I have 5 different email accounts: iCloud, GMail, Hotmail and two others which my iPhone does not give the option to sync its contacts.   So, I have only synced my contacts with iCloud and since barely a month ago, when I edit a contact it appears immediately a copy of it and if I delete one, both of the are deleted.  Does anyone know what is going on?
I have two exchange accounts on my iPhone 4. One that connects to my gmail, the other connects to my work's Lotus Notes. There are no overlapping contacts in the two accounts. There are also no contacts saved locally on my phone.   When I enable contacts in both accounts, I get two identical entries for each of the contacts in my gmail. If I disable the Notes exchange account, then there are no more duplicates. If I have Notes contacts enabled, and gmail contacts disabled then I have no contacts at all.  Does anyone know what is going on? Is this a problem with having multiple exchange accounts or is it a Lotus Traveler problem? (I tend to blame Notes for all the trouble in the world, but that is just my bias)  Thanks all.
Show that G is a group, if G is finite, the operation is associative, and cancellation law holds Let $G$ be a non-empty finite set with an associative binary operation so that cancellation law holds, i.e. $ab=ac$ or $ba=ca$ implies $b=c$, for any choices of $a,b,c$ in $G$. Assume that there is an identity element $e$ in $G$. Show that $G$ is a group.  Proof: To show $G$ is a group, conditions must hold. Suppose that $ab=ac$, then $b=eb=(a^{-1}a)b =a^{-1}(ab)=a^{-1}(ac) =(a^{-1}a)c=ec=c$. So left cancellation holds in $G$.  2) Suppose $ba=ca$, then $b=be=b(aa^{-1}) =(ba)a^{-1}=(ca)a^{-1} =c(aa^{-1})=ce=c$. So right cancellation holds in $G$.  3) If $a$ exists in $G$ then $aa^{-1}=a^{-1}a=e$, where $a$ is an inverse of $a^{-1}$. Since inverses are unique, $(a^{-1})^{-1}=a$.  4) Let $x$ be the inverse of $ab$. Then $(ab)x=e$. By associativity we have $a(bx)=aa^{-1}$. Through left cancellation we have  $bx=a^{-1}bx=ea^{-1}=b(b^{-1}a^{-1})$ and $x=b^{-1}a^{-1}$.  Thus $(ab)^{-1}=b^{-1}a^{-1}$. So all conditions hold, $G$ is a group.  Is this proof correct? I know to show $G$ is a group these conditions have to be met. This is all I have to show right? $x^TAx=0$ for all $x$ when $A$ is a skew symmetric matrix Let $A$ be an $n\times n$ skew symmetric matrix. Show that $x^TAx =0 \ \forall x \in \mathbb R^n$.  How to prove this? Distribution of range of Uniform $(0,1)$ distribution How do I use multirow in LaTeX? How do I code a table to look like this? I'm not the best at LaTeX and can't seem to wrap my head around \multirow. I checked other examples prior to posting but they used \multicolumn and it just confused me even more. Thanks in advance!    \begin{center} \begin{tabular}{ |c|c|c|c|c|}   \hline  TextA &amp; TextB &amp; TextC &amp; TextD &amp; TextE\\  \hline  A &amp; TextF &amp; TextG &amp; TextH &amp; TextI\\  B &amp; TextJ &amp; TextK &amp; TextL &amp; TextM\\  C &amp; \multirow{2}*{TextF} &amp; TextG &amp; TextH &amp; TextI\\  \cline{3-3}  &amp; TextJ &amp; TextK \\ \hline \end{tabular} \end{center}   I was trying something like this.. I'm starting to have problems as I'm trying to multirow within a multirow? I'm not sure of the process here. I would like TextG to be split into 2 and TextH and TextI to be the cells which are split in 3 but not sure how to go about it. Will then TextJ and TextK be the contents of the split TextG cell? I'm a fourth year undergraduate student in a university in the U.S., and this is my last semester. I have already applied to graduate schools, and I'm currently awaiting responses. Since I have already finished all my requirements and am ready to graduate, I wanted to go part time this semester. I am aware of how it affects my financial aid; however, I do not know if it has an effect on my admittance to graduate school. I do not mean whether or not I get accepted (the decisions will happen without knowledge of my current semester), but whether I am eligible to attend graduate school if I have been part time for a semester. That is, will there be any potential issues when the schools that have accepted me see my final transcript and see I was part time? Is there a universal answer to this? Or should I contact each school individually and ask about their policy?   