3TB HDD showing 512 logical sector size when connected via SATA
Why is my USB drive showing corrupted data when plugged as an internal SATA drive?
Match the size of multiple background images In  tutorial in the first couple of minutes it is explained how to set the dimensions of a cube and match the background images to this mesh. I have tried to get it right but till now I did not succeed. This is what the creator of the tutorial says in the comments:      I'm keeping only one mesh and just changing the x and y values of my   background images you can see me add at 3:00. We want all the   background images to match that one mesh.   Here are my images:     I think front and back images match to the mesh. But for the right, left and top view I only get one dimension matching. I don't see how you can match both dimensions matching without changing the mesh Examples of patterns that eventually fail Often, when I try to describe mathematics to the layman, I find myself struggling to convince them of the importance and consequence of "proof". I receive responses like: "surely if Collatz is true up to $20×2^{58}$, then it must always be true?"; and "the sequence of number of edges on a complete graph starts $0,1,3,6,10$, so the next term must be 15 etc."  Granted, this second statement is less logically unsound than the first since it's not difficult to see the reason why the sequence must continue as such; nevertheless, the statement was made on a premise that boils down to "interesting patterns must always continue".  I try to counter this logic by creating a ridiculous argument like "the numbers $1,2,3,4,5$ are less than $100$, so surely all numbers are", but this usually fails to be convincing.  So, are there any examples of non-trivial patterns that appear to be true for a large number of small cases, but then fail for some larger case? A good answer to this question should:   be one which could be explained to the layman without having to subject them to a 24 lecture course of background material, and have as a minimal counterexample a case which cannot (feasibly) be checked without the use of a computer.   I believe conditions 1. and 2. make my question specific enough to have in some sense a "right" (or at least a "not wrong") answer; but I'd be happy to clarify if this is not the case. I suppose I'm expecting an answer to come from number theory, but can see that areas like graph theory, combinatorics more generally and set theory could potentially offer suitable answers. Centos mysql version is 5.5 however PHPmyadmin still says version 5.1 When i run the following in my console:  [root@****~]# mysql -u root -p -e 'SELECT VERSION();' Enter password: +-----------+ | VERSION() | +-----------+ | 5.5.39    | +-----------+   Which should be the correct version.  However when i enter my PHPMYADMIN on my server it has the following specs:  Server: Localhost via UNIX socket Program: MySQL Programversion: 5.1.73 - Source distribution   So which version is the correct one and how do i make sure that the database is running on 5.5?  Note  I have already restarted sql several times without any changes I'm running a VPS of a german provider and want to switch from Ubuntu to CentOS. There I tried to install firewalld (was not preinstalled), but it always fails with the error  ERROR: Failed to load nf_conntrack module: modprobe: ERROR: could not find module by name='nf_conntrack' modprobe: ERROR: could not insert 'nf_conntrack': Function not implemented modprobe: ERROR: Error running install command for nf_conntrack modprobe: ERROR: could not insert 'nf_conntrack': Operation not permitted   Obviously the nf_conntrack kernel module was not found. Since this is a VPS, I cannot tinker with the kernel modules. On the support site of my provider I found a list of available kernel modules, for example:  ip_conntrack_netbios_ns ipt_conntrack    ip_conntrack    ip_conntrack_ftp    ip_conntrack_irc   Since nf_conntrack is not listed here, does that mean, that I cannot use firewalld? Is it possible to run it without this module?  