If I install Ubuntu 16.04 Beta 1 now, will it be easy to upgrade to the full release when it's out in late April?
I have an alpha version of Ubuntu.  When the stable version is released do I have to upgrade or is it already stable from the installed updates?
This is exercise 1.6.1 of   Suppose that 501 distinct integers are selected from 1 . . . 1000. Show that there are distinct selected integers $a$ and $b$ such that $a | b$. Show that this is not always true if 500 integers are selected.  This seems like it should be simple but it's has been stumping me for a few days.  Here's my idea for a proof:  Let $S$ be a set of 500 distinct integers between 1 and 1000 that don't divide each other. Let $S_{1-500}$ and $S_{501-1000}$ partition $S$ into sets containing the elements ≤ and > than 500, respectively. Then consider $2 S_{1-500}$ and $\frac{1}{2}S_{501-1000}$, the result of multiplying the elements of these sets by 2 and 1/2, respectively. Because elements of S are coprime, $S_{1-500}$, $S_{501-1000}$, $2 S_{1-500}$, and $\frac{1}{2}S_{501-1000}$, are disjoint. Also note that each of these sets is a subset of the integers from 1 to 1000. One can deduce that the cardinality of the union of these sets is 1000, and therefore they form a partition of the integers from 1 to 1000.  Now, I know this demonstrates that you can't add another number to $S$ that is coprime with all the elements in $S$, which means that a coprime subset of the integers from 1 to 1000 can have at most 500 elements. Can someone articulate why this is true for me? Also, this was in a section on the Pigeonhole principle, can someone rework the proof to utilize that, and possibly make it simpler? Thanks. Short story about a robot who wants to become a writer I remember reading it while in middle school in English in the United States, so the latest it would have come out was 1998. I don't remember if it was all one author, or even the same universe. These are the stories I remember:   A man finds a way to create a medicine that prevents radiation poisoning (or possibly makes someone fireproof... it's a little confused in my head) and learns that part of the problem is finding a market for it. I vividly remember the inventor telling someone to not "let the doorknob ream you" as it slams shut. A bout of graffiti artists leads to the city buying anti-graffiti paint that dissolves any other paint put on top of it. After learning the futility of trying to paint over it, the protagonist consults with a friend and learns that the anti-graffiti paint will eat away at the paint above it at a steady rate, and will even eat successive layers of the anti-graffiti paint. he uses this property to engineer an animation involving a harlequin thumbing this nose at the officials even as they try to wash it away. Some guys (I want to say a gang) go to a clinic for an illegal nanotech transformation. The viewpoint character gets turned into a woman while a friend gets turned into a dog. After roaming about in their new forms, they return to find the clinic being raided, meaning there's no one to turn them back. I think I remember something bad happening to the one transformed into a dog where the transformation continued, erasing his human thought patterns. There was also a scene where the viewpoint character submitted to being sexually assaulted by his former friends as if it was simply to be expected given his form.   I don't remember if the first or the second story was the actual first story of the collection... I want to say that those are the order that they showed up as in the book. Should we use plural or singular for a fraction of a mile? I have seen people say both 0.25 mile and 0.25 miles. Should we use plural or singular for a fraction of a mile? Question regarding use of low voltage high current outputs I see every day high voltage, high current; high voltage, low current. I rarely see low voltage, high current; why?  I know that I can take a high voltage, high current signal, send it through a step-down transformer and theoretically get a low voltage high current (with the same power output, of course), but I never see this done.  Can someone give me a reason as to why I wouldn't want a low-voltage high-current scenario? Is there some special case where a fermion can mediate a force? I updated MacOS Sierra's Apache and PHP, and now whenever I $ sudo apachectl restart I get this:  AH00557: httpd: apr_sockaddr_info_get() failed for My-MacBook-Pro.local AH00558: httpd: Could not reliably determine the server's fully qualified domain name, using 127.0.0.1. Set the 'ServerName' directive globally to suppress this message   Things I've tried so far that didn't work:   Setting ServerName localhost in /etc/httpd.conf Setting ServerName localhost:80 in /etc/httpd.conf Setting ServerName 127.0.0.1 in /etc/httpd.conf Setting ServerName 127.0.0.1:80 in /etc/httpd.conf Ensuring 127.0.0.1       localhost is set in /etc/hosts Repeatedly restarting Apache Is the use of a hyphen between "non" and an adjective strictly necessary? Do I need to put a "-" between "non" and an adjective? As an example in physics we say "a non isolated photon", "non tight photon"... The context is very formal (paper publications and similar). Is there a general rule? Are there some differences between countries? Skyrim - Companions attacked me for no reason? Async call generates " Error: Can't wait without a "fiber", even with _wrapAsync Prove $\frac{a+b+c}{abc} \leq \frac{1}{a^2} + \frac{1}{b^2} + \frac{1}{c^2}$. So I have to prove $$ \frac{a+b+c}{abc} \leq \frac{1}{a^2} + \frac{1}{b^2} + \frac{1}{c^2}.$$  I rearranged it   $$ a^2bc + ab^2c + abc^2 \leq b^2c^2 + a^2c^2 + a^2b^2 .$$  My idea from there is somehow using the AM-GM inequality. Not sure how though. Any ideas?  