I have below program:  double tax = 180.09; double gTotal = 277.08;  double total = tax + gTotal;  System.out.println(total);   After execution it outputs 457.16999999999996.  After Google search I found that one of the cause for this behavior is that there may be no precise binary representation of the fraction part.  To verify that I tried below:  double dNum = 457.17; System.out.println(dNum);   It gave correct output as 457.17. In this case, why it is not printing 457.16999999999996.
Consider the following code:   0.1 + 0.2 == 0.3  -&gt;  false   0.1 + 0.2         -&gt;  0.30000000000000004   Why do these inaccuracies happen?
Book about classical mechanics I am looking for a book about "advanced" classical mechanics. By advanced I mean a book considering directly Lagrangian and Hamiltonian formulation, and also providing a firm basis in the geometrical consideration related to these to formalism (like tangent bundle, cotangent bundle, 1-form, 2-form, etc.).  I have , but I would like to go into more details about the [symplectic] geometrical and mathematical foundations of classical mechanics.  Additional note: A chapter about relativistic Hamiltonian dynamics would be a good thing. Is there a difference between "Alpha Helix" and "Alpha subunit"? How can I reduce the ever-increasing time to push a subtree? How can I expand a partition into non adjacent free space using GParted? My dual-boot machine has partitions as follows:   sda1 50 GB NTFS sda2 15 GB unallocated sda3 20 GB ext3 sda4 20 GB ext4   I would like to allocate the unused space on sda2 to my Ubuntu partition on sda4, hopefully leaving the other two partitions untouched, leaving this configuration:    sda1 50 GB NTFS sda3 20 GB ext3 sda4 35 GB ext4   Is this possible? If so, how can it be done, preferably using GParted? Countable axiom of choice: why you can't prove it from just ZF This is a follow-up question to the discussion about the finite axiom of choice .  Suppose we have a countable collection of non-empty sets $\{A_1, A_2, A_3,\cdots\}$ Reasoning as indicated in that discussion, we can prove the existence of a choice function $c_n$ such that $c_n(i)$ belongs to $A_i$ for $i = 1,\cdots,n$  Again reasoning as suggested and using induction, we can prove the existence of a function $C$ defined over $\{1, 2, \cdots\}$ such that $C(n)$ is a choice function defined for $i=1,\cdots,n$ with $C(n)(i)$ an element of A_i. We can require in addition that $C(n)(i)$ and $C(n-1)(i)$ are equal for $i=1,\cdots,n-1$.  Now it would it seem that we can prove the countable axiom of choice by taking the union of $C(1)$, $C(2)$, $\cdots$  The question is as follows: why is that proof wrong? I suspect the answer may have something to do with the axiom of union. Why is my find not recursive? I am running the following command, but it is not performed recursively:  find . -name *.java   I know there are java files further down in the current directory but it is performing the find on the current directory only. I am using OS X, 10.9. Is there a way to bypass resistance/immunity to fire damage? I want to use fire-based spells for thematic reasons and a lot of things have immunity to it.   Is there a feat or class feature I could use to bypass/reduce those? For example, is there something that ignores fire resistance and reduces fire immunity to just resistance?   I know the easy way around it is just to pick another damage type spell but I really want to roleplay a pyromancer/firebender-type character. Unable to forward search Bash history similarly as with CTRL-r ON creating BITMAP INDEX on a table in mysql throws error I have database named "demo_dev" and added a table named "countries".  I wanted to create a bitmap index on a column, say, region as it has fewer unique values, using following query.   CREATE BITMAP INDEX ON countries (region);   It threw an error as shown below:     You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near 'BITMAP INDEX ON countries (region)'   What shoud be done for it to run successfully?  I just refered the following link :   mysql version : 5.5 I am trying to get an Epson WF-2760 scanner that is network-connected working. I'm using Ubuntu 16.04.2 64-bit and the printer works a treat. I have installed the Epson drivers from their site, including the plugins. I have edited /etc/sane.d/dll.conf to enable epson, epson2, and epsonds. I have edited each of the respective .conf files to include the network address of the device (IPV4: 192.168.128.11).   The scanner is not detected in any software that I have tried (including Image Scan and Simple Scan).  Any help is appreciated! What do bookcases do for enchanting? Customise date-time format in Windows Is it possible to customize data (or date-time) format in Windows (I am using Windows&nbsp;XP)?  