I guess I could use iptables, if I wanted to (it seems to run correctly). But as I have more experience with firewalld, I would like to stick with it.    CentOS Linux release 7.7.1908 (Core)  uname -a: Linux xxxxxx.xxxxxxxx.xxx 3.10.0-042stab140.1 #1 SMP Thu Aug 15 13:32:22 MSK 2019 x86_64 x86_64 x86_64 GNU/Linux I am trying to use the  package.  I have the following counters defined (hopefully this is the right way to do it!)  \newtheorem{thm}{Theorem}[section] \newtheorem{lemma}[thm]{Lemma} \newtheorem{cor}[thm]{Corollary}   This works as I would like (i.e. Theorem 1.1, Corollary 1.2, Lemma 1.3, etc.)  My problem is \cref always returns Theorem 1.2, Theorem 1.3. I   Perhaps this is not right? (In my preamble)  \crefname{thm}{theorem}{theorem's} \crefname{lemma}{lemma}{lemma's} How do I turn a String into a InputStreamReader in java? How can I transform a String value into an InputStreamReader? Using a function in two different ways group of units in a topological ring How do Stack Overflow questions appear in Google search results in seconds? Probability of the union of $3$ events? I need some clarification for why the probability of the union of three events is equal to the right side in the following:  $$P(E\cup F\cup G)=P(E)+P(F)+P(G)-P(E\cap F)-P(E\cap G)-P(F\cap G)+P(E\cap F\cap G)$$  What I don't understand is, why is the last term(intersection of all) added back just once, when it was subtracted three times as it appears from a Venn Diagram?  Here on page 3, this is explained but not in enough details that I can understand it: Is the intersection of a closed set and a compact set always compact? I am going through Rudin's Principles of Mathematical Analysis in preparation for the masters exam, and I am seeking clarification on a corollary.  Theorem 2.34 states that compact sets in metric spaces are closed. Theorem 2.35 states that closed subsets of compact spaces are compact. As a corollary, Rudin then states that if $L$ is closed and $K$ is compact, then their intersection $L \cap K$ is compact, citing 2.34 and 2.24(b) (intersections of closed sets are closed) to argue that $L \cap K$ is closed, and then using 2.35 to show that $L \cap K$ is compact as a closed subset of a compact set.  Am I correct in believing that this corollary holds for metric spaces, and not in general topological spaces? This is what I would like to do:  morekeywords={SENÃO, ENTÃO, FAÇA, ATÉ, ENQUANTO, PARA, SE, DECLARA, DECLARE, E, OU, FIM_ENQUANTO, FIM_PARA}   I'm defining a new language, and I would like to use natural language words as keywords.  The problem is with keywords: SENÃO, ENTÃO, FAÇA, ATÉ.  I have solved the first problem, in showing special chars with:   The alsoletter here, doesn't work for me, I got an error when using it: alsoletter={Ç,É,Ã}.  test.tex  \documentclass{article}  \usepackage[brazilian]{babel} \usepackage[T1]{fontenc}  \usepackage[utf8]{inputenc} \usepackage{listingsutf8}  \usepackage{listings}  \lstset{%         inputencoding=utf8,         extendedchars=true,         literate=%         {é}{{\'{e}}}1         {è}{{\`{e}}}1         {ê}{{\^{e}}}1         {ë}{{\¨{e}}}1         {É}{{\'{E}}}1         {Ê}{{\^{E}}}1         {û}{{\^{u}}}1         {ù}{{\`{u}}}1         {â}{{\^{a}}}1         {à}{{\`{a}}}1         {á}{{\'{a}}}1         {ã}{{\~{a}}}1         {Á}{{\'{A}}}1         {Â}{{\^{A}}}1         {Ã}{{\~{A}}}1         {ç}{{\c{c}}}1         {Ç}{{\c{C}}}1         {õ}{{\~{o}}}1         {ó}{{\'{o}}}1         {ô}{{\^{o}}}1         {Õ}{{\~{O}}}1         {Ó}{{\'{O}}}1         {Ô}{{\^{O}}}1         {î}{{\^{i}}}1         {Î}{{\^{I}}}1         {í}{{\'{i}}}1         {Í}{{\~{Í}}}1 }  \lstdefinelanguage{pseudo} { extendedchars=true, alsoletter={_}, morekeywords={ENQUANTO,PARA,SE,SEN\~{A}O,ENTÃO,ATÉ,FA\c{C}A,DECLARA,DECLARE,E,OU,FIM_ENQUANTO,FIM_PARA,FAÇA}, ndkeywords={NUMERO,TEXTO,LEIA,ESCREVA}, sensitive=true, morecomment=[l]{//}, morecomment=[s]{/*}{*/}, morestring=[b]" }  \begin{document} \lstinputlisting[language=pseudo]{foo.pseudo} \end{document}   foo.pseudo  ENQUANTO nota != -1 FAÇA // Comment example  LEIA nota  SE nota &gt;= 7 ENTÃO    ESCREVA "Aprovado"  SENÃO    ESCREVA "Reprovado"    TEST "Algo mais" /* mais  comentário */  FIM_ENQUANTO    I have seen: Currently selected indicator's colour in flag summary and help pages, can be the same as the site's colour code How do I prove/disprove that $F_n^2 + F_{n\pm 1}^2 = F_{2n\pm 1}$, where $F_n$ is the $n$th Fibonacci number? I was looking at the Fibonacci sequence:  $$1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,\ldots, F_n : F_n + F_{n - 1} = F_{n + 1} \land F_0 = 0$$  Here I noticed something; $\qquad F_n^2 + F_{n\pm1}^2 = F_{2n\pm1} : n\in \mathbb{N}$  For example; $$\ \ F_3^2 + F_{3 + 1}^2 = F_3^2 + F_4^2 = 2^2 + 3^2 = F_{2\times3 + 1} = F_{6 + 1} = F_7 = 13$$ $$F_3^2 + F_{3 - 1} = F_3^2 + F_2^2 = 2^2 + 1^2 = F_{2\times3 - 1} = F_{6 - 1} = F_5 = 5$$ However, no matter how true this can seem, I cannot seem to prove/disprove it.    My Attempt: $$\because (a + b)^2 = (a + b)(a + b) = a^2 + ab + ba + b^2 = a^2 + b^2 + 2ab : (a,b)\in \mathbb{Z}$$ $$\implies F_n^2 + F_{n\pm 1}^2 = (F_n + F_{n\pm 1})^2 - 2F_nF_{n\pm 1}$$ $$\implies F_n^2 + F_{n - 1}^2 = F_{n + 1}^2 - 2F_nF_{n - 1} : F_n + F_{n - 1} = F_{n + 1}$$ $$\implies F_n^2 + F_{n + 1}^2 = F_{n + 2}^2 - 2F_nF_{n + 1} : F_n + F_{n + 1} = F_{n + 2} \iff F_n + F_{n - 1} = F_{n + 1}$$ $$\implies F_{2n\pm 1} + 2F_nF_{n\pm 1} = F_{n + 2\lor1}^2 : F_n^2 + F_{n\pm 1}^2 = F_{2n\pm 1} \tag{+2 if +, +1 if -}$$ $$\implies F_{2n\pm 1} + 2\sqrt{F_{2n\pm 1} - F_{n\pm 1}^2}\sqrt{F_{2n\pm 1} - F_n^2}= F_{n + 2\lor1}$$ $$\implies F_{2n\pm 1} + 2\sqrt{(F_{2n\pm 1} - F_{n\pm 1}^2)(F_{2n\pm 1} - F_n^2)} = F_{n + 2\lor1}^2$$ $$\implies F_{2n\pm 1} + 2\sqrt{F_{2n\pm 1}(F_{2n\pm 1} - F_n^2 - F_{n\pm 1}^2) - (F_nF_{n\pm 1})^2} = F_{n + 2\lor1}^2$$.  $$\because F_n^2 + F_{n\pm 1}^2 = F_{2n\pm 1}$$ $$\implies F_{2n\pm 1} + 2\sqrt{-(F_nF_{n\pm 1})^2} = F_{n + 2\lor1} \neq F_{2n\pm 1} + 2\sqrt{\big(-(F_nF_{n\pm 1})\big)^2}$$ $$\therefore F_{2n\pm 1} + 2F_nF_{n\pm 1}i = F_{n + 2\lor1} : i = \sqrt{-1}$$  I have looked over every step and cannot see where I am wrong. The only part that must be wrong is that:  $$F_{2n\pm 1} + 2F_nF_{n\pm 1}i = F_{n + 2\lor1} \iff F_n^2 + F_{n\pm1}^2 = F_{2n\pm 1}$$  I can seperate $F_{2n\pm 1}$ as $F_n^2 + F_{n\pm 1}^2$ (if true) so I turn the equation into:  $$F_n^2 + F_{n\pm 1}^2 + 2F_nF_{n\pm 1}i = F_{n + 2\lor1}$$ $$\therefore (F_n + F_{n\pm 1})\bigg(\frac{F_n}{F_{n\pm 1}} + \frac{F_{n\pm 1}}{F_n} + 2i\bigg) = F_{n + 2\lor1}$$ Now I know that the greater the value of $n$, one of the fractions in the above equation (depending on which sign is used in $F_{n\pm 1}$) will get closer to the golden ratio $φ = \frac{1 + \sqrt{5}}{2}$ but $i = \sqrt{-1}$ is not a "real" number, although $F_n$ is.  I then searched for other formulae for finding $F_n$ and came across the one below (being Binet's Formula):  $$F_n = \bigg\{\frac{φ^n - ψ^n}{φ - ψ} : ψ = φ - \frac{\sqrt{20}}{2} = \frac{1 - \sqrt{5}}{2} \ \land \ φ - ψ = \sqrt{5}\bigg\}$$  But I do not know what how to turn that into $F_{n\pm 1}$. Could you please show me where I went wrong (because I must have gone wrong somewhere), and also if you wish, could you please show me how to turn the above fraction into $F_{n\pm 1}$ (if possible).  I only used the $(a + b)^2$ expansion rule because my skill level in mathematics is not particularly high compared to most of the users on this site (especially when logging into the MSE and finding fancy symbols like $\nabla$ and $\partial$ and $\sum$ which all look Greek to me, however the only "fancy" thing I know is that $i = i^5 = \cdots = \sqrt{-1}$) so if you used any other techniques in trying to prove this formula, could you please show me step by step?  