Also, are there any other potential issues with going part time that I haven't mentioned? Anything noteworthy I might have missed? Command and Conquer 3 exeption in exception handler I have command and conquer 3 from Origin, but when I try to start it, I get the 'exception in exception handler' error and the game exits.   I've tried the Origin launcher fix as well as -runver to make the game run a different version (although this just says that it can't find any version). I run Windows 10 (I know, experimental) but this game worked at one point, and then stopped working suddenly - there wasn't even an update in between.   I suspect that it's got to do with Origin, but any help would be appreciated. So this homework question is in the context of $\mathbb{R}$ only, and we are using Lebesgue measure.  The sum $A+B$ is defined to be $A+B=\{a+b|a\in A,b\in B\}$. The question is: If $m(A),m(B)&gt;0$, is it necessarily the case that $A+B$ contains an open interval?  This question is quite annoying, since it is quite difficult to calculate the sum even after you construct an example. However, it seems like no matter how I constructed a set of positive measure, there is a region that have a lot of point in it (yet this region is not necessarily dense). This suggest that when summed up, the holes should be covered up somehow and thus there would be an open interval, and so the answer is yes. Sorry for a rather vague idea, but I'm just not sure what to do with this problem. I have a feeling that somehow topology would have a way to capture precisely the idea above about a region with a lot of point.  (also, I think my middle school teacher mentioned this once, and I remembered the answer to be yes; but that is quite a while ago though)  Thank you. Any help will be appreciated.  EDIT2: So Camilo's answer is gone. I am looking at the convolution method right now. Because the convolution is continuous, if it is nonzero I am done. But then there is no guarantee that the convolution is nonzero even if $x\in A+B$. I still need help with this direction. Can someone give me some hints?  EDIT: Camilo's answer below essentially suggest the method of getting 2 open interval from regularity theorem, one cover a subset of A and one cover a subset of B such that the sum of the measure of these two subset is bigger than the measure of the larger interval. user99680's answer point to a wiki which show a method that essentially simply acquire an open set. After some thinking, I believe that these method simply can't be made to work. I constructed this example in the hope that it would convince you that it is the case:  Let $I_{0},I_{1},\ldots$ be disjoint open interval such that the distance between any 2 of them is nonzero and $m(I_{n})=9^{-n}$ and all of them are inside $[0,2]$. Let $J_{0},J_{1},\ldots$ be disjoint open interval such that the distance between any 2 of them is at least $3$ and $m(J_{3n})=m(J_{3n+1})=m(J_{3n+2})=\frac{m(I_{n})}{3}$. Let $O=\bigcup I_{n}$ and $H=\bigcup J_{n}$. Construct $A\subset O$ such that $m(A\bigcap I_{n})=\frac{3m(I_{n})}{4}$. Construct $B\subset H$ such that $m(B\bigcap J_{n})=\frac{3m(J_{n})}{4}$. Now if you apply Camilo's method, it is possible that your $I$ would be one of the $I_{n}$ above, and your $J$ is one of the $J_{m}$ above. No matter which $I_{n},J_{m}$ you have, the argument does not work. Rewrite $m=3q+r$ where $0\leq r\leq 2$. If $q&lt;n$ then $m(J_{m})&gt;m(I_{n})$ so the longer interval have length $\frac{m(I_{q})}{3}$; $m(A\bigcap I_{n})$ is at most $\frac{3m(I_{q+1})}{4}=\frac{m(I_{q})}{12}$ and $m(B\bigcap J_{m})=\frac{3m(J_{m})}{4}=\frac{m(I_{q})}{4}$. Thus $m(A\bigcap I_{n})+m(B\bigcap J_{m})$ is no larger than the larger