How Can I Import android.util.Log from InetAddress.java (or any file in libcore/luni/src/main/java/java/net)? [Not a]
Why is using a wild card with a Java import statement bad?
Proving $T$ and $U$ are equal if I know $(X,T)$ and $(X,U)$ are hausdorff and compact This question is from Wayne Patty Exercise 4.2  Let $T$ and $U$ are Topologies on set X. Suppose $ (X,T) $ and $(X,U)$ are compact Haurdsorff Spaces. Prove that $T=U$ or $T$ is not a subset of $U$ or $U$ is not a subset of T.  I thought of proving it by this way: Assuming that if $T$ is a subset of $U$ or $U$ is a subset of $ T$ then $T=U$ must be true. But I was unable to think on how to use compactness or hausdorff property and was unable to proceed. Well, also this question was asked before on this website. But I am unable to understand how the solution will work despite trying to understand it for a fair amount of time as it was just outlined. So, I am looking for a detailed solution. Given a simple graph and its complement, prove that either of them is always connected. I was tasked to prove that when given 2 graphs $G$ and $\bar{G}$ (complement), at least one of them is a always a connected graph.  Well, I always post my attempt at solution, but here I'm totally stuck. I tried to do raw algebraic manipulations with # of components, circuit ranks, etc, but to no avail. So I really hope someone could give me a hint on how to approach this problem. I'm using an unsigned repo in Ubuntu 16.04 from Debian multimedia:  deb http://www.deb-multimedia.org jessie main   To install deb-multimedia-keyring, I'm running:  apt-get update &amp;&amp; apt-get install deb-multimedia-keyring -y   This gives an error:  W: GPG error: http://www.deb-multimedia.org jessie InRelease: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY 5C808C2B65558117 E: The repository 'http://www.deb-multimedia.org jessie InRelease' is not signed. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details. Prove that $\sin(2A)+\sin(2B)+\sin(2C)=4\sin(A)\sin(B)\sin(C)$ when $A,B,C$ are angles of a triangle Prove that $\sin(2A)+\sin(2B)+\sin(2C)=4\sin(A)\sin(B)\sin(C)$ when $A,B,C$ are angles of a triangle   This question came up in a miscellaneous problem set I have been working on to refresh my memory on several topics I did earlier this year. I have tried changing $4\sin(A)\sin(B)\sin(C)$ to  $$4\sin(B+C)\sin(A+C)\sin(A+B)$$ by making substitutions by reorganizing $A+B+C=\pi$. I then did the same thing to the other side to get $$-2(\sin(B+C)\cos(B+C)+\sin(A+C)\cos(A+C)+\sin(A+B)\cos(A+B))$$ and then tried using the compound angle formula to see if i got an equality. However the whole thing became one huge mess and I didn't seem to get any closer to the solution. I am pretty sure there is some simpler way of proving the equality, but I can't seem to figure it out. Maybe there is a geometric interpretation or maybe it can be done using just algebra and trig. Any hint's would be appreciated (I would prefer an algebraic approach, but it would be nice to see some geometric proofs as well) Do synonyms have exactly the same meanings as each other in all contexts? I have a question about synonyms: I'm wondering for quite a while if synonyms always stand exactly for the same thing. Is there sometimes a little difference in meaning? Let's use clumsy and clunky for example. Can I always replace clunky with clumsy? Since I'm not a native speaker, as you may have noticed, I cannot tell them apart. According to my dictionary, they mean exactly the same. Is it always true?  If the question has already been ask, sorry I couldn't find it.  Edit: Thank you very much! Every answer has helped a lot and thank you so much for it. I really appreciate it. I've voted all your answer because every answer helped me in a different way. I've accepted Barrie England's answer because it was the best one in my case. But all of yours were really good and helpful :) How do I get and modify the source code of packages installed through apt-get? I am assuming that all application installed through apt-get are open source; but for those that are available in that manner, where can I get the source code for these applications as well as update them?   I have a couple applications I use regularly that aren't being actively developed any longer and I would like to add features. Where would I go to get the rights to update these applications?  In this case specifically, I am referring to the hellanzb package Smallest Width for Galaxy S and Galaxy S2 I am trying to boot Ubuntu on my computer.  When I boot Ubuntu, it boots to a black screen.  How can I fix this? Table of Contents: So first let me state my homework problem:  Let $X$ be a set, let $\{A_k\}$ be a sequence of subsets of $X$, let $B = \bigcup_{n=1}^{+\infty} \bigcap_{k=n}^{+\infty} A_k$, and let $C = \bigcap_{n=1}^{+\infty} \bigcup_{k=n}^{+\infty} A_k$. Show that (a) $\liminf_k\; {\xi_A}_{_k} = \xi_B$, and $(b)$ $\limsup_k \;{\chi_A}_{_k} = \chi_C.$  I know that, in the context I am familiar with, that $$\liminf_{k\rightarrow +\infty}\; X_k = \bigcup_{k=1}^{+\infty} \bigcap_{n=k}^{+\infty} X_n$$ and $$\limsup_{k\rightarrow +\infty}\;X_k = \bigcap_{k=1}^{+\infty} \bigcup_{n=k}^{+\infty} X_n.$$   I also know that the characteristics (indicator) function is defined as $\chi_A(x) = \begin{cases} 1, &amp; x \in A \\ 0, &amp; x \notin A .\end{cases} $  So I wrote out $B$ in some of its `glory': $B= (A_1 \cap A_2 \cap A_3 \cap \cdots) \cup (A_2 \cap A_3 \cap \cdots) \cup (A_3 \cap A_4 \cap \cdots) \cup \cdots$, and as the first argument is the smallest, with increasing size to the right, the last term in the expression for $B$ would be $B$, which would be the largest.  