I am reading text file contains values like below     125602365  119653955   126374444   124463807   127312438   128395899   and the below code to read it.  if(!(pvtcheck(0)))   {      fscanf(fp,"%f",&amp;deltime);      printf("\ndeltime0=%f\n",deltime);    ///Actual value is 125602365, but i am getting 125602368.   }    if(!(pvtcheck(1)))   {       fscanf(fp,"\t%f",&amp;deltime);        printf("\ndeltime1=%f\n",deltime);///Actual value is 119653955, but i am getting 119653952.   }   /// same for pvtcheck(2),pvtcheck(3),pvtcheck(4)   if(!(pvtcheck(5)))   {       fscanf(fp,"\t%f",&amp;deltime);        printf("\ndeltime5=%f\n",deltime); ///Actual value is 128395899, but i am getting 128395896.   }   In the Comment i have written output , any solution to not change the values
Consider the following code:   0.1 + 0.2 == 0.3  -&gt;  false   0.1 + 0.2         -&gt;  0.30000000000000004   Why do these inaccuracies happen?
Use mathematical induction to prove $ (2n)!\geq 2^n(n!)^2$ for $n \in \mathbb{N}$ Please don't throw this one out as a duplicate of  I'm not asking about the plurality of the noun immediately following those two words - I'm interested in exactly why the example below is problematic (context: I have several children, one named John)...     1: One of my children's name is John.   I can't see any obvious reason why singular name there is completely unacceptable, but it certainly doesn't sit well with me. It seems to turn on whether one of my children can be treated collectively as the "subject" of the Saxon genitive 's, but I don't see a problem with...     2: It's actually one of my children's, but you can sleep in this bed.   I realise that in practice we'd normally pluralise names in the first example. But of course, this implies that one of attaches to my children's names, which isn't really the same construction.  So - is there some kind of "rule, principle" debarring #1 above? Or is it just "one of those things"?    (Apologies if my later switch from brothers to children invalidates any comments or answers.) Geometric proof that a Pythagorean triple has a number divisible by $3$? Can I infer from “If $a,b \in \mathbb{N}$ such that $(a,3)=(b,3)=1$ then $a^2+b^2\neq c^2$ for any $c\in\mathbb{N}$” that any pythagorean triple has a number which is divisible by $3$? If so, how can this relationship be proved geometrically? Is it correct to say "I kindly request you to..."? Isn't kindness already implied when you say "I request you to..."?  When I say "I humbly request you to...", the word humbly helps me to label the state of my behavior during the request.  On the other hand, what value does the word kindly add to the request? Derivation of survival copula $$ \begin{align}F(x,y) &amp;= P(X\leq x, Y\leq y) \\  &amp;= C(F(x), F(y)) \end{align}$$ The copula of a bivariate distribution is equal to its CDF, $C(u,v) = F(x,y)$. The density of the data's CDF therefore can be expressed as $$f(x,y) = c(u,v) \times f_X(x) f_Y(y)$$ where $c(u,v)$ is the copula density and $f_X(x)$ is a marginal. If $\hat{C}(u,v)$ is the survival copula for determining $$ \begin{align}\bar{F}(x,y) &amp;= P(X&gt; x, Y &gt; y) \\  &amp;= \hat{C}(1-F(x), 1-F(y)) \end{align}$$ how is the first equation of the ordinary copula, $C(u,v)$, linked to the survival copula as $$\hat{C}(u,v) = u + v - 1 + C(1-u,1-v)$$ are $u$ and $v$ merely vectors containing the (ranked) observations of the uniform marginals? A derivation in integrals and probabilities (rather than $F$s) would be good. Evaluate the following limit of finite sum I have a Python regular expression that contains a group which can occur zero or many times - but when I retrieve the list of groups afterwards, only the last one is present. Example:  re.search("(\w)*", "abcdefg").groups()  this returns the list ('g',)  I need it to return ('a','b','c','d','e','f','g',)  Is that possible? How can I do it? Physics history book with some math I am looking for a book explaining physics from, say, Galileo and Newton till now; the book should be written using some math, similarly to my physics books when I was at the university (Halliday Resnik). I am searching a book that take care of explaining the true "evolution" of reasoning, discoveries, experiment to prove or disprove something.  I do not like a book that gives definitions without explaining what had happened. I also like to find, on that book, explanations on how actual measurements are taken (how can we measure the speed of light, the mass of celestial bodies, the attributes of electron, and how were the measurements taken in the past - how was possible to measure the speed of light in 1700-1800?).  I am not very interested in recent theories like strings, branes.... so it is OK if these are not discussed.  I like to find a lot of discussions on concept that are related, like for instance the implications on space dimensionalities, ether non-existence, strange facts, missing explanations. White lines between objects in render I am kind of new to the whole animation aspect and in fact still in high school.  