\ =\frac{1}{2}H_{q1}\{\frac{1}{2} H_{q2}[\mathcal{H}_{q3}...\mathcal{H}_{qn} 0]+\frac{1}{2}h_{q2}\} +\frac{1}{2}h_{q1}=\\ \frac{1}{2}H_{q1} \frac{1}{2} H_{q2} [\frac{1}{2}H_{q3}(\mathcal{H}_{q4}..\mathcal{H}_{qn}0)+\frac{1}{2}h_{q3}]+ \frac{1}{2}h_{q2}+\frac{1}{2}h_{q1}=...\\          =(\frac{1}{2^n})H_{q1}H_{q2}H_{q3}..H_{qn}0+ (\frac{1}{2^n})H_{q1}H_{q2}H_{q3}..H_{qn-1}h_{q1}\\+(\frac{1}{2^n})H_{q1}H_{q2}H_{q3}..H_{qn-2}h_{qn-1}+.. \\+ (\frac{1}{2})h_{q1}=\sum^n_{j=1} (\frac{1}{2^j}) H_{qo}H_{q1} H_{q2}H_{q3}..H_{qj-1} h_{qj} \end{align} \end{multline} Why doesn't a block rotate due to friction? My grandparents bought a flight on United Airlines, as the one and same ticket, from Toronto, to ORD with one 55-minute layover, then to Maui. :     You won’t need to pay extra for airfare if you miss the flight, but on the other hand, you will most likely not be compensated by the airline for the incurred delay. It always depends on the amount of time, the reason for the delay and the airline’s policies. As soon as it’s weather-related, you won’t be getting a penny (and that’s normal: airlines can’t control the weather).    Yet they obviously prefer to avoid such charges from missing the 2nd flight.   Please see the titled question? Would they need to hotfoot or scamper from one gate to another, to not miss the 2nd flight? If yes to 2, can they request an airport electric shuttle cart now, before the flight? General way to determine $\mathbb{Q}(\gamma) = \mathbb{Q}(\alpha,\beta)$ given $\alpha$ and $\beta$