interval. If $n\geq q$ then $m(I_{n})&gt;m(J_{m})$ so the larger interval is of length $m(I_{n})$; $m(A\bigcap I_{n})=\frac{3m(I_{n})}{4}$ and $m(B\bigcap J_{m})$ is at most $\frac{3m(J_{3n})}{4}=\frac{m(I_{n})}{4}$. Once again $m(A\bigcap I_{n})+m(B\bigcap J_{m})$ is no larger than the larger interval. Hence the Camilo's argument does not work. user99680's method does not work either, since you get $O$ and $H$ which is even bigger than any interval. Proof for Property of Complex Numbers Is the inequality $\lvert z_1 + z_2 \rvert \ge \lvert z_1 \rvert - \lvert z_2 \rvert$ incorrect, where $z_1$ and $z_2$ are any two complex numbers? I need an example to prove that it is. And in case it is correct, can you please give the proof? Thanks for any help. Why doesn't my "Nikkor AF" lens autofocus on my Nikon D3300? Is the null set a subset of every set? Ever since day one of of my Mathematical Logic course, this fact has really bothered me. I cannot wrap my head around how an empty set is a subset of every possible set. Could someone kindly explain how this is true? Any help is appreciated! How do I install .run files? When I type uname -a, it gives the following output.  Linux mars 2.6.9-67.0.15.ELsmp #1 SMP Tue Apr 22 13:50:33 EDT 2008 i686 i686 i386 GNU/Linux   How can I know from this that the given OS is 32 or 64 bit?  This is useful when writing configure scripts, for example: what architecture am I building for? How to add ground to DC circuit? I'm just a dabbler in electronic circuits and I'm really still kind of a noob. I am working on a project called the "Atari Punk Console" (Originally known as the "Stepped Tone Generator") but there are some parts of the wiring schematic that I don't understand, specifically the parts with the ground symbol.  Here is the schematic:   See those two ground symbols? I don't understand how to properly connect the circuit to ground at these points. How can I do this and be sure that I did it properly. I don't understand grounding at all so any pointers or clarification is also welcome. Thanks in advance. How do you remove the axis multiplier? This question is asked in various forms here but the question boils down to:  I know shrinking a database is risky. In this case, I've removed so much data and I'll never use it again.   How can I shrink my database? What files do I shrink?  What should my considerations be while doing this?  Should I do anything after? What if it is a large database? Can I shrink it in smaller increments? In Java, for a string x, what is the runtime cost of s.length()? Is it O(1) or O(n)? I've been told that code such as:  for (int i = 0; i &lt; x.length(); i++) {     // blah }   is actually O(n^2) because of the repeated calls to x.length(). Instead I should use:  int l = x.length(); for (int i = 0; i &lt; l; i++) {     // blah }   Is this true? Is string length stored as a private integer attribute of the String class? Or does String.length() really walk the whole string just to determine its length? How to run scripts on start up? How can I run scripts automatically when Ubuntu starts up so I don't have to run them manually after startup? How do I pre-install Ubuntu for someone (OEM install)? I would like to pre-install Ubuntu on a computer for someone. I may want to customize it for them, but in the end they need to be able to choose a username, password, etc. when they first boot it up. (Also called an OEM install).  How do I do this? Calculating size of particular area below buffer in QGIS? I have a point shapefile of villages where data was collected in Northern Kenya. I created a buffer around those villages.   The second vector layer contains polygons defining areas according to vegetation type. So for example, a forest might be surrounded by a narrow ring of woodland in an area which is mainly grassland. I'm trying to obtain a percentage of each vegetation type within the buffer per village.   I'm using QGIS 1.7 GPG Error while downloading software: "Clearsigned file isn't valid, got 'NODATA'"