Subtraction of Double type Values in C++
Is floating point math broken?
I'm a US passport holder. What documents do I need when I fly from the U.S. to Germany?  Assume I'm going for a few weeks of vacation.  Obviously I need my passport.  What about a "visa"?  Anything else? Does the new finding on "reversing a quantum jump mid-flight" rule out any interpretations of QM? new finding by Minev et al. seems to suggest that transitions between atomic states are not instantaneous, but continuous processes wherein a superposition smoothly adjusts from favoring one state to another (if I understand it correctly). The authors also claim to be able to catch a system "mid-jump" and reverse it. Popular articles are  and .  I am curious if this finding rules out any interpretations of QM. It seems to generally go against the Copenhagen attitude, which describes measurements as collapsing physical systems into a definite classical state. The popular articles indeed claim that the founders of QM would have been surprised by the new finding.  The link with the asterisk mentions that something called "quantum trajectories theory" predicts what was observed. Is this an interpretation, or a theory? And are they implying that other interpretations/theories don't work? Children's book with "square triangles" in parallel universe? In the 1960s I read book--an older children's book, I think--which I loved, and still remember, roughly.  I have no idea what the title is or who the author is, and I'm wondering if anyone knows this one:  Scientists had invented a device which they didn't fully understand, and which had puzzling effects.  For example, when a pencil was put into the machine, it disappeared, and then reappeared inside out: The lead was on the outside.  When people went into the machine, they came back dead, having died from fright.  Finally they sent a very open-minded person into the machine.  She was an artist, I think.  She was able to return alive, and described an alternate universe in which geometry was very different.  I distinctly remember that there were supposedly square triangles or four-sided triangles--or was it three-sided squares?  (This is, of course, a literally contradictory claim, but I didn't see the matter as clearly then.)  Thanks! Meta duplicates don't require an answer. Don't suggest there is one when that's not true Restoring open software after a restart event in windows I find that at the end of a long day, I sometimes have a large number of programs running. All which I will need to use tomorrow. Normally, this isn't an issue, I can simply lock the machine and come back tomorrow. My problem arrises when windows update launches in the middle of the night and force restarts my computer. That in turns closes all my open software. I of course save everything regularly so I don't loose anything, but I waste time reopening all of those resources whenever there is a restart.   [EDIT]  I should clarify that I still want to be able to restart my computer when an update comes down. Preventing the restart only delays the problem until later. I should have been more specific in that I want to be able to recover my working environment after a restart for any reason. Things like scheduled maintence, power loss, updates, and software installs.  [EDIT]  I can't simply have them setup to launch at startup becasuse those files change from week to week. So I need something that monitors what I have open, and gives me the option to "recover" those software sessions when I log back in.  Anyone have any suggestions on what I can do? I'd even be willing to purchase software to do this for me if that is the only option.  Thanks Argument list too long error for rm, cp, mv commands Wikipedia onebox is dropping random text Random text is getting dropped from Wikipedia oneboxes. See . Screenshot:  This occurs regardless of HTTP/HTTPS and of whether a redirect URL is entered into chat. I initially thought the bug is triggered by &lt;span&gt;s or other HTML formatting elements, but in the Burj Khalifa article's HTML source code, there is no formatting around one of the deleted words. Possibly related to , but this is not specific to numbers. If I change the password for the root user is that going to automatically change the password for the user account?   I found this link for root:    How do I change the user account password? Installing python module within code Is copper piping required within a certain distance from a water heater? I have read that National Code requires you to use copper for 18 inches from your water heater.  How can I do this when everything existing is PEX?   I need to replace my existing low boy water heater next to my kitchen sink.  It was installed by the builder ten years ago. All the pipe in the house is PEX.  The existing water heater is connected using PEX as well.    The supply line comes directly thru the wall to the HW Heater. There is no space to run 18 inches of copper! The heater is under the kitchen counter, and the countertop is directly over it. Only about an inch clearance. How can we communicate short messages long-distance? Why does water take a "wet" path? Allow me to explain what I mean... ((I am asking this question in the physics section in hopes of finding a "physics" argument))  I shall make it clear what I mean by demonstrating an experiment...  