I am trying to make a Minecraft character rig and I want to make some 3D hair. I did not know how to quite make it so I kind of when just did something pretty simple. It isn't the greatest in any means, but any how the point is every time I render it white lines show up between objects or joined objects. I don't know how to fix this and would like help (a picture is posted below of the problem). Is it legal/well-defined C++ to call a non-static method that doesn't access members through a null pointer? Unable to open any graphical app with "sudo" Tried to find some answer here: , but it didn't solve my problem.  $ sudo gedit Failed to connect to Mir: Failed to connect to server socket: No such file or directory. Unable to init server: Could not connect: Connection refused.  (gedit:4574): Gtk-WARNING **: cannot open display:   only gedit in terminal works fine. This is my local computer, not a remote system. I can show that the following limit exists but I am having difficulties to find it. It is $$\lim_{n\to \infty} \sum_{k=1}^n \frac{k^n}{n^n}$$ Can someone please help me? Limit $\frac{x^2y}{x^4+y^2}$ is found using polar coordinates but it is not supposed to exist. Consider the following 2-variable function:     $$f(x,y) = \frac{x^2y}{x^4+y^2}$$   I would like to find the limit of this function as $(x,y) \rightarrow (0,0)$.   I used polar coordinates instead of solving explicitly in $\mathbb R^2 $, and it went as the following:  $$ x = r \cos \theta, \qquad y = r\sin\theta $$   Hence,  $$\lim_{(x,y) \to (0,0)} \frac{x^2y}{x^4 + y^2} = \lim_{r \to 0}\frac{r^2\cos^2\theta(r\sin\theta)}{r^4\cos^4\theta + r^2\sin^2\theta}$$  This simplifies to,  $$ \lim_{r \to 0} \frac{r^3 \cos^2\theta\sin\theta}{r^2(r^2\cos^4\theta + \sin^2\theta)}$$  Simplifying $r^3/r^2$, we finally get;  $$\lim_{r \to 0} \frac{r (\cos^2\theta\sin\theta)}{r^2\cos^4\theta + \sin^2\theta}$$  Now from the above, we find that as $r \to 0$ the limit is $0$.   I wanted to verify this answer so I checked on Wolfram Alpha. Explicitly without changing to polar coordinates, it said that the limit does not exist at $(0,0)$ and rightly so. Then how is it that with polar coordinates, the limit exists and is $0$? Am I doing something wrong in this method?  Also, what should I do in this situation, and when should I NOT use polar coordinates to find limits of multi-variable functions? Why is inductance (L) proportional with turns-square (N²)? We start from the   $$ \mathbf{\nabla} \times \mathbf{B} = \mu \mathbf{J} + \overbrace{\mu \epsilon \dfrac{\partial \mathbf{E}}{\partial t}}^0. $$  We take surface integration of both sides, for the surface (\$s\$) inside the mean path (\$c\$) of the core.  $$ \int_s \left( \mathbf{\nabla} \times \mathbf{B} \right) \cdot d\mathbf{s} = \mu \int_s \mathbf{J} \cdot d\mathbf{s} $$  We use the  to rewrite the left hand side; where \$c\$ is in the same direction with the magnetic flux \$\Phi\$.  $$ \oint_c \mathbf{B} \cdot d \mathbf{\ell} = \mu N I $$  (The integral on the left hand side results \$NI\$, because there are \$N\$ different wires on the winding.)  The magnetic field density inside these kind of cores are considered to be uniform. So, we can write  $$ B \ell_c \overset\sim= \mu NI \implies B = \dfrac{\mu NI}{\ell_c}; $$  where \$\ell_c\$ is the mean path lenght of the core.  We can find magnetic flux from the magnetic flux density we have found by using the cross sectional area of the core \$A_c\$.  $$ \Phi = BA_c = \dfrac{\mu NIA_c}{\ell_c} $$  By definition, inductance is the amount of magnetic flux generated per applied current, that is  $$ L \overset\triangle= \dfrac{\Phi}{I}. $$  So, we find inductance of the system as  $$ \boxed{ L = \dfrac{\Phi}{I} = \dfrac{\dfrac{\mu NIA_c}{\ell_c}}{I} = \dfrac{\mu NA_c}{\ell_c} }. $$  But, all other sources () give inductance of an inductor like this as  $$ L = \dfrac{\mu N^2A_c}{\ell_c}. $$  What is the mistake I did in my derivation? Please explain in detail. Calling Overridden Constructor and Base Constructor in C# I have two classes, Foo and Bar, that have constructors like this:  class Foo {     Foo()     {       // do some stuff     }      Foo(int arg)     {       // do some other stuff     } }  class Bar : Foo {     Bar() : base()     {       // some third thing     } }   Now I want to introduce a constructor for Bar that takes an int, but I want the stuff that happens in Bar() to run as well as the stuff from Foo(int).  Something like this:  Bar(int arg) : Bar(), base(arg) {   // some fourth thing }   Is there any way to do this in C#?  The best I have so far is putting the work done by Bar() into a function, that also gets called by Bar(int), but this is pretty inelegant. Let $\left| {{a_{ii}}} \right| > \sum\limits_{i \ne j} {\left| {{a_{ij}}} \right|} $.Why does $A$ is nonsingular? . Date comparison : which date format? Are there any organised resources available from where I can begin my quantum computing studies? I am a computer science student and am currently searching for resources from where I can learn about quantum computers, quantum computing models, their working principles, their gates and some simple quantum algorithms. I'm currently in the process of making a custom map and I want to add blocks that can only be placed on a certain colour clay.  This is the command I tried using.  /give @p cobblestone 1 0 {CanPlaceOn:["hardened_stained_clay"],Damage:3}   However, even with this command the cobblestone can be placed on any colour of stained clay. What command can I use for placing only on a certain block? What is the difference between if(CONST==variable) or if(variable==CONST)?