A continuous function $f:\Bbb R\to \Bbb R$ is injective if and only if it is strictly increasing or strictly decreasing
A continuous, injective function $f: \mathbb{R} \to \mathbb{R}$ is either strictly increasing or strictly decreasing.
Headphones microphone is not working I'm trying to use my headphones with my Ubuntu 13.10. My headphones are Nokia BH-905i, which can be connected via Bluetooth or green+pink wires.  If I use bluetooth, voice quality is terrible or microphone doesn't work. If I try to choose "Headset" option from In and Out tabs in Sound Settings, they're disabling each together.  In Out tab, I'm using "High sound quality A2DP", because it betters voice quality.  How could I get my microphone working? Sound out works fine. shade plane with a color function color(x,y) Where is the Task Manager? I have created screenShot() method to take the screenshot of the web page. When I used this method in my code first time it will capture the screen and it will save the image with image1 name. When I used the same method screenShot() to capture screens for other pages with the use of this.screenShot(); this will again capture the current web page screen but it stores With the same name image1 in the same folder (which overrides to previously captured screen image1).  Now, I have to take screenshots for the number of web pages &amp; want to store it into the same folder with different names like image1, image2, image3...etc. by using the same method screenShot().  public void screenShot() throws IOException, InterruptedException {     File scr = ((TakesScreenshot)driver).getScreenshotAs(OutputType.FILE);     File dest = new File("filPath/image1.png");     FileUtils.copyFile(scr, dest); }   Any workaround to achieve this scenario? Correct tracked camera orientation I have been playing around with camera tracking and I'm happy enough with the tracking and alignment of the markers with the footage when viewed through the camera.    The problem is, when I am not looking through the camera I can see that the grid isn't aligned to the camera.    How do you correctly align the grid to this tracked camera? I have set a floor and two points for scale, also clicked setup tracking scene, but this just added cube and plane which were on the grid. Windows Activation FAQ: How do language, version, 64-bit or 32-bit, and source affect ability to install and transfer Windows licenses? We get a lot of questions on Super User about Windows activation and licensing. This question is an attempt to answer the most common questions in one place with a .   When reinstalling Windows, the following questions often come up:   Can I transfer the copy of Windows from my old computer to a new one? Does the license key on the sticker on my computer work on any computer? If I have a 32-bit version, can I install a 64-bit version? I have an OEM version of Windows, but only a retail disk. Can I still use it? I want to install Windows with a different language. Do I need a new license in that language? I changed some hardware. Will I be able to reactivate my computer? Can I back up my activation before doing a reinstall? How many computers can I install my license on? Do I have to deactivate my old installation before transferring a license? If so, how? How does licensing work in Windows ? What are the restrictions on transferring, reinstalling, and changing versions of Windows? Ubuntu halts after few seconds of starting and nothing works command, virtual terminal, GUI Cyclic Group Generators of Order $n$ Let $X$ be a set and consider the collection $\mathcal{A}(X)$ of countable or cocountable subsets of $X$, that is, $E \in \mathcal{A}(X)$ if $E$ is countable or $X-E$ is countable. If $X$ is countable, then $\mathcal{A}(X)$ coincides with the power set $\mathcal{P}(X)$ of $X$. Now suppose that $X$ is uncountable. Assuming the axiom of choice, we can conclude that $\mathcal{A}(X) \ne \mathcal{P}(X)$, since $|X| = |X| + |X|$. So the question is:     Can we prove in ZF that $\mathcal{A}(X) \ne \mathcal{P}(X)$ for every uncountable set $X$?   I'm assuming that a set $X$ is uncountable if there is no injective function $f : X \rightarrow \mathbb{N}$. I found the question  Regarding the number of answers votes and also according to my personal taste I like to capitalize titles. But what exactly are titles? Only the single main book title? What about other smaller semantic parts? Chapter headings, sub-chapter, ... Movie: Creature crawls out of its current hosts mouth into next hosts mouth Where can we find frequently updated details about travel/entry restrictions due to Coronavirus (nCoV-19)? What do potential postdoc advisers seek in research statement letters? I am putting together my application for a postdoctoral position in theoretical condensed matter physics. The position is not a fellowship and is a regular postdoc position. If you have gone through the process of applying for such positions a number of times, or, even better, if you have reviewed such research statement letters, what are the main points that are sought/you seek in such letters? Specifically, should I put more emphasize on my PhD research to demonstrate my "depth of knowledge" on projects I have worked on (past research), or dwell more on things that I want/am capable to do (future research)? Quaternion for beginner I have 2 points in 3d space ,point A= &lt;5,3,6> and B=&lt;8,2,3>  I want to rotate "point B" by 30 degree from point A.  how do I solve this question using quaternion.  