The current format which is followed by the OS [to show date-modified, etc.] is MM/DD/YYYY or M/D/YYYY, whereas I have been comfortable with DD/MM/YYYY or D/M/YYYY format. I am finding it hard to refer Date-modified [which I use often] of files and folders. What level is a spell if you cast it without expending a spell slot? There are ways to cast spells without expending a spell slot such as:  Master Transmuter (PHB 119):     Restore Life. You cast the raise dead spell on a creature you touch   with the transmuter’s stone, without expending a spell slot or needing   to have the spell in your spellbook.   Armor of Shadows (PHB 110):     You can cast mage armor on yourself at will, without expending a spell slot or material components.   Whispers of the Grave (PHB 111):     You can cast speak with dead at will, without expending a spell   slot.   See also: Channel Divinity: Read Thoughts (PHB 59-60), Mystic Arcanum (PHB 108), Beast Speech (PHB 110), Chains of Carceri (PHB 110), Eldritch Sight (PHB 110), Fiendish Vigor (PHB 111), Mask of Many Faces (PHB 111), Master of Myriad Forms (PHB 111), Misty Visions (PHB 111), Otherwordly Leap (PHB 111), Signature Spells (PHB 115), Spell Mastery (PHB 115), Shapechanger (PHB 119), Boon of Spell Mastery (DMG 232) and Boon of Spell Recall (DMG 232).  What level are these spells if you cast them without expending a spell slot? population and subsamples : mean equality? I want to perform a two sample test, to see whether theirs means are equals. One of the sample is rather big (#60000 values) and represents the scores of a whole population. This population is partitioned in small classes of less that 1000 people. The other sample of the test is a subsamble of the former. It corresponds to people of the same class. So, each time, there is less than 1000 values in it. I have no idea about the variances, so I'd think of using Welch's t-test.  But I'm concerned regarding the independence hypothesis: can it be valid, considering that the second sample is negligible when compared to the overall population? Show inbox updates in the page title Background  Recently  was implemented. With this feature the amount of questions with new activity is shown in parenthesis at the beginning of the page title, e.g.     (2) Meta Stack Overflow   means that MSO has two questions with new activity since the user last viewed it.   this feature is unrelated to inbox updates. Here is an example to illustrate this:    Even though there are two inbox messages in this screenshot this is not reflected by the page title. The page title is currently only sensitive to questions with new activity.  Suggestion  I suggest that the page title also reflects inbox updates. For the screenshot above this would mean that the page title shows that there are two inbox updates and two questions with new activity.  I am not sure what format is best for showing this. For chat * in the page title is used to show that there are messages directed at you which is similar in meaning to inbox updates. However, * if is placed after the number in parenthesis to denote inbox updates there might be confusion as there is no connection between the number in parenthesis and * like in chat. Thus, one might prefer another format such as one of the following (all are meant to reflect the status of the screenshot above):      * (2) Meta Stack Overflow     2* (2) Meta Stack Overflow     [2] (2) Meta Stack Overflow     2i 2q  Meta Stack Overflow     (2/2)  Meta Stack Overflow     (2|2)  Meta Stack Overflow    For the alternatives without an explicit hint of which number refers to what it might be best to place the number for questions with new activity first as it will in most cases be greater. This will to a greater degree avoid combinations such as "(0/2)" which may be confused zero of two.  An advantage of the suggested feature is that if the user has a browser tab with a Stack Exchange site then they will be instantly notified of inbox updates. They do not need to focus a tab with a Stack Exchange site to know if there are inbox updates, they merely have to check the relevant page titles among their tabs.  A disadvantage of the suggested feature is that it might be experienced as verbose. I suggest that it is implemented such that it is as unobtrusive as possible while still being informative. Think of a situation where a user has   one Meta Stack Overflow tab with two inbox updates relating to Meta Stack Overflow and two questions with new activity, and one Super User tab with one inbox updates relating to Super User and three questions with new activity.   