Prove that there is a non-zero distance between any point outside an open set and any point in a closed-bounded subset (Complex Analysis)
A and B disjoint, A compact, and B closed implies there is positive distance between both sets
Default port for SQL Server I need to know the default  port settings for the following services   SQL Server SQL Browser SQL Reporting services SQL Analysis services   I neeed to know the port settings for these services for different versions of SQL Server (2000,2005,2008)  Also let me know whether the default port setting will change based on sql server versions  Thanks in advance. Difference between "I have got" and "I have gotten" I see these two expressions are used almost identically in different contexts. Is there a difference between I have got and I have gotten? Data recovery from an accidental format on ext4 partition When I was installing Mint Debian edition unlike the classic edition, the installation automatically formated my home partition when I did not specify to format.  So the formatting previously was ext4 as is now. I believe the data is still there as it was a quick format.   I have now booted the computer up on a live USB to prevent writing on it.  Ran testDisk. Is there anyway to recover to a previous superblock so i can recover my data? Proving an inclusion related to algebraic sets and interpreting it How can I upgrade to Java 1.8 on an Amazon Linux Server? I tried sudo yum update but it just keeps java "1.7.0_75". I need 1.8 for it to work with another application but can't figure out how to upgrade it. Do I need to manually install it somehow? There's not much information on this on the internet as far as I can see. Specs:   java version "1.7.0_75" OpenJDK Runtime Environment (amzn-2.5.4.0.53.amzn1-x86_64 u75-b13) OpenJDK 64-Bit Server VM (build 24.75-b04, mixed mode)   When I try update now:     [ec2-________]$ sudo yum update Loaded plugins: priorities, update-motd, upgrade-helper amzn-main/latest                                         | 2.1 kB     00:00 amzn-updates/latest                                      | 2.3 kB     00:00 No packages marked for update   Is there anything else I need to do? Thanks. How to finish current activity in Android What is the percentage increase to any value when initial value is 0? This is a very simple maths problem, which doesn’t seems simple to me when I just put some extra thoughts on it. So need to borrow some extra brains for this.   Question: If cost of coffee in my office was Dollar 0 till yesterday and today it is Dollar 2.5 then what is the percentage increase in the cost of coffee?  Initially it seemed like 2.5% increase, simply by distributing number from 0 to 100, but this is not the case.   Some suggested it is infinitely more than the previous value, because we are calculating percentage by dividing by zero. But what about this if the cost of coffee was $0.25? Isn’t still infinitely more! Something is wrong here.   PS: Yes, coffee were free in our office but not anymore, and we are still recovering from this shocker. 😥 I faced a problem to answer a negative question, for example, when someone asks you:      Don't you have any money?   It's a yes/no question but how should one answer the question without ambiguity?  When you answer "yes", does it mean "yes, I don't have any money"? or the other way "Yes, I do have money"? the questioner may think you are agreeing to the negative, that yes, you do not have any money.  I know it's better to answer with "on the contrary" but is it possible to answer yes or no? What's the deal with the phrase "could care less"?  Whilst growing up, I've always known people (parents etc) to use the phrase "couldn't care less", but I've also come across people who use the phrase "could care less" to mean the same thing (that is, "I do not care at all about that").  To me "couldn't care less" seems a lot more logical. If I couldn't care less about something, that implies I do not care about it at all. In contrast to this, to my mind the phrase "could care less" seems to indicate "I do care about this to some degree at least", but that's definitely not the meaning intended.  What's going on here? Is my (logical) analysis correct or in error? is the Turkish version of mancala, with its own set of rules.  I am planning on doing a project in it. Are there any game engines that either specifically play it, or universal Mancala players that plays it after supplying the options?  