I wrote this code that simply sums a list of n numbers, to practice with floating point arithmetic, and I don't understand this:  I am working with float, this means I have 7 digits of precision, therefore, if I do the operation 10002*10002=100040004, the result in data type float will be 100040000.000000, since I lost any digit beyond the 7th (the program still knows the exponent, as seen ).  If the input in this program is   3 10000 10001 10002   You will see that, however, when this program computes 30003*30003=900180009 we have 30003*30003=900180032.000000  I understand this 32 appears becasue I am working with float, and my goal is not to make the program more precise but understand why this is happening. Why is it 900180032.000000 and not 900180000.000000? Why does this decimal noise (32) appear in 30003*30003 and not in 10002*10002 even when the magnitude of the numbers are the same? Thank you for your time.  #include &lt;stdio.h&gt; #include &lt;math.h&gt; #define MAX_SIZE 200   int main()  { int numbers[MAX_SIZE];  int i, N; float sum=0; float sumb=0; float sumc=0;  printf("introduce n" ); scanf("%d", &amp;N);  printf("write %d numbers:\n", N); for(i=0; i&lt;N; i++) {     scanf("%d", &amp;numbers[i]); }  int r=0;  while (r&lt;N){     sum=sum+numbers[r];     sumb=sumb+(numbers[r]*numbers[r]);      printf("sum is %f\n",sum);     printf("sumb is %f\n",sumb);     r++; } sumc=(sum*sum); printf("sumc is %f\n",sumc); }
Consider the following code:   0.1 + 0.2 == 0.3  -&gt;  false   0.1 + 0.2         -&gt;  0.30000000000000004   Why do these inaccuracies happen?
No, this is not a , nor is it a solicitation on  to backup or  and only a little bit about Where to backup and When to do it.  This is basically a strategy question: what, where and when all together. "How" is not really relevant: there are tons of back-up programs out there and they all do the same basic thing: make copies of data.  But the real question is: are these back-up programs making copies of the data important to you?  How should you install&amp;run Ubuntu while safeguarding your data?  There is no "one size fits all" when it comes to computers, Ubuntu versions or a backup strategy, therefore I've split this up into 5 basic user types with each their own answer:       (or you're running in UEFI mode!)   And as the above does not fit everyone, one for the impatient:   !    So click one of the above links and go to your user type!  P.S. If you're running a server farm and you've read this question so far, I'm sorry: this is about a single PC, not a network, nor a server farm. Evaluating $\lim\limits_{n\to\infty}(a_1^n+\dots+a_k^n)^{1\over n}$ where $a_1 \ge \cdots\ge a_k \ge 0$ Need to find $\lim\limits_{n\to\infty}(a_1^n+\dots+a_k^n)^{1\over n}$ Where $a_1\ge\dots\ge a_k\ge 0$  I thought about Cauchy Theorem on limit $\lim\limits_{n\to\infty}\dfrac{a_1+\dots+a_n}{n}=\lim a_n$ and something like what happen if all $a_i=0$ or $a_1=\dots=a_k$, but may be something I am thinking wrong?  Maybe it is too simple but I am not getting it; please help. MSBuild exec task with for I am trying to run the following commands as part of an MSBuild script:  for /R . %f in (*.targets) do copy /Y "%f" "C:\Program Files (x86)\MSBuild\Microso ft\VisualStudio\TeamBuild"   The commands is implemented in an exec the following way:  &lt;Exec WorkingDirectory="$(SolutionRoot)" Command="for /R . %f in (*.targets) do copy /Y &amp;quot;%f&amp;quot; &amp;quot;$(MSBuildExtensionsPath)\Microsoft\VisualStudio\TeamBuild&amp;quot;" /&gt;   The command works fine from console, but when trying to run it from MSBuild I get the error:   Task "Exec"   Command:   for /R . %f in (*.targets) do copy /Y "%f" "C:\Program Files (x86)\MSBuild\Microsoft\VisualStudio\TeamBuild"   f" "C:\Program was unexpected at this time. C:\Users\rd-build\AppData\Local\Temp\OH Test2\Continuous.BuildTargets\BuildType\TFSBuild.proj(98,5): error MSB3073: The command "for /R . %f in (*.targets) do copy /Y "%f" "C:\Program Files (x86)\MSBuild\Microsoft\VisualStudio\TeamBuild"" exited with code 255. Done executing task "Exec" -- FAILED.   Any suggestions? Why is it that they decided to make String immutable in Java and .NET (and some other languages)? Why didn't they make it mutable? C# Change A Button's Background Color passthrough graphics card to virtualbox So I'm trying to get my laptops NVIDIA fx 880m to pass to a virtual box running window seven on a linux mint 17 install.  