Much appreciated. Thank you in advance.    Edit: I believe this question is a duplicate of this other question $\longrightarrow$   and I can go here to serve as a little hint $\longrightarrow$ How can I embed a View inside a content of a node? How can I embed a view inside a content of a node in Drupal 8?   I found something similar, for example in the question about "" or the  module, but it is all for Drupal 7.  I tried with an Entity reference field pointing to a View but it display only a label and from the Manage Display tab I can choose only from Label and Entity ID. I need something like the "Rendered entity" option that is present on Entity reference fields pointing to other nodes. Show that $d(z,a)=|\frac{z-a}{1-\overline{a}z}|$ is a metric on the unit disk For any $z, a$ in the open unit disk, we define$$d(z,a)=\left \vert \frac{z-a}{1-\overline{a}z} \right \vert$$  Show that $d$ is a metric on the open unit disk.     It is easy to show $d(z,a)=d(a,z)$ and $d(z,a)=0$ $\rm iff$ $z=a$. However, I am having trouble showing that it satisfies triangle inequality. Any help would be appreciated! Replace \input{fileX} by the content of fileX automatically Suppose I have a document with multiple include or input statements  \input{fileA} \input{fileB}   etc.   Is there an easy way to generate a single .tex file where \input{fileA} is replaced by the actual content of fileA etc. without copying it manually? How to install tzdata on a ubuntu docker image? I have the following line in the Dockerfile.  RUN apt-get install -y tzdata   When I run it, it asks for my input. After I provided my input, it hung there. Does anybody know how to solve this problem?  Step 25/25 : RUN apt-get install -y tzdata  ---&gt; Running in ee47a1beff84 Reading package lists... Building dependency tree... Reading state information... The following NEW packages will be installed:   tzdata 0 upgraded, 1 newly installed, 0 to remove and 0 not upgraded. Need to get 189 kB of archives. After this operation, 3104 kB of additional disk space will be used. Get:1 http://archive.ubuntu.com/ubuntu bionic-updates/main amd64 tzdata all 2018i-0ubuntu0.18.04 [189 kB] debconf: unable to initialize frontend: Dialog debconf: (TERM is not set, so the dialog frontend is not usable.) debconf: falling back to frontend: Readline debconf: unable to initialize frontend: Readline debconf: (This frontend requires a controlling tty.) debconf: falling back to frontend: Teletype dpkg-preconfigure: unable to re-open stdin:  Fetched 189 kB in 1s (219 kB/s) Selecting previously unselected package tzdata. (Reading database ... 25194 files and directories currently installed.) Preparing to unpack .../tzdata_2018i-0ubuntu0.18.04_all.deb ... Unpacking tzdata (2018i-0ubuntu0.18.04) ... Setting up tzdata (2018i-0ubuntu0.18.04) ... debconf: unable to initialize frontend: Dialog debconf: (TERM is not set, so the dialog frontend is not usable.) debconf: falling back to frontend: Readline Configuring tzdata ------------------  Please select the geographic area in which you live. Subsequent configuration questions will narrow this down by presenting a list of cities, representing the time zones in which they are located.    1. Africa      4. Australia  7. Atlantic  10. Pacific  13. Etc   2. America     5. Arctic     8. Europe    11. SystemV   3. Antarctica  6. Asia       9. Indian    12. US Geographic area: `` Chat reputation in left bar seems different than any other reputation displayed for users How to compute $\int_0^{\pi/2}\frac{\sin^3 t}{\sin^3 t+\cos^3 t}dt$? Calculating with Mathematica, one can have $$\int_0^{\pi/2}\frac{\sin^3 t}{\sin^3 t+\cos^3 t}\,\mathrm dt=\frac{\pi}{4}.$$   How can I get this formula by hand? Is there any simpler idea than using $u = \sin t$?     Is there a simple way to calculate $$ \int_0^{\pi/2}\frac{\sin^n t}{\sin^n t+\cos^n t}\,\mathrm dt $$ for $n&gt;3$? Could anyone come up with a reference for this exercise?