EDIT:  I am not looking for an app, but for a game engine. For example in chess,  is a playing app, while  is an open-source engine. I know that the Naruto movies are outside the timeline in the sense that they don't affect whatever happens after them. However, they must fall somewhere in the Naruto timeline — based on who are in the movies and how the characters look like, etc. For example, if Sasuke isn't in the movie, it should take place after he left. For each of the movies, approximately what timeframe (between episodes/arcs) are they set?  The movies:   Ninja Clash in the Land of Snow Legend of the Stone of Gelel Guardians of the Crescent Moon Kingdom Naruto Shippuden the Movie Bonds The Will of Fire The Lost Tower Blood Prison Road to Ninja The Last - Naruto the Movie Boruto: Naruto The Movie Area of a weird ellipse shape. A propeller has the shape shown below. The boundary of the internal hole is given by $r = a + b\cos(4α)$ where $a &gt; b &gt;0$. The external boundary of the propeller is given by $r = c + d\cos(3α)$ where $c - d &gt; a + b$ and $d &gt; 0$.  Calculate the total area of the propeller as shown by the shaded region and calculate the average temperature of the propeller, given by $T (r, α) = C/r$, where $C$ is a constant.     Have absolutely no idea how to solve this. Invest money and get 120% back - a site says Multilingual careers CVs tl/dr : Is it/will it be possible to fill out our Careers CV with localized information ?  Is it/will it possible to have different versions of the CV posted at careers (not totally different but just translated)?  Being in non English oriented country, this can be very helpful if I send local companies a link to my Careers CV and they could read it in a language other than English. LinkedIn has an implementation of this feature where you can create your profile in another language and it's up to the user to fill in the information in that language (first and last name, past experiences, etc)  The reason for this is primarily because my CV on careers contains more than just a list of bullet points, it reveals who I really am as a software developer (top tags, top answers, links to github projects, etc). I have tried a little bit which as follows- Since $f(x_n)\in[0,1]$, $\{f(x_n)\}$ has a convergent subsequence say $y_n=f(x_{r_n})\ \forall n\in\Bbb{N}$ Let, $\lim y_n=l\implies \lim \frac{y_1+y_2+\cdots+y_n}{n}=l\implies \lim \frac{f(x_{r_1})+f(x_{r_2})+\cdots+f(x_{r_n})}{n}=l$ But I am getting no idea to proceed and prove the convergence of $\{x_n\}$. I have also tried to prove the sequence to be cauchy which goes- $x_{m+1}-x_{n+1}={\sum_{i=1}^m f(x_i)\over m}-{\sum_{i=1}^n f(x_i)\over n}\le {\sum_{i=1}^m f(x_i)\over n}-{\sum_{i=1}^n f(x_i)\over n}$ (since $m\ge n)$ $\implies |x_{m+1}-x_{n+1}|\le \frac{|f(x_m)|+|f(x_{m-1})+\cdots+|f(x_{n+1})|}{n}\le\frac{m-n}{n}$ (since $f([0,1])\subseteq [0,1])$ Now, what will I get if I tend $m,n\to\infty$? But I need to do something more in the 2nd case since I have nowhere used the continuity of $f$.  Can anybody give an idea to prove it? Thanks for assistance in advance. Is my mobile AMD card being used? True or false: {{∅}} ⊂ {∅,{∅}} What is the command to minimize the gnome terminal? How can I minimize the Terminal window using a command? For example: I use the clear command to clear the terminal output, which command can I have to use to minimize the terminal window? I am really having trouble working a problem in my course. I will post it and then add what I have thought etc.  Let p be an odd prime, then using the Euclidian Algorithm, calculated the GCD of of $x^{p-1}-1$ and $x^2+1$ in $\mathbb{Z} / p\mathbb{Z}[x]$  Also, how does $p=1 (mod4)$ tell us that  $-1$ is a square in $\mathbb{Z} / p\mathbb{Z}$, infact that $-1$ is a square here if and only if $p=1(mod4)$.  My thoughts:   I know that $$x^{p}-x=(x)(x-1)(x-2)…(x-(p-1))$$ and so that in this sense our roots will be the congruence classes of $1,2,…p-1$  and also that $$x^{p-1}-1=(x-1)(x-2)…(x-(p-1))$$  But I get lost when trying to apply the EA to these polynomials,  like how can I do it when p is arbitrary?  Preferably id like to be able to understand/see how to do the first part first i.e. using division with residue and then move on to the second part. Any insight/hint or solution to this would be great,  Thank you all  Update:  When I try to do division with residue, I just get  $$x^{p-1}-1=(x^2+1)(x^{p-3}-x^{p-5}+x^{p-7}-x^{p-9}...)$$  for example,  $p=7$  $$(x^{6}-1)=(x^2+1)(x^4-x^2+1)$$  for $p=11$  $$(x^{10}-1)=(x^2+1)(x^{8}-x^{6}+x^{4}-x^{2}+1)$$  which for specific cases tells me that 1 is the gcd, but I dont know how to generalize that for the case with arbitrary prime p. SQL Server: Cannot insert an explicit value into a timestamp column