How to control sound of connected external monitor?
HDMI/Displayport audio control for OS X
Is it possible to include one CSS file in another? Is it possible to include one CSS file in another? Here is my question:  Is a homeomorphism, that is, a continuos function whose inverse function is also continuous, always bijective? How can I change the default "ens33" network device to old "eth0" on Fedora 19? Indecomposable limit ordinals A limit ordinal $\gamma&gt;0$ is said to be indecomposable iff $\nexists\alpha,\beta&lt;\gamma$ such that $\alpha+\beta=\gamma$.  In view of this definition, I’m trying to prove the equivalence of the following statements for limit ordinals $\gamma$:  (1) $\gamma$ is indecomposable.  (2) $\alpha+\gamma=\gamma$ $\forall\alpha&lt;\gamma$.  (3) $\gamma=\omega^\alpha$ for some $\alpha\in\mathrm{ON}$.  I’ve been able to get $(1)\implies(2)$ and $(3)\implies(1)$, but I have nothing more than scratch work for $(2)\implies(3)$.  Any suggestions would be appreciated. Is there an easy way to convert a number to a word in PHP? If I have a 18-55mm lens, is there a point in buying a 35mm prime lens? What is the cause for the validity of Newton's third law? What, specifically, causes newton's third law?  For instance, if I push on a wall, why is it that I experience a force in the opposite direction?    I seem to vaguely understand that is has something to do with electronic repulsion or molecular compression (maybe that's completely wrong, I don't know).  As a related question, what would happen if two objects that were /infinitely/ immovable (at the molecular level, it cannot be broken or compressed) collided with each-other? I tried to install ffmpeg in trusty/Ubuntu 14.04 and got the following message:  $sudo apt-get install ffmpeg  Reading package lists... Done Building dependency tree        Reading state information... Done Package ffmpeg is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source  E: Package 'ffmpeg' has no installation candidate   Why isn't the package available? So I wanted to make some minecoins and I also heard that anyone become a marketplace creator could but I don't know where to apply. I'm in Minecraft Pocket Edition 1.14.30. Can you tell me where I can apply? Is logical implication always determinable from just the given statements? I am reading introductory texts on logic and am having a hard time understanding intuitively logical implication.  Specifically, I am wondering if logical implication can always be determined by two statements, P and Q alone? I'll try to give an example to clarify my question.  For example if the statement P is $x = 2$, and the statement Q is $x^2 &lt; 6$, then determining the truth of P $\Rightarrow$ Q is fairly straightforward:   If $x$ does equal 2, then $4&lt;6$ and Q is true, so $P \Rightarrow Q$ is true. And if $x$ does not equal 2, $P \Rightarrow Q$ is vacuously true.  In this example, with two statements P and Q, I can evaluate the truth/falsity of the statement P implies Q. However, what if the statement Q is changed such that it is now the statement $y = 5$?  So now I am trying to prove from that $$x = 2 \Rightarrow y = 5$$  Here is where things get murky for me. Say $x$ is not equal to 2, then $P \Rightarrow Q$ is vacuously true. But what about when $x$ does equal 2, now the statement Q could be true, but it could also be false, depending on some 'context'.   For example, if I said at the start: "Here are two statements, P and Q. Know that x = 2 and y = 4." Given this 'context', $P \Rightarrow Q$ is false. But if I say "Here are two statements, P and Q. Know that x = 2 and y = 5", then now $P \Rightarrow Q$ is true.  My discomfort here is that I assumed with two statements P and Q, I can determine the truth/falsity of $P \Rightarrow Q$ with just this information. Is this the wrong assumption?  As a secondary question, how can the truthfulness of the statement $P \Rightarrow Q$ be variable, depending on context? I have read on some other questions that implication can be interpreted as a promise. So how could it be that depending on some context the promise is sometimes true but sometimes false? Wouldn't this actually mean the promise is not always consistent and is therefore always false?  Some further information in case it is relevant, I recognise that in the first example, the statement Q is 'dependent' in some way on the statement P, since the object under examination in both statements is $x$, whereas in the second example there are two different objects which I am trying to make a logical connection between, which I am thinking may not be valid for some reason. I also recognise that there is still 'context' in the first example, in that we need information on whether $x$ is equal to 2 or not, however in that case it doesn't matter, since $P \Rightarrow Q$ is always true anyway.  Thanks very much in advance. How to evaluate $\int_0^{2\pi} \frac{d\theta}{A+B\cos\theta}$? I'm having a trouble with this integral expression:  $$\int_0^{2\pi} \frac{d\theta}{A+B \cos\theta}$$  I've done this substitution: $t= \tan(\theta/2)$  and get: $\displaystyle \cos\theta= \frac{1-t^2}{1+t^2}$ and $\displaystyle d\theta=\frac{2}{1+t^2}dt$ where $\displaystyle \cos^2\theta/2=\frac{1}{1+t^2}$  then the integral becomes:  $$\int\frac{2 \, dt}{(A-B)t^2+(A+B)}= \sqrt\frac{A+B}{A-B} \arctan \left(\left(\sqrt\frac{A+B}{A-B} \right) t\right)$$   However, I'm not sure about the new limits since $\tan$ has period $\pi$ so what I have to do at this point to decide the new limits? And of course if you find some mistake in what I've done before, please let me know! How can you prove that the square root of two is irrational? Given two sets$$A=\{1,3,5\}\quad,\quad B=\{1,3,8\}.$$ Then I compute the $A\setminus B=\{5\}.$   But my book$^\dagger$said: ... . Also, observe that $x\notin A\setminus B$ does not mean that $x\notin A\lor x\in B$. Why?  I don't know how to explain the Why, please give me some example.    $^\dagger$, second edition, page $4$.  EDIT: My intuition tells me that it does mean that. I guess there is some special case about null-set or about the restriction of the universal set. How can I add a bookmark in my nautilus folder explorer Is it correct to sometimes capitalize words mid-sentence in computer user interfaces? Why the names Type 1, 2 error? So, today is July 21st and . gives me an option to download 16.04.1 LTS. However, attempting to upgrade gets me this message -  $ sudo do-release-upgrade Checking for a new Ubuntu release No new release found   What is wrong? Does it matter that I am running apt-get update behind apt-cacher-ng?  Note: Commenting out the files in apt.conf.d that used apt-cacher-ng did not make a difference.  Edit: Explanation for possible duplicates:  deals with upgrade from 12.04LTS to 14.04LTS. My question is specific to 14.04 LTS to 16.04.1 LTS upgrade. Old answers, while good for archival purposes are less relevant in a fast changing package like ubuntu. Moreover none of the answers answer what is wrong. The link  pointed out is mentioned in one of the comments. This Q &amp; A is more helpful for people upgrading today than the work around mentioned in "". Find a bijection to prove a fact about integer partitions Prove that for fixed positive integers $k$ and $n$, the number of partitions of $n$ is equal to the number of partitions of $2n + k$ into $n + k$ parts.  I tried this with different values of n but can't seem to get a bijection between the two partitions. How do I type Arabic text in Photoshop? I want to type Arabic text in Photoshop, but the text appears disjointed and the letters do not connect at all. For example محمد appears as م ح م د.   I'm using Photoshop CS6 on OSX Mountain Lion. I have a PDF that consists of several hundred pages of bilingual text. Since I need to use OCR on each language separately, I want to grab the even and odd pages and make two separate PDFs, using convert or ghostscript. The language I want to do first is on the odd-numbered pages. What convert or ghostscript command can I use to grab these and write them to a new file?