Hold your hand upright with your index finger pointing up towards the sky. Now drop about 2-3 drops of water right on top of your finger. Water drop should (theoretically) stay there. Now tilt your hand ever so slightly towards one side. The water drop rolls down your finger down your wrist leaving a trail towards the tilted side right?  Now's here comes my question. Now if you bring your finger and the hand to the initial upright state and place another water drop on the same finger. Now we see that the water drop takes the same trail! Why does it happen?  My argument: The water trail which was previously left off reduced the friction in that path by filling the gaps between the molecules. Hence the new drop tends to slide more on that path and hence ends up travelling in it.  ((This "effect" is also observed when tear drops keep rolling down in the same path. But that could just be because that path is the steepest.)) Help with proof that $\mathbb Z[i]/\langle 1 - i \rangle$ is a field. I have been having a lot of trouble teaching myself rings, so much so that even "simple" proofs are really difficult for me. I think I am finally starting to get it, but just to be sure could some one please check this proof that $\mathbb Z[i]/\langle 1 - i \rangle$ is a field. Thank you.  Proof: Notice that $$\langle 1 - i \rangle\\  \Rightarrow 1 = i\\  \Rightarrow 2 = 0.$$ Thus all elements of the form $a+ bi + \langle 1 - i \rangle$ can be rewritten as $a+ b + \langle 1 - i \rangle$. But since $2=0$ this implies that the elements that are left can be written as $1 + \langle 1 - i \rangle$ or $0 + \langle 1 - i \rangle$. Thus  $$ \mathbb Z[i]/ \langle 1 - i \rangle = \{ 0+ \langle 1 - i \rangle , 1 + \langle 1 - i \rangle\}. $$  This is obviously a commutative ring with unity and no zero-divisors, thus it is a finite integral domain, and hence is a field. $\square$ Is there a word for happiness made possible by a tragic situation? Why is the decay of a neutral rho meson into two neutral pions forbidden? What metadata does a LibreOffice file contain and how to remove it? I am using LibreOffice on Linux. One way I know of viewing and removing metadata from a LibreOffice file is going to File -&gt; Properties -&gt; General, unchecking  “apply user data” and click reset. Then go to “Description” and “Custom” Properties and remove information from there, if exists.   Does it truly remove all the metadata or something is left and what is it and what other methods can I use to remove it?   Also, if I unzip a LibreOffice file, is contents.xml the only place where metadata may be found?  If I forgot to remove any metadata, is it possible that the username is transmitted? Please be kind, I am an electronics nub.  This is in reference to getting an LED to emit photons.  From what I read (Getting Started in Electronics - Forrest Mims III and Make: Electronics) electrons flow from the more negative side to the more positive side.  In an example experiment (involving a primary dry cell, a SPDT switch, a resistor and an LED) it states that the resistor MUST be connected to the anode of the LED.  In my mind, if the electrons flow from negative to positive, wouldn't the electron flow run through the LED before the resistor; thereby making the resistor pointless? What are the requirements for national parks? I'm trying to place a national park here:    But the button to create one with the Naturalist is greyed out:    I know the civopedia lists the requirements for building a national park, but they are either wrong or I'm having a hard time understanding them:   The tiles must be natural wonders, Mountains or a tile with an Appeal of Charming or better. As you can see the top are both Breathtaking and the bottom ones are part of the Great Barrier Reef wonder All four tiles must be owned by the same city. All tiles are within the boarders of Mbwila The tiles for a diamond shape. All tiles are connected close to each other in a diamond shape No tile can have an improvement or district on it. All tiles are in their initial condition.   So I'm probably missing something. Can someone tell me what's the problem? What does string theory predict for the singularity inside a black hole? The usual explanation for what's going on inside a black hole goes something like "General Relativity predicts a singularity with infinite curvature, but when matters gets so tightly compressed we should expect quantum effects to become important, so the singularity will probably be blurred". Authors then proceed to say that we need a quantum theory of gravity to answer such things, and quickly abandon the subject.  Well, while we don't have an experimentally confirmed quantum theory of gravity, we do have a speculative one, string theory. What does it say about singularities? Are they smeared out like the books say? Do they remain points (or rings for a rotating black hole) with infinite curvature and density? Do we not know? Names of higher-order derivatives Specific derivatives have specific names. First order is often called tangency/velocity, second order is curvature/acceleration. I've also come across words like Jerk, Yank, Jounce, Jolt, Surge and Lurch for 3rd and 4th order derivatives. Is there a widely agreed list of names for these? How many orders have specific names?  In this case, I'm dealing with NURBs curves, so the "tangency" and "curvature" related words are to be preferred over "velocity" and "acceleration" words.