I'm trying to read double values from a file into a std::vector. However, I've noticed that the values do not match what is on the file, but has a slight but consistent shift of ~0.000000007. Is this normal? #include &lt;iostream&gt; #include &lt;fstream&gt; #include &lt;iomanip&gt; #include &lt;string&gt; #include &lt;vector&gt;   std::vector&lt; double &gt; readFromFile(const std::string&amp; file_name) {     std::vector&lt; double &gt; values;     std::ifstream file(file_name.data(), std::ios::in);     file.precision(9);   // makes no difference     double value = 0.0;     if (file.is_open()){         while (file &gt;&gt; value) {             values.push_back(value);         }             file.close();     }     return values; }  int main(int argc, char const *argv[]) {      auto vals = readFromFile(&quot;src/samples.txt&quot;);      std::cout.precision(9);     for (auto&amp; val : vals) {         std::cout &lt;&lt;  std::fixed &lt;&lt; val &lt;&lt; std::endl;     }      return 0; }  My samples.txt: 1595519203.966806166 1595519204.000087015 1595519204.033377640 1595519204.066651098  And the code output: 1595519203.966806173 1595519204.000087023  1595519204.033377647 1595519204.066651106  This is something I have never dealt with, and am left wondering if the issue is in how the file is read, or in how I am printing it.
Consider the following code:   0.1 + 0.2 == 0.3  -&gt;  false   0.1 + 0.2         -&gt;  0.30000000000000004   Why do these inaccuracies happen?
How do I search events between two set dates inside WP? Summation of Central Binomial Coefficients divided by even powers of $2$ Whilst working out  the following summation emerged: $$\sum_{m=0}^n\frac 1{2^{2m}}\binom {2m}m$$ The is equivalent to  $$\begin{align} \sum_{m=0}^n \frac {(2m-1)!!}{2m!!}&amp;=\frac 12+\frac {1\cdot3}{2\cdot 4}+\frac{1\cdot 3\cdot 5}{2\cdot 4\cdot 6}+\cdots +\frac{1\cdot 3\cdot 5\cdot \cdots \cdot(2n-1)}{2\cdot 4\cdot 6\cdot \cdots \cdot 2n}\\ &amp;=\frac 12\left(1+\frac 34\left(1+\frac 56\left(1+\cdots \left(1+\frac {2n-1}{2n}\right)\right)\right)\right) \end{align}$$  and terms are the same as coefficients in the expansion of $(1-x)^{-1/2}$.  Once the solution  $$ \frac {n+1}{2^{2n+1}}\binom {2n+2}{n+1}$$ is known, the telescoping sum can be easily derived, i.e.    $$\frac 1{2^{2m}}\binom {2m}m=\frac {m+1}{2^{2(m+1)-1}}\binom {2(m+1)}{m+1}-\frac m{2^{2m-1}}\binom {2m}m$$  However, without knowing this a priori, how would we have approached this problem? Bounds of $I=\int_0^1\frac{\sin x}{\sqrt x}$ and $J=\int_0^1\frac{\cos x}{\sqrt x}$? How to find bounds of $$I=\int_0^1\frac{\sin x}{\sqrt x}$$ and $$J=\int_0^1\frac{\cos x}{\sqrt x}$$     A) $I&gt;2/3$ and $J&gt;2$   B) $I&lt;2/3$ and $J&gt;2$   C) $I&gt;2/3$ and $J&lt;2$   D) $I&lt;2/3$ and $J&lt;2$ I'm not normally a fan of mac software implementations, but recently I saw a copy of Parallels Desktop for mac that I was very much impressed by. I looked into parallel's offerings for Linux (I was initially excited that they developed for *nix) but found that it has essentially the same features as VMware.   Does anyone know if there is a software solution for linux that offers the level of integration that the current Parallels Deesktop for mac has?  I looked into wine for the programs I want to run and was very frustrated. I feel like all the ratings in their application database were fabricated honesty. I've tried wine once every Ubuntu release since 8.10 and have never gotten it to work stably. When I run the command to install the package solr-jetty, I am told   You don't have enough free space in /var/cache/apt/archives/   Here's the result of the df -H command:    I have installed Ubuntu with VirtualBox on my Mac.  