So if I replace the $X_k$'s above with $\chi$'s I still don't see how I can get the correct answer - though it looks pretty clear from the definition of $B$ and that of $\liminf$ being basically the same, except in this case for the $\chi$.  Any direction would be greatly appreciated. By the way, I have checked out  but I was somewhat confused by the topology, the meets/joins, etc.  Thanks much, Nate $\mathbb{R}$ with the lower limit topology is not second-countable I am trying to prove that $\mathbb{R}$ with the lower limit topology is not second-countable.  To do this, I'm trying to form an uncountable union $A$ of disjoint, half-open intervals of the form $[a, b)$, $a &lt; b$. Is this possible? I think this would imply the $A$ is open but no countable union of basis elements could coincide with $A$ therefore making the real numbers with the lower limit topology not second-countable.  I think there must exist something like $A$ described above but I am having trouble visualizing it and coming up with a formula to represent it.  Maybe there is some other way to show it is not second-countable. What should I do if a user posts sensitive information as part of a question or answer? Are there alternatives to LibreOffice? Differences between /bin, /sbin, /usr/bin, /usr/sbin, /usr/local/bin, /usr/local/sbin I have six directories with command files. These are /bin, /sbin, /usr/bin, /usr/sbin, /usr/local/bin and /usr/local/sbin.  What are the differences between these? If I'm writing my own scripts, where should I add them?    Related: difference between accuracy and Rand index (R) I'm very confused, when I read on the wikipedia "From a mathematical standpoint, Rand index is related to the accuracy, but is applicable even when class labels are not used."   and   But when I use in R the rand.index function from fossil package and the Accuracy function from MLmetrics it doesn't give the same answer  &gt; Accuracy(predicted, real) [1] 0.8266667  &gt; rand.index(predicted,real) [1] 0.7114989  Please can someone explain to me the difference between these two and which one should I use?  NB:I use the k-medoids clustering algorithm (function pam from cluster package) MacBook Pro (15-inch, 2016) with 2 USB-C to HDMI adapters. The setup works great if I start up in that configuration.   If I connect the adapters while the machine is running or simply sleeping, one of the monitors will never get a signal and stay in low power mode. The OS sees the monitor, it shows in the display arrangement settings and I can move the mouse into it, but until I restart, I can't see anything on it.  Once I have restarted I can let the machine sleep or whatever, and the display still works unless I disconnect the adapter. As soon as I do that a restart is required to use it again.   Using MacOS Sierra (10.12.4)  Using this adapter: I hear the word architect used as a verb in the technical field and now more often in other industries and groups, for example:     We need to architect a better solution to the problem.   I am interested if this is considered acceptable usage, as I see this word being used more in published technical documents (not necessarily books, but corporate publications).  I can see how a conductor can conduct, a typist can type, but can a scientist "science"?  A scientist might research, analyze, and so forth, as an architect might design, create, build, etc.  Merriam-Webster , however, I have been told that other dictionaries exist that define architect as both a noun and a verb&nbsp;— is there a credible reference or source that authoritatively answers this question? do_shortcode() within Admin Page I'm using a few plugins that have shortcodes ... however, instead of creating a public page for the content, I've created some new pages within the admin using add_menu_page and I need to know how to utilize do_shortcode() within this context.  As it stands, all the function does it spit out the string. I'm assuming it's because the shortcode API isn't available within an admin page.  How do I get around this? There is no documentation that I can find that explains how to utilize shortcodes within the WP Admin... or if it's even possible.    Specifically I'm trying to utilize WooCommerce shortcodes within the WP Admin. I hate the fact that plugins don't utilize the WP Backend for account/user management. Prove that if $ f\mathrm{(}z\mathrm{)} $ is analytic at the infinity  ,then :  $ {\lim}_{{z}\mathrm{\rightarrow}\mathrm{\infty}}{f}\prime{\mathrm{(}}{z}{\mathrm{)}}\mathrm{{=}}{0} $ Why exactly did the Sorting Hat originally want to put Harry in Slytherin? I just signed up, a day or two ago, and I've received a notification that there's something in my inbox.  Unfortunately, my email client isn't able to show me a link to my Inbox, or the message, because of the format of the email.  I normally use the email address that I gave when I signed up, just with MailWasher, which is intended to safely preview emails, as plain text, to decide whether or not to open them in a normal HTML email client.  I would be nice if that email contained a link to my inbox, which could be shown in MailWasher.  In order to collect that email in a normal email client, I'd also have to collect or delete all the other emails sent to that address.  I'm not entirely clear what's been done in that email to stop MailWasher seeing the link.  I can see a link to leave feedback, and one to unsubscribe, but not one to check my inbox.  Sure, I can live without one, but those emails would be a lot more useful to me if I could just click a link to go to my Inbox.