Sites concept conflicts with the functionality
Should I not answer my own questions?
Why is the Converse to Lagrange's Theorem False? I might end up teaching philosophy in Finnish lukio/gymnasium. I will not get an opportunity to practice teaching it - I do get to practice teaching mathematics a fair deal, though. (The situation is somewhat unfortunate.) I have taken subject studies in philosophy at university. They amount to around 60 credits (ECTS).  Suppose I give the students an exam, which asks them to write an essay or two. After that my task is to grade the exams in a fair way and comment them in such a way that the students can learn from the feedback.  -  Suppose the task was to write an essay on the problem of universals - nominalism and realism, say. Let us say 6 points is the perfect score for this task.  I would expect the students to define nominalism and realism (2 points, maybe?) and explain the problem (2 points). Remaining two points for taking some stance and arguing for it - realism is more reasonable because so and so. Partial credits for demonstrating only partial understanding.  -  Am I missing some important aspects of philosophical thinking? Should I emphasize the different parts of an answer in a different way? I suspect my perspective is influenced by fairly extensive mathematics education - is there something particular I should watch out for