How can I fix this problem? Parallel universes: are there an infinite amount of universes? Parallel universe: in every universe, you are presented with a different decision. Does that mean there are an infinite amount of parallel universes? I.e., if in one universe I choose to go left, I am then presented with different choices vs if i choose right, and that creates more universes with more decisions to be made.  Or does it mean that in the end of one's life we end up in the same place, meaning that its just one parallel universe that eventually collides with the other. Where are icons stored? I want to change an icon of a specific theme. Where do themes save their icons? What are the limits on how I can cast, change, and retract votes? What limits are there on how I can vote?  How often can I vote? How do my votes become locked/unlocked? Show reference label when it is undefined What is the "show desktop" keyboard shortcut? I just upgraded to 11.10 from 11.04. Previously the shortcut to show the desktop was Super +D (same as in Windows), But now it is not working. What is the new shortcut? Group of order $8p$ is solvable, for any prime $p$ Consider the following question:     Show that a group $G$ of order $8p$ is solvable, for any prime $p$.   I am kind of stuck, but here are my first attempts:  I chose the series of subroups $G&gt;H_8&gt;H_4&gt;H_2&gt;H_1=\{e\}$ where $H_k$ has order $k$. All of these subgroups exist due to Sylow's Theorems. We have the quotients $H_8/H_4\cong H_4/H_2 \cong H_2/H_1 \cong \mathbb Z/2\mathbb Z$, so $G&gt;H_8\rhd H_4\rhd H_2\rhd H_1=\{e\}$. Only the factor $G/H_8 \cong \mathbb Z/p\mathbb Z$ is causing me a headache, because although its of prime order (and hence abelian) I don't know whether $H_8$ is normal in $G$ (unless $p=2$).  If $p\ne 2$, then the number $k$ of Sylow $2$-subgroups is $1$ mod $2$. Since $k$ divides $|G|$ we might have $k=1$ or $k=p$. If we had $k=1$ then $H_8$ would be the only Sylow $2$-subgroup (and hence normal in $G$). But how could we show this?  Or is there even an easier way to approach this problem?  $\ $  edit: I am going to try a different approach: The case $p=2$ is clear. When $p=3$ or $p=7$ the group has order 24 or 56 and since the smallest simple non-abelian group has order 60, the group must also be solvable in these exceptional cases (as Mariano pointed out).  In any other case we get a Sylow $p$-subgroup $H_p$ of order $p$, which is is normal in $G$. The quotient $G/H_p$ has order $8=2^3$; and prime power order implies solvable. So $G/H_p$ is solvable and $H_p$ is also solvable. And since the composition factors of $G$ are those of $H_p$ together with those of $G/H_p$, we conclude that $G$ is solvable iff $H_p$ and $G/H_p$ are solvable, which is the case. Hence $G$ is solvable if $|G|=8p$. Install Ubuntu on Intel Mac I've recently taken up a position in an all Mac workshop - We have Intel based Apple machines. Can I dual boot Ubuntu on my machine, if so how? I have to compute this integral $$\int_{0}^{\infty} \frac{dt}{1+t^4}$$ to solve a problem in a homework. I have tried in many ways, but I'm stuck. A search in the web reveals me that it can be do it by methods of complex analysis. But I have not taken this course yet. Thanks for any help. Let $x,y,z\ge 0$, show that $$\dfrac{y}{xy+2y+1}+\dfrac{z}{yz+2z+1}+\dfrac{x}{zx+2x+1}\le\dfrac{3}{4}$$  I had solve $$\sum_{cyc}\dfrac{y}{xy+y+1}\le 1$$ becasuse After some simple computations, it is equivalent to  $$(1-xyz)^2\ge 0$$ I have just discovered that my local bank, Nordea, has decided to remove the only good thing about their entire operation: the so-called "simplified login" feature on their website, which allows (soon allowed) the customer to log in to a kind of very limited "read-only" mode which basically just allowed you to see your current balance, the last few transactions (limited descriptions) and see whether or not there are any new "customer support messages", but not read those messages, not make any kind of payments, edit accounts, etc.  