What's the math behind this? Please explain. Thank you.
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 to add desktop shortcut for URL, ignoring web app manifest? Goal:  Have a desktop shortcut that opens  , ignoring the contained web app manifest that otherwise "overrides" the saved shortcut to  and with "display": "standalone".  I had this working previously on an older Android phone before a replacement / upgrade.  Prior to the upgrade, I was able to long-press and open individual articles in new tabs - as well as copy link shortcuts to specific articles, as well as all of the other features and functionality that Chrome has to offer.  Here is just a partial selection of references of other users complaining about the same:       Using  provides a temporary successful work-around.  However, I can't find a successful way to add a link for this to my home screen.  The "Add to Home screen" option within Chrome instead saves a link to  - and in such a way that it opens as a web application instead of a web page within Chrome:       On a desktop operating system, this would be a non-issue.  (Create shortcut, enter desired URL, done.)  Attempt 1: Provide my own Manifest  So I created my own manifest - editing  to change the start_url attribute to https://news.google.com/news/i#0, and the display attribute from standalone to browser.  I then created my own HTML page that simply contained the below - then self-hosted both on a local web server:  &lt;html&gt;         &lt;head&gt;                 &lt;Title&gt;Google News&lt;/Title&gt;                 &lt;link rel="manifest" href="/news/manifest.json"/&gt;         &lt;/head&gt;         &lt;body&gt;                 Test         &lt;/body&gt; &lt;/html&gt;   However, this doesn't work:  Despite the shortcut being saved with the desired name and icon, it links back to my self-hosted HTML page, and not the indicated start_url.  Unfortunately, it appears that cross-domain URLs are not allowed per the manifest intent - as per  and  .  Attempt 1b: MITM website  Within the confines of my own local network, I figured I could try to  (MITM) the website to temporarily provide a desired manfiest to use for addition to the home screen.  Unfortunately, the website uses  here, which appropriately blocks the attempt.  Regardless - this is way too much work for what should be a simple effort.  Attempt 2: Widget Bookmark  Unfortunately, it looks like the 1x1 bookmark widget was removed in Chrome 48, as per  .  The suggested work-around is to use the "Add to Home screen" feature within Chrome.  Goto 10 / see beginning.  Attempt 3: Use the default-provided "Internet" browser  Unfortunately, using "Add shortcut on Home screen" in the default-provided "Internet" browser produces the same result as Chrome.  Consideration 4: Use a custom app / widget  Could probably write and install a custom application or widget that could be added to the home screen to meet the goal.  Or don't re-invent the wheel, and use an existing one.  Some possibilities:   "More Shortcuts":  "Shortcut Customizer":    Conclusion  How can someone create a desktop shortcut to an arbitrary URL, ignoring a provided web app manifest? Is God either immoral or not omnipotent? The usual (Christian) justification for suffering/evil in the world created by a benevolent God is freedom of the will. However, the more interesting question is not about the source of evil (which the free will may very well be) but why God chose to create the world such as it is. Why not create a world with freedom of the will, but without suffering? Even assuming that God is bound by logic such combination doesn't seem to be logically impossible: creatures certainly can do good of their own free will. There are two alternatives.  1) God is powerful enough for all practical intents and purposes, enough to be called God, but not omnipotent. He created only the best of all possible worlds (Leibniz). This position is perhaps the most defensible philosophically, it also avoids logical problems with , etc., but it does diminish deity's status and invites unpleasant questions like what limits God (logic only, inert matter, outer chaos, other beings), is there someone/thing more powerful, etc.    Interestingly enough, the original Christian theodicy wasn't free will. St.Augustine says poetically "the canvas of creation requires both the black and the white paint". "Requires" here can be interpreted differently,  is to explain the black by the "just punishment" for the original sin, which brings us to Adam and Eve, and back to the free will. But if God is still omnipotent and hence omniscient creating creatures he knew would sin, and then punishing them for it is hardly an improvement.   2) However, Augustine can be read more straightforwardly. Evil is "required" for the perfection of the world just like black paint is required for the perfection of a painting (evil can be interpreted as lack of good rather than something onto itself but that is beside the point). God is immoral, and he is beyond our conception of morality, his notion of perfection is his own. This is much bolder, and similar to Plotinus's position on the existence of the One, the One can not exist because it is "prior to all existence". But it does evoke the unpleasant taste of "ends justify the means". It is one thing to use "God is beyond our logic and comprehension" to get rid of unliftable stones, it is quite another to convince people to worship an immoral perfectionist.  