Then the sum of the inbox notification in the page titles should be local to sites and not global. The page titles for the tabs above should be something like the following pair:      2i 2q  Meta Stack Overflow     1i 3q  Super User When adding image from Wikimedia Commons, automatically add author/license/link Many Stack Exchange questions and answers embed images from Wikimedia Commons. It is probably the most used image source here. Good news Thanks to their license, all images from Wikimedia Commons can be legally used inside Stack Exchange. Bad news The only requirement is to cite the author/license (), an easy task, but we are totally failing at it, only maybe 1% of Commons images used here are properly cited. That makes our use of these images illegal, and could expose Stack Exchange to various legal threats. Not my problem, you could say, but this is also important because , bringing Stack Exchange closer to closed-data sites like Yahoo! Answers or Experts-Exchange. Proposed solution When using the image addition widget, the widget should detect whether the image's URL has a *.wikimedia.org domain, and if yes:  (optional) Transfer the image to imgur, for perennity reasons. Retrieve the author name and license name from Commons (there is a very reliable API that gives that). Concatenate into a proper citation, maybe something like &quot;*Credit: [&quot; + author + &quot;](&quot; + commonsPageURL + &quot;) , [&quot; + license + &quot;](&quot; + licenseURL + &quot;)*&quot; Insert the citation at the same time as the image's MarkDown.  Benefits:  Remove a large part of Stack Exchange's copyright violations. Makes us a good citizen in the open data world. Remember what happens to sites who disregard ethics (Experts Exchange). Consistent citations. Zero added burden for the users. The black book knowledge How do I split a string, breaking at a particular character? Why do clocks measure arc-length? Apologies in advance for the long question.  My understanding is that in GR, massive observers move along timelike curves $x^\mu(\lambda)$, and if an observer moves from point $x^\mu(\lambda_a)$ to $x^\mu(\lambda_b)$, then his clock will measure that an amount of time $t_{ba}$ given by the curve's arc length; $$   t_{ba} = \int_{\lambda_a}^{\lambda_b}d\lambda \sqrt{-g_{\mu\nu}(x(\lambda))\dot x^\mu(\lambda)\dot x^\nu(\lambda)} $$ will have elapsed where $g_{\mu\nu}$ is a metric on spacetime with signature $(-,+,+,+)$.    Why is this so?     Here is how I would attempt to justify this fact in special relativity with $g_{\mu\nu} = \eta_{\mu\nu}$.  Consider an inertial observer $O$ in $\mathbb R^{3,1}$, and suppose that this observer sees a clock, which I'll call observer $O'$ moving around on a curve $x^\mu(\lambda)$.  If $O'$ were also an inertial observer, then given any event with coordinates $x^\mu$ as measured by $O$, observer $O'$ would measure the coordinates of the event to be $x'^\mu = \Lambda^\mu_{\phantom\mu\nu} x^\nu + x_0^\mu$ for some Lorentz transformation $\Lambda$.  If $O'$ is not inertial, then this is no longer true, and there is some more complicated family of transformations, say $T_\lambda$ between events as seen by both observers.  I would argue, however, that if we were to partition the interval $[\lambda_a, \lambda_b]$ into a large number $N$ of intervals $I_1=[\lambda_a, \lambda_i], \dots, I_N=[\lambda_{N-1}, \lambda_b]$ with $\lambda_n = \lambda_a+n\epsilon_N$ and $\epsilon_N=(\lambda_b-\lambda_a)/N$, then on each interval $I_n$, $O'$ is approximately an inertial observer in the sense that $$   T_{\lambda_n} = P_n + \mathcal O(\epsilon_N), \qquad (\star) $$ for some Poincare transformation $P_n$.  Then we would note that since $O'$ is stationary in his own reference frame, he measures his worldline to have the property $\dot x'^\mu(\lambda) = (\dot t(\lambda), \mathbf 0)$ so that $$   I_{ba}=\int_{\lambda_a}^{\lambda_b}d\lambda \,\sqrt{-\eta_{\mu\nu}\dot x'^\mu\dot x'^\mu} = \int_{\lambda_a}^{\lambda_b} d\lambda \, \sqrt{\dot t^2} = t(\lambda_b) - t(\lambda_a) = t_{ba} $$ On the other hand the integral on the left can be written as a Riemann sum using the partition above, and we can invoke ($\star$) above to get \begin{align}   I_{ba}  &amp;= \lim_{N\to\infty}\left[\sum_{n=1}^N \epsilon_N\sqrt{-\eta_{\mu\nu}\dot x'^\mu(\lambda_n)\dot x'^\nu(\lambda_n)}\right] \notag\\ &amp;= \lim_{N\to\infty}\left[\sum_{n=1}^N \epsilon_N\sqrt{-\eta_{\mu\nu}\dot x^\mu(\lambda_n)\dot x^\nu(\lambda_n)} + \mathcal{O}(\epsilon_N^2)\right] \notag\\ &amp;= \int_{\lambda_a}^{\lambda_b}d\lambda \,\sqrt{-\eta_{\mu\nu}\dot x^\mu\dot x^\mu} \end{align} Combining these two computations gives the desired result.  How do others feel about this argument?  I'm not completely comfortable with it because of the assumption $(\star)$ I made on $T_\lambda$.  I imagine that in GR a similar argument could be made by invoking local flatness of the metric. Allowing all/different file type uploads