Plz, explain the steps.... How to create an annuity timeline on LaTeX I was wondering, how can I create a timeline exactly like this one:    on LaTeX?  I am a Finance student, and write all of my notes using LaTeX. These timelines, are giving me a headache. Since we use a lot of different timelines because of annuities. I want to learn how to create one basic timeline, so that I can then change anything I want. But basically, I want something like this, with the arrows and everything.  Thank you so much guys! Why upload to academic preprint sites like arXiv? The recent question  made me realize that I don't have any understanding of why one would upload to a preprint site.  (I don't work in a field where they seem to be common.)  Why would one be concerned about getting a manuscript on arXiv, if it's already under review with a journal?   Is it because of the long publishing timeline of journals?  (That could explain why computer science &mdash; which publishes much more in conferences &mdash; doesn't seem to do much with them.) After the  of registering an account to book train tickets online using my British VISA card, I finally got into a position of being able to book a ticket, but what it appears to be telling me is that I'm only being added to a wait list, which I assume means my tickets aren't confirmed.  Can someone explain how the wait list works, and what my chances are of getting on the train successfully?    It currently says the wait list is 7 The train is the Mandor Express, from Delhi to Jodhpur on the 18th of Nov   Update: So I got the train! Although it didn't get confirmed until a few hours before it was due to leave. Intel HD Graphics 620: Does my display adapter support HDMI 2.0 necessary for a 4k display? I want to connect my laptop (Inspiron 15 5000 Series) to a 4k display. When I read online about this it seems that HDMI 2.0 is a necessaity to handle the large resolutions / refresh rates involved to get full benefits of a 4k display.  Use case: I'm not going to use this to play games. Most of my use-case is editing documents, emails, spreadsheets and some engineering drawings and video (watching not editing).   The goal behind going 4k is to boost productivity by having more things open at once to read side by side.   I looked into the Dell specs and they only mention an HDMI without going into the details of what type or whether it will support HDMI 2.0 / 4K TV.     How do I tell whether my Dell Inspiron Laptop (i7 7500 U processor) supports this?  I looked under the Display Adapters and can see that I have an "Intel HD Graphics 620"  listed.   Will this suffice to tell me if this display adapter will support HDMI 2.0 / 4k display?   Or should I be checking out some other settings?  Thanks! Suppose a cleric casts Zone of Truth on a captured enemy. Unbeknownst to them, the enemy is a rakshasa. Zone of Truth says (PHB, p. 289):     You know whether each creature succeeds or fails on its saving throw.   But (MM, p. 257):     The rakshasa is immune to spells of 6th level or lower unless it wishes to be affected.   Assuming the rakshasa doesn't wish to be affected by the Zone of Truth spell, does the caster know this?  More generally, does a caster know when targets are unaffected by a spell they have cast, either because they have made saving throws, or because they are outright immune to the spell or its effects (e.g., casting Ray of Sickness on a shadow demon, which is immune to poison damage and the poisoned condition)? I need to install a new TeX/LaTeX/ConTeXt package on my computer.  I'm running Ubuntu/Fedora/Slackware/Some-Version-Of Linux.  What are the possible ways to do this?    Note:&nbsp;&nbsp; We get a number of questions that essentially reduce to this one; it was felt a good idea to have one question-and-answer that can cover all the standard methods.  See  for the discussion.  The question-and-answer are CW so that more information can be easily added.  If you have information to add, please do so.  If you are unsure, leave a comment here or (preferably) in .  Comments on the question and answer will be periodically removed to ensure that the information is clear.