Formally, there is another logical possibility of asserting both morality and omnipotence, but defending the morality of creating a world full of suffering, for a higher purpose perhaps. For example, the suffering only appears bad to us, not to an absolute being in its wisdom. But this simply redefines morality and is only different in phraseology from the Augustine's position. The question is asked in human terms and has to be answered in kind. One is free to argue that God is beyond human logic and/or morality, but it still leaves him immoral as commonly understood.   There does not appear to be a way to square this circle, one has to accept Leibniz's or Augustine's alternative (or both) and deal with the downsides. Option 2) looks more consistent, but it is rarely embraced, at least not openly. Perhaps, for "public relations" reasons it is more attractive to dismiss the question with something like "this is beyond us" or change the subject to the free will.      What are the modern theological positions on the morality/omnipotence in catholisism, protestantism, etc.? Is the question relevant to other religions?   EDIT: I am not sure that it came through but by immoral I did not mean morally deficient or evil. Rather at the God's plane of being morality becomes meaningless, like tastes or smells are meaningless when applied to elementary particles. How does printf with multiple arguments separated by space work I have the following printf function:  $ printf '%s %s %s\t%s\n' 100644 blob 8e1e f1.txt 100644 blob 9de7 f2.txt | git mktree   Can anyone please explain what it produces and why? I expected to have equal number of formatting options %s for each argument string but I have a lot more arguments strings here. I have an old Facebook account that I created, uploaded a couple of photos and simply ignored (i.e. no friends added). Now, I can't remember the email address associated with the account and I don't remember the password either. How can I find out which email address I had associated with that account?  P.S. I have created a new Facebook account and my picture can be used to identify me (if I can get someone at Facebook to take a look). Other than that, I'm willing to have that old account deleted altogether if recovery isn't possible.  Is there a way to resolve this issue? We've just been learning about complex numbers in class, and I don't really see why they're called numbers.  Originally, a number used to be a means of counting (natural numbers).  Then we extend these numbers to instances of owing other people money for instance (integers).  After that, we consider fractions when we need to split things like 2 pizzas between three people.  We then (skipping the algebraic numbers for the purposes of practicality), we use the real numbers to describe any length; e.g. the length of a diagonal of a unit square.  But this is when our original definition of a number fails to make sense- when we consider complex numbers, which brings me to my main question: what is a rigorous definition of 'number'?  Wikipedia claims that "A number is a mathematical object used to count, label, and measure", but this definition fails to make sense after we extend $\mathbb{R}$.     Does anyone know of any definition of number that can be generalised to complex numbers as well (and even higher order number systems like the quaternions)? setTimeout and "this" in JavaScript I have a method that uses the  function and makes a call to another method. On initial load method 2 works fine. However, after the timeout, I get an error that says method2 is undefined. What am I doing wrong here?  ex:  test.prototype.method = function() {     //method2 returns image based on the id passed     this.method2('useSomeElement').src = "http://www.some.url";     timeDelay = window.setTimeout(this.method, 5000); };  test.prototype.method2 = function(name) {     for (var i = 0; i &lt; document.images.length; i++) {         if (document.images[i].id.indexOf(name) &gt; 1) {             return document.images[i];         }     } }; I seen many times how people describe how to's about LBP-2900, and 10-12 steps from start to end of how to download, unpack, build driver, fix driver, make it work... Could be there some .deb package with ready-to-go driver for Ubuntu? This printer is very popular... I have no idea how to prove that the set $\{(x, |x|): x\in\mathbb{R}\}$ is not the image of an immersion of $\mathbb{R}$ into $\mathbb{R}^2$  For example   If $f(t)=(t^3, |t|^3)$ then $f'(0)=(0, 0)$. Find the equation of a plane containing a point and passing through a line Find the general form equation of a plane that contains the point $(2, -2, 1)$ and passes through a line $(x, y, z) = (1, 2, -3) + t(2, -3, 2)$.  I managed to use the fact that it contains a given point to write the equation of the plane as $A(x-2) + B(y+2) + C(z-1) = 0$ but got stuck there. Most people know the famous equation:    What were his steps of thinking for this equation that helped us discover so much about our world? $$\lim\limits_{n\to\infty} \int_{0}^{1} f(x^n)dx = f(0)$$  when f is continuous on $[0,1]$  I know it can be proved using bounded convergence theorem but,  I wanna know proof using only basic properties of riemann integral and fundamental theorem of calculus and MVT for integrals ...   