So far everything seems to be (maybe) heading in the right direction:  the device passed through happily, when I booted the virtual box it installed a bunch of new drivers, but when I try to install the NVIDIA driver on the guest it can't find the card. I looked under the device manager and there's no listing for the nvidia card under the pci bus, my guess would be that I need to disable it in the host so that it can be passed through to the guest (the virtual box manual said they can't be shared) but I'm not sure how to do so. Can anybody help with this? This question does not seem to me to be a duplicate of , because here the given solution was that it was not possible with a windows host, however in this case the host is linux wordcount with xesearch errors How to create functions of arbitrary number of variables? How could a statement be true without proof? My passport is expiring; can I still travel? Prove that $\langle a^n \rangle \bigcap \langle a^k \rangle = \langle a^{lcm (n,k)} \rangle$ I've taken multivariate calculus and am wondering if I can see a specific function where the order of taking the partial derivative matters. I've been told that there are some exceptions where $ \dfrac{\partial ^2 f}{\partial x \partial y} \ne \dfrac{\partial ^2 f}{\partial y \partial x} $, so I'm curious to see what this looks like.  EDIT: And why would this true? For what longest possible time it was possible to hold light in a closed volume with mirrored walls?   I would be most interested for results with empty volume but results with solid-state volume may be also interesting. Calendar link to different page views Whoever or whomever: 'happy for ___ has the pleasure of working with you next.' So sad to lose you, yet happy for whomever has the pleasure of working with you next. How do volume control headphones work? A recent question over on  got me to wondering how volume control headphones work.  I don't mean volume control which works by , but the kind of volume control that signals to the device to increase or decrease the signal output.  For instance, according to the , the volume controls are only for apple devices:     Universal Compatibility and Microphone Communication   LP comes with 2 cables for universal compatibility with all modern mobile and audio devices. The 3-Button remote microphone cable is designed for the latest Apple devices, including iPhone®,iPad®, iPod®, and Macbook series. The long audio-only cable and 1/4" adapter is universally compatible with all audio devices and professional equipment.   However this sort of device apparently works with some android phones and the question implies that it works with some computer sound cards on Windows machines too, but not being an Apple buyer (and only recently getting my first smartphone) I haven't seen this sort of thing before. I've done a quick google search, but can't find anything on standards for this technology.   How does this work?   Is it something as simple as shorting left/right/mic channels? If so, could using headphones of this type with equipment that doesn't support this technology, damage that equipment? Is it a serial signal, for instance sent over the mic channel? Does it just require a headphone  connector or a headphone  +microphone TRRS connector?   Does this technique have a name?  Incidentally, is someone could answer this, I can probably look up the rest of the information myself. *8') Is it as standard as it appears, or is everyone just following Apple? Is this something that is patented?   If so, who holds the patent and do they charge a license fee for people to use this technology? If not, is there an open standard for it?    There is some excellent information in  to the question  but it doesn't answer the specifics of how this type of volume (etc.) control works, since it now seems to be rather more common and standard. How to add percent sign to NSString Quantum entanglement for faster-than-light (FTL) network communication? Quantum entanglement is 2 atoms that are paired together and when you stop one from spinning the other also stops with the same spin. Can you use these pairs to have faster-than-light (FTL) communication between 2 computers? Let ${\rm f}:\left[a, b\right]\to\mathbb{R}$ be twice differentiable, and suppose   $$\lim_{x\to a^{+}} \frac{{\rm f}\left(x\right) - {\rm f}\left(a\right)}{x - a} = \lim_{x\to b^{-}}\frac{{\rm f}\left(x\right) - {\rm f}\left(b\right)}{x - b} =0 $$  Show that there exists $\xi \in \left(a, b\right)$ such that $\displaystyle{% \left\vert\vphantom{\Large A}\,{\rm f}''\left(\xi\right)\right\vert \geq \frac{4\left\vert\vphantom{\Large A}% \,{\rm f}\left(a\right) - {\rm f}\left(b\right)\right\vert} {\left(b - a\right)^{2}}}$.  I don't know how to start. Any hints ?. If matrix $A$ is unitary and $B^2=A$, is $B$ necessarily unitary?