Now, they will only allow "full" logins, which 100% prevents any kind of automation and requires you to sit with a hardware device and enter numbers into it and then into the webpage before it allows you to see as much as your account balance. Other than being very obnoxious for every customer, it also blocks me and other "advanced" users out from our custom-programmed bots which have always regularly logged in with that "simplified" login method just to regexp out the current balance/new messages and then notify us via whatever mechanism we use privately.  I have previously asked them if they have any kind of JSON/RSS API of any kind, but no. They don't even have as much as e-mail notifications! Nothing except their spyware "smartphone app" which I would never install, nor would I ever allow such a surveillance device to track me 24/7 in the first place. Only by being a registered corporation with special, way more costly account types do you get any kind of "API" access from them, even to do this most basic imaginable task.  Before you tell me to switch banks, the others are at least just as bad (even worse from what I can tell, and for a longer time), and the act of switching banks is practically impossible for me personally.  What I'm asking is if maybe somebody knows of some sort of "hidden standard" or something which all banks in the world support, but don't have documented, for people like me to automate basic things such as knowing my account balance. Needless to say, I have looked for this countless times on their website, asked them about it, and asked other people about it. Nobody seems to know anything, or, if they do, won't tell me.  I know that there are a bunch of "Nordea-supporting" PHP libraries and whatnot on Github, but they are all ancient and even if they were up to date, they were most likely using the same method as I have been using: automating the login process through their "simplified login" mechanism, which is "soon" to be gone. (Probably at new year; they didn't even mention any dates or time frames.)  And yes, I have a Bitcoin wallet and have that fully automated. The problem is that virtually nobody else in the world cares about my Bitcoin, so "switching to Bitcoin" remains a pipe dream which I would be ready to do, but the world clearly isn't. Poisson Distribution of sum of two random independent variables $X$, $Y$ Find the set of $x>0$ such that the series $\sum\limits_n x^{\ln{n}}$ converges If $x&gt;0$, find the set of all values of $x$ such that series is convergent$$\sum_{n=1}^{\infty} x^{\ln{n}}$$   My attempt:- I used Ratio test for finding the set of all values of $x$ such that series is convergent.   $$\lim_{x\to\infty}\frac{x^{\ln{n+1}}}{x^{\ln{n}}}$$  $$=\lim_{x\to\infty}x^{\ln\frac{n+1}{n}}$$ This quantity must be less than one for getting a convergent series, I am not able to judge. Can you please help me to find the interval of convergence? How to search inside files on Windows 7? In Windows XP we can search for files that contain a defined keyword (inside all files types).  Windows 7 can look inside files for a keyword, but only for text files. (*.doc, *.txt, *.inf, ...), not (*.conf, *.dat, *.*, ...).   don't contain any filter I can use for this.  How is this possible? If $\lambda_{max} = n$, then $n\times n$ positive, reciprocal matrix A is consistent At the end of . the author states that  Suppose we have $n \times n$ matrix $A$ having only positive elements and satisfying the property $a_{ij}=1/a_{ji}$ (a matrix satisfying this property is called a reciprocal matrix).  If its largest eigenvalue $\lambda_{max}$ is equal to $n$, then the matrix $A$ satisfies the property (consistency property) $a_{ij} a_{jk} = a_{ik}$ where $i,j,k=1,2,...,n$.  I'm not convinced this theorem is true. Could anyone help? What is the best way to dump entire objects to a log in C#?