I've come across something which appears strange to me, but at the same time makes some sense for reasons I don't know.  I have this enum:  [Flags] public enum Flags { RemoveQuoteMarks = 1, t1 = 2, t2 = 4, t3 = 8, t4 = 16, t5 = 32, t6 = 64, t7 = 128 }   Before, I didn't manually set the enum values, they index from 0 and standardly increase by 1 right?  Well I noticed odd behavior when I tried to load this string:  string value = "t1, t3, t4, t7";   and parse it using:  Flags flags = (Flags)Enum.Parse(typeof(Flags), value);   and the result was just 't7', so I did some research, and noticed a lot of others used manual indexing where each enum value was doubled by its previous (e.g. 't3 = 8', 't4 = 16'), so I applied this rule to mine, and it worked, my parsed enum had now shown as:  t1, t3, t4, t7   as desired, why do I have to manually configure my enum values like that?
From time to time I see an enum like the following:  [Flags] public enum Options  {     None    = 0,     Option1 = 1,     Option2 = 2,     Option3 = 4,     Option4 = 8 }   I don't understand what exactly the [Flags] attribute does.  Anyone have a good explanation or example they could post?
Solving functional equation $f(x+y)+f(x-y)=2f(x)\cos y$? How can I solve this functional equation, where $x,y$ are any real numbers and $f:\mathbb{R}\to \mathbb R$ is a function such that : $$f(x+y)+f(x-y)=2f(x)\cos y$$    I tried substituting $x=0$ to get $f(y)+f(-y)=2f(0)\cos y$ . Taking $x=y$ gives $f(2x)+f(0)=2f(x)\cos x$. I similar get some more relations like that, but its not really helping me in finding anything useful. I also think the function must either be $\sin$ or $\cos$ looking at the product to sum formulae. Can anyone tell me how should I solve this? Is there a way to export each rendered layer as its own image? My scene uses multiple render layers.  I'd like to edit each rendered layer in Photoshop, and composite it in Photoshop.  Is there a way to export each layer as an individual image? Can a wealthy investor invest in or make a deal with a company before it goes public / IPO? Can a wealthy investor invest his money in any company before it goes public / IPO? I am referring to a recent Goldman Sachs and Facebook deal worth $450 Million at a valuation of $50 Billion dollars.   I want to know what is the procedure and how are these valuations made prior to the company going public? Is is possible that an investor could raise capital from investment banks, private equity, or commercial banks to re-invest in a pre-IPO deal at some valuation?  Knowing that angel investors don't provide so much money, can they play their role here with a normal investor? Why do games run slow on CPU Maybe my question sounds naive because I'm not a game developer but I dont see objective reasons for this. An average cpu is in times more powerful than an average gpu like a few graphics cards in one. The most repeated reasons in internet:  the GPU isn't as busy as the CPU  If the gpu renders the screen how it can not be busy The modern cpus are powerful enough. They are not busy most of time. For example my cpu's usage is 3%.  many GPU's are designed to process graphics commands in parallel, CPU single threads them  What bothers the games to run a few parallel processes even on one cpu core? In my opinion its not correct to tell that the gpu is better if games never use 100% of the cpu's capacity. To be specific they dont use even 50%.  To clarify my question based on responses in the comments:  Did you mean to ask &quot;Why do games render more slowly on the CPU?&quot;  Yes I mean why the cpu cant do the whole work for games when it is underloaded and especially if it does the largest part of work in any case.  You can not compare GPUs and CPUs directly, because they do different things.  What bothers them to do the same things?  The CPU isn't as well suited to performing rendering calculations  I dont understand what &quot;suited&quot; means. And why the cpu is not suitable for primitive tasks aka paint roller.  adding additional parallel processes doesn't improve performance  Then why do you produce multicore graphics cards and multicore central processing units? Just give various parts of one task to a few processes if one process is slow and 100% of the capacity is not used. What bothers to emulate the gpu? Its also unclear for me why when you play without a separate graphics module the games see only one cpu core when you play with the gpu they see and use all the cpu cores. May be some magic. People often use sans, the French word for ‘without’ in English.   