I have the following code:  ALTER TABLE users MODIFY id int unsigned;   Which throws the following error:  ERROR 1025 (HY000) at line 114: Error on rename of './mydb/#sql-146dd_1d' to './mydb/users' (errno: 150)   I'm fairly certain this is because of a foreign key issue, but I'd like to find more details on the error.  I seem to remember that there was something I could enter into the mySQL command line that would display a list of the most recent errors for various types of issues (including foreign key problems) along with more detail on the exact cause (like the tables involved).  Does anyone know what i am talking about?
I tried this in mysql:  mysql&gt; alter table region drop column country_id;   And got this:  ERROR 1025 (HY000): Error on rename of './product/#sql-14ae_81' to './product/region' (errno: 150)   Any ideas? Foreign key stuff?
Multiplicative group $(\mathbb R^*, ×)$ is group but $(\mathbb R, ×)$ is not group, why? $\mathbb R^*$ refers to $\mathbb R$ without zero.  Please explain the statement "$\mathbb R$  is not a group under multiplication, it is a group under addition." in the . Basically:   Why is multiplicative group $(\mathbb R^*, ×)$ a group? Why is $(\mathbb R, ×)$ not group? Why are $(\mathbb R^*, +)$ and $(\mathbb R, +)$ groups? Take the function  $$ \begin{cases}f(x,y)=(x^2+y^2)/\sin(\sqrt{x^2+y^2}) &amp; \text{when } 0&lt;\lvert (x,y)\rvert&lt;\pi\\   0 &amp; \text{when } (x,y)=(0,0) \end{cases}$$  I got that this function is differentiable at $(0,0)$. I calculated the partial derivatives at $(0,0)$ of which both were $0$ and trying to show the definition of differentiability is not satisfied but I keep getting that it is. Plz help. Prove that if $n$ is a composite, then $2^n-1$ is composite. Not sure if I'm doing this correctly but this is what I've done:  Assume that $n$ is composite and suppose $2^n-1$ is a prime for $n \gt 2$. Then, $2^n-1 = 2k$ for some $k \in \Bbb Z $, $\forall n$.  But this would be a contradiction since $n \gt 2$.  I'm not sure if this a correct proof.  EDIT: I realized that it's to prove $2^n - 1$ NOT $2^{n-1}$ so my attempt above is completely wrong. Class not found loading JDBC org.postgresql.Driver How come $32.5 = 31.5$? (The "Missing Square" puzzle.) If you willingly fall on your turn does it cost movement?  As a DM I'm thinking about how to handle things such as creatures who are immune to being prone, diving into the water from a height, or a flying creature diving off a cliff and taking a fall before taking flight. There are many circumstances where you can fall without taking damage or being knocked prone afterward, and I'm not sure how to determine movement following the dive.  For example, my character walks up to a ledge above a 10 foot drop to the ground below. After taking 5 feet of movement to step off the ledge, I allow myself to fall. When I hit the ground have I used 15 feet of movement or just 5? 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? Let $ a_{n} = \sum_{k=1}^{n} \frac{n}{n^{2}+k}$ . I would like to know whether the given sequence converges.   I see  that,  $ a_{n} = \sum_{k=1}^{n} \frac{n}{n^{2}+k}= \sum_{k=1}^{n} \frac{1}{n+\frac{k}{n}}.$ When $n$ gets sufficiently large the contribution by the $ \frac{k}{n} $ term is diminishing and $ a_{n} &lt; \sum_{k=1}^{n} \frac{1}{n} = 1 $.   Thank you. What kind of questions can I expect to see on a qualifying exam? Minimum requirements of Ubuntu 20.10 Does anyone know what are the minimum requirements to install Ubuntu 20.10? Why is my variable local in one 'while read' loop, but not in another seemingly similar loop? I have two separate Armatures that I want to join together. I have no problem combining the meshes, but the problem is the bones/rigs. When you do the Object mode > join, I lose all of my weight paint on one of my armatures. Is there any way I can join two separate armatures and keep all the weight paint. I turn my models into XPS and use XNA Lara to view them, but XNAlara cannot use both armatures at once. What was Tauriel doing during the events of The Lord of the Rings movies? [Yes, The Hobbit movies are nonsense. But how could I call myself a fantasy fan if I didn't demand my nonsense be as logical as possible?]  Tauriel is presented as a highly-skilled fighter and a combatant for the side of good. Despite this, she apparently did nothing during Sauron's war on the free peoples.  Was she somehow     still mourning Killi, after all these decades?   Was she dead? Or is there another reason she didn't participate? One thing I liked about Mint was that the terminal would usually show two colors: everything from the left to the $ would be one color, and everything past the $ would be another.   Is there a way to have this setup with Ubuntu? Why are one-way plane tickets more expensive than return tickets? "Reality" of length contraction in SR I was in argument with someone who claims that length contraction is not &quot;real&quot; but only &quot;apparent&quot;, that the measurement of a solid rod in its rest reference frame is the &quot;real length&quot; of the rod and all other measurements are somehow just &quot;artificial&quot; and &quot;apparent&quot;. Seemed to me like a bad conversation about poorly defined words and not really relevant to physics, but then some quotes were offered:  ...so that the back appears closer to the front. But of course nothing has happened to the rod itself.  (Rindler)  The effects are apparent (that is, caused by the motion) in the same sense that proper quantities have not changed.  (Resnick &amp; Halliday) At the same time, the  insists that length contraction and time dilation are &quot;real&quot;, with observable consequences:  Time and space dilation are often referred to as ‘perspective effects’ in discussions of STR. Objects and processes are said to ‘look’ shorter or longer when viewed in one inertial frame rather than in another. It is common to regard this effect as a purely ‘conventional’ feature, which merely reflects a conventional choice of reference frame. But this is rather misleading, because time and space dilation are very real physical effects, and they lead to completely different types of physical predictions than classical physics. [...] However, this does not mean that time and space dilation are not real effects. They are displayed in other situations where there is no ambiguity. One example is the twins' paradox, where proper time slows down in an absolute way for a moving twin. And there are equally real physical effects resulting from space dilation. It is just that these effects cannot be used to determine an absolute frame of rest.  I went through a lot of Einstein, Minkowski and Lorentz original material, and didn't find anything about what is &quot;real&quot; and what is not. Finally, I know about muons, where the effects of SR seem to be very real (from , but I had seen it in a physics class before):  When a cosmic ray proton impacts atomic nuclei in the upper atmosphere, pions are created. These decay within a relatively short distance (meters) into muons (their preferred decay product), and muon neutrinos. The muons from these high energy cosmic rays generally continue in about the same direction as the original proton, at a velocity near the speed of light. Although their lifetime without relativistic effects would allow a half-survival distance of only about 456 m (2,197 µs×ln(2) × 0,9997×c) at most (as seen from Earth) the time dilation effect of special relativity (from the viewpoint of the Earth) allows cosmic ray secondary muons to survive the flight to the Earth's surface, since in the Earth frame, the muons have a longer half life due to their velocity. From the viewpoint (inertial frame) of the muon, on the other hand, it is the length contraction effect of special relativity which allows this penetration, since in the muon frame, its lifetime is unaffected, but the length contraction causes distances through the atmosphere and Earth to be far shorter than these distances in the Earth rest-frame. Both effects are equally valid ways of explaining the fast muon's unusual survival over distances.  So which is which? Why do Rindler, Resnick &amp; Halliday use the word &quot;apparent&quot;? File issues after importing Drupal site I recently tried to move my Drupal site to a new server using this page: . But now the style doesn't seem be loaded and more importantly I get this error on every page in the site (even on the frontpage):  Warning: file_put_contents(temporary://filef76T9k): failed to open stream: &quot;DrupalTemporaryStreamWrapper::stream_open&quot; call failed in file_unmanaged_save_data() (line 1900 of /Library/Server/Web/Data/Sites/Default/drupal/includes/file.inc). The file could not be created.  Any ideas what this could be about? Why don't C++ compilers define operator== and operator!=? I am a big fan of letting the compiler do as much work for you as possible.  When writing a simple class the compiler can give you the following for 'free':   A default (empty) constructor A copy constructor A destructor An assignment operator (operator=)   But it cannot seem to give you any comparison operators - such as operator== or operator!=.  For example:  class foo { public:     std::string str_;     int n_; };  foo f1;        // Works foo f2(f1);    // Works foo f3; f3 = f2;       // Works  if (f3 == f2)  // Fails { }  if (f3 != f2)  // Fails { }   Is there a good reason for this?  Why would performing a member-by-member comparison be a problem?  Obviously if the class allocates memory then you'd want to be careful, but for a simple class surely the compiler could do this for you? Is there a way to use the covariance matrix to find coefficients for multiple regression? For simple linear regression, the regression coefficient is calculable directly from the variance-covariance matrix $C$, by  $$ C_{d, e}\over C_{e,e} $$ where $d$ is the dependent variable's index, and $e$ is the explanatory variable's index.  If one only has the covariance matrix, is it possible to calculate the coefficients for a model with multiple explanatory variables?   ETA: For two explanatory variables, it appears that $$\beta_1 = \frac{Cov(y,x_1)var(x_2) - Cov(y,x_2)Cov(x_1,x_2)}{var(x_1)var(x_2) - Cov(x_1,x_2)^2} $$ and analogously for $\beta_2$. I'm not immediately seeing how to extend this to three or more variables. Is an empty set equal to another empty set? I have a definition that claims that two sets are equal A = B, if and only if:  $\forall x ( x \in A \leftrightarrow x \in B)$  An empty set contains no elements. If I define the sets:  A = $\emptyset$  B = $\emptyset$  then can I conclude that A $\neq$ B? Since they contain no elements? Or would I have to show that an elements exists in one but not the other? To me it seems that these are not equal, but I'm struggling to wrap my head around this.  Thanks, Paul