Thank you. function main() {    Hello(); }  function Hello() {   // How do you find out the caller function is 'main'? }   Is there a way to find out the call stack? How do I install iTunes? I have an iPhone and run Ubuntu on all of my personal computers. Since I did not want to keep a separate partition with Windows on it for the sole purpose of running iTunes, I attempted to install It using Wine.   I installed Wine 1.4 from the Software Center and installed iTunes 10.6.3. When I tried to run it I got a slew of error messages. I hopped over to google where it was suggested that I install it through PlayOnLinux. I did so with the same result. Further googling revealed that iTunes 10.6.x is confirmed to work with Wine 1.5.1 and up.   I installed Wine 1.5.1 following the instructions I found and was unable to get it to open. I did the same with 1.5.9 with the same results. I opened the Package Manager and installed the Wine 1.5.9 packages through it, and it appears to have installed properly.   When trying to install iTunes I got he error "This iTunes installer requires Windows Vista 64 bit or later". Realizing that Wine uses XP as a default I ran winecfg and changed it to Windows 7. This changed nothing and I tried changing it through winetricks to no avail. I even changed it to Vista with the same results.   Does anyone know what is going wrong here and how to fix it? Thanks What does "proverbial" mean? Custom 500 Error page: Is there a way to theme a fatal error? In /core/includes/errors.inc, when there is a fatal error it outputs a response with the message "The website encountered an unexpected error. Please try again later." and a back-trace, if error_level is set to verbose, and without the back-trace otherwise.  It seems like at this point, there's no way, with an event subscriber to capture the response and alter it.  Is that correct?  Or is there a way to wrap the output from line 268 of errors.inc in Drupal 8.4 with markup?    Note, there's another , but that doesn't offer a complete solution.  Also, I looked into .htaccess and Apache ErrorDocument directive, but that . Once Apache passes off to PHP, it can no longer use that directive.  That's for real server errors. Connect to SQL Server with Windows Authentication in a different domain It seems that a List object cannot be stored in a List variable in C#, and can't even be explicitly cast that way.  List&lt;string&gt; sl = new List&lt;string&gt;(); List&lt;object&gt; ol; ol = sl;   results in Cannot implicitly convert type System.Collections.Generic.List&lt;string&gt; to System.Collections.Generic.List&lt;object&gt;  And then...  List&lt;string&gt; sl = new List&lt;string&gt;(); List&lt;object&gt; ol; ol = (List&lt;object&gt;)sl;   results in Cannot convert type System.Collections.Generic.List&lt;string&gt; to System.Collections.Generic.List&lt;object&gt;  Of course, you can do it by pulling everything out of the string list and putting it back in one at a time, but it is a rather convoluted solution. I am trying to put two subscripts at the left and right of a character. For example, something like:  _{t} p_{x}  where p is in the middle. How do you do this? Which one is correct?   Neither my friend nor I feel my best in the morning. Neither my friend nor I feel her best in the morning. Neither my friend nor I feel our best in the morning.    I already know that the verb agrees with the subject closer to the verb:   Neither my friends nor my brother understands me. (correct) Neither my friends nor my brother understand me. (wrong)   AND   Neither my brother nor my friends understand me. (correct) Neither my brother nor my friends understands me. (wrong) In "Knots and Primes: An Introduction to Arithmetic Topology", the author uses the following proposition   Let $h: Y \to X$ be a covering. For any path $\gamma : [0,1] \to X$ and any $y \in h^{-1}(x) (x = \gamma(0))$, there exists a unique lift $\hat{\gamma} : [0,1] \to Y$ of $\gamma$ with $\hat{\gamma}(0) = y$. Furthermore, for any homotopy $\gamma_t (t \in [0,1])$ of $\gamma$ with $\gamma_t = \gamma(0)$ and $\gamma_t(1) = \gamma(1)$, there exists a unique lift of $\hat{\gamma_t}$ such that $\hat{\gamma_t}$ is the homotopy of $\hat{\gamma}$ with $\hat{\gamma_t}(0) = \hat{\gamma}(0)$ and $\hat{\gamma_t}(1) = \hat{\gamma}(1)$.  The author then follows with; "In the following, we assume that any covering space is connected. By the preceding proposition, the cardinality of the fiber $h^{-1}(x)$ is independent of $x \in X$."   I am not sure why this results is true. This is my attempt at explaining it to myself. Take two different $x_1, x_2$ and their fibers $h^{-1}(x_1), h^{-1}(x_2)$ such that $y_1 \in h^{-1}(x_1)$ and $y_2 \in h^{-1}(x_2)$. Take two paths $\gamma_1, \gamma_2$ such that $\gamma_1(0) = x_1$ and $\gamma_2(0) = x_2$. Then we get two lifts $\hat{\gamma_1}, \hat{\gamma_2}$ with $\hat{\gamma_1}(0) = y_1$ and $\hat{\gamma_2}(0) = y_2$. Now, since our covering space is connected we can continuously deform $\hat{\gamma_1}$ into $\hat{\gamma_2}$ and conclude that every elements in $h^{-1}(x_1)$ is also in $h^{-1}(x_2)$ and vice versa. I feel that this is wrong but cannot figure out the right way to see this. Any help would be appreciated.