What I don’t get, is when should that switch be made. When should I say sans when I really want to say without. Are there any general rules regarding usage, or is it kind of a person-to-person basis/feeling of flowerness. Can polymorph and true polymorph change a PC's race and sex? rewrite script to use wp_remote_get instead of file_get_contents_curl C++ virtual function from constructor Why the following example prints "0" and what must change for it to print "1" as I expected ?  #include &lt;iostream&gt; struct base {    virtual const int value() const {       return 0;    }    base() {       std::cout &lt;&lt; value() &lt;&lt; std::endl;    }    virtual ~base() {} };  struct derived : public base {    virtual const int value() const {       return 1;    } };  int main(void) {    derived example; } Prove that $\frac{a_1^2}{a_1+a_2}+\frac{a_2^2}{a_2+a_3}+ \cdots \frac{a_n^2}{a_n+a_1} \geq \frac12$ Let $a_1, a_2, a_3, \dots , a_n$ be positive real numbers whose sum is $1$. Prove that $$\frac{a_1^2}{a_1+a_2}+\frac{a_2^2}{a_2+a_3}+ \ldots +\frac{a_n^2}{a_n+a_1} \geq \frac12\,.$$  I thought maybe the Cauchy and QM inequalities would be helpful. But I can't see how to apply it. Another thought (might be unhelpful) is that the sum of the denominators on the left hand side is $2$ (the denominator on the right hand side). I would really appreciate any hints. can't send email to addresses at my own domain Someone's car hit our metal bar gate, so one of the rods is bent as shown in the photo. What kind of a tool can I use to bend this back, so it's straight? Thank you! Careers Stack Overflow - Tag "ruby-on-rails" returns jobs that don't contain the tag I have a UK Refugee passport. Do I need a visa to go to France?   I want to go for two days with my husband, but I'm not quite sure if I can go without a visa. Alternatives to "and/or"? Is there a difference between "" and {} in BibTeX? Max Block Height for a Redstone Contraption What's the max height of blocks for a redstone contraption to still work even I'm in the surface below?  Like if I build a pillar to the max height of blocks and build a redstone contraption there, is it still going to work even I'm on the surface below? Someone recently asked me why a negative $\times$ a negative is positive, and why a negative $\times$ a positive is negative, etc.  I went ahead and gave them a proof by contradiction like so:  Assume $(-x) \cdot (-y) = -xy$  Then divide both sides by $(-x)$ and you get $(-y) = y$  Since we have a contradiction, then our first assumption must be incorrect.  I'm guessing I did something wrong here. Since the conclusion of $(-x) \cdot (-y) = (xy)$ is hard to derive from what I wrote.  Is there a better way to explain this?  Is my proof incorrect?  Also, what would be an intuitive way to explain the negation concept, if there is one? We have two PHP5 objects and would like to merge the content of one into the second. There are no notion of subclasses between them so the solutions described in the following topic cannot apply.    //We have this: $objectA-&gt;a; $objectA-&gt;b; $objectB-&gt;c; $objectB-&gt;d;  //We want the easiest way to get: $objectC-&gt;a; $objectC-&gt;b; $objectC-&gt;c; $objectC-&gt;d;   Remarks:   These are objects, not classes. The objects contain quite a lot of fields so a foreach would be quite slow. So far we consider transforming objects A and B into arrays then merging them using array_merge() before re-transforming into an object but we can't say we are proud if this. Encode/Decode URLs in C++ Does anyone know of any good C++ code that does this? My eth0 has gone and I don't have internet and network connection I had internet connection, but when I upgraded my VGA and restarted my PC then everything for eth0 has gone.     When I used ifdown:     ifdown: interface eth0 not configured   Is there something I could do?    EDIT: Content of /etc/network/interfaces    auto lo iface lo inet loopback   When I ifconfig I don't have these lines:    inet addr:192.168.1.5  Bcast:192.168.1.255  Mask:255.255.255.0 inet6 addr: fe80::219:5bff:fe5e:a5e/64 Scope:Link   In the Terminal typed:  sudo gedit /etc/network/interfaces   and then added these lines in the bottom:  auto eth0 iface eth0 inet dhcp   then I typed:    sudo ifdown eth0 sudo ifup eth0   when I send the second command I received the below message:    No DHCPOFFERS received No working leases in persistent database - sleeping   Any help?