Thanks The class will be over in 10 minutes. The class will be over after 10 minutes.  I know the first is correct but why? Why does turning Caps Lock off take such a long time to work? This is my biggest issue with Linux and the main reason I don't use it as my main working OS.  Whenever I use caps lock to write something in upper case and disable it in order to keep writing the next letter AFTER I've disabled it is written in upper case.  So, my text comes out weird, as SOMETHING *L*ike this  I've tried Linux Mint, Fedora ... and the issue keeps happening.  Searching Google I've found some very rare persons have the same issue, but I was unable to find any solution.  Is there any way to solve this or am I DOOMED *F*or life?  BTW, whenever I ask this question someone suggest I should learn to use shift, instead of caps lock. I know, that's the right way, but I'm used to use caps lock and, well, it should work. The Help Vampire problem It is asked to solve the PDE  $$u_x + u_y + u = e^{x+2y}$$  My attempt: We have that $$\frac{dx}{1}=\frac{dy}{1}=\frac{du}{e^{x+2y}-u} $$  $\Rightarrow \frac{dy}{dx}=1 \Rightarrow y=x+C_1 \iff C_1=y-x$  $\Rightarrow \frac{du}{dx}= e^{x+2y}-u \iff \dot{u}+u=e^{x+2y} \iff \\ \frac{d}{dx}(e^x u) = e^{2x+2y} \iff u = e^{-x} ( \frac{1}{2}e^{2x+2y} + C_2)$  As $u$ is constant along its characteristics:  $$u(x,y)=\frac{e^{-x}}{2}(e^{2x+2y} + 2C_2(y-x))$$  where $C_2$ is any function of one variable. But wolfram gave the following answer  $$u(x,y)=\frac{e^{-x}}{4}(e^{2x+2y} + 4C_2(y-x))$$  as you can check   What am I doing wrong? As I finished programming the MCU in the Arduino Uno board to receive some RF Signal and drive relays, I moved it into a standalone board I made with Eagle. The circuit is pretty basic, the MCU receives data from a RF Receiver, processes it and then turns on/off some pins that drive 5V relays (through transistors, of course). When I test it on the Arduino Board, you can see that the LEDs toggle ON and OFF whenever I send the data through the RF Transmitter. You send once, it toggles ON, you send another time, it toggles OFF and so on. This works for all the 4 PINS that it has programmed. In my standalone board, each of these four pins are connected to transistors that drive 5V relays. The problem is that only one pin seems to activate, and then it won't even toggle OFF, like you send the data once and you can hear the relay's coil go ON, but then if you try to toggle it OFF it just won't, it's latched ON and I have to unplug and plug the USB cable again to reset it. The ATMEGA328P has a 16MHz crystal, two 22pF caps for the crystal, and a 10K resistor that goes from the Reset Pin to VCC. I'm not sure why the MCU behaves so weird in my board. There's also another VERY weird detail I didn't mention. If instead of using the RF Receiver, I connect the Data Output pin of the PIC that drives the RF Transmitter directly into the Receiver board, that one pin I mentioned that works is able to toggle OFF and ON again, but still, the other pins just don't work. I've tested it not only by hearing the relay's coil but also by using a multimeter. Any help would be really appreciated.  EDIT:  Here is the Eagle Schematic of the board:    It's true that I really didn't concern about the noise, but since it was quite a simple project I didn't think that noise was going to attack so violently, plus  I don't really know how to protect the circuit from inductive noise. Thank you for answering fast!  EDIT 2:  Okay so here goes more detail:    Real photos:      The soldering seems quite awkward but I probed all the traces to check for continuity.  I could make some extra holes to, for example, add a 100nF decoupling capacitor for the MCU and so, but if you think I should enhance the schematic and add a lot more components, then I'll gladly remake the board.   About the supply, right now (for debugging) I'm connecting the Arduino Uno to a Cellphone Charger (Notebook won't supply enough current for relays), and I'm connecting those red and black cables to the Arduino Uno. I'm using that Cheap 433MHZ RF Receiver so if the circuit is so vulnerable to noise as you say, it may also be getting fouled up by the noise. How do I minimize total cost of separate flights to the same destination plus optionally accommodation? My girlfriend and I are currently living in different countries, and meet occasionally for a few days every month or so. We don't really care all that much where we are going, as long as we don't need a visa (we're both in EU), just so we are at the same place and time for a couple of days.   In short:     I'm flying from airport AAA, she's flying from airport BBB, we need to find an airport XXX (not a euphemism!) which is cheapest to fly to overall.   Bonus task: Flights are first and foremost, and we could live with a somewhat more expensive accommodation as long as we can get in and out easily. Since the accommodation cost is comparable to flight cost for such a short stay, we'd like to have some sort of rough idea what we're going to pay for a certain type of accommodation, for example three-star hotel. How do you post to an iframe? How do you post data to an iframe? 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! Nullable type issue with ?: Conditional Operator Could someone explain why this works in C#.NET 2.0:      Nullable&lt;DateTime&gt; foo;     if (true)         foo = null;     else         foo = new DateTime(0);   ...but this doesn't:      Nullable&lt;DateTime&gt; foo;     foo = true ? null : new DateTime(0);   The latter form gives me an compile error "Type of conditional expression cannot be determined because there is no implicit conversion between '&lt;null&gt;' and 'System.DateTime'."  Not that I can't use the former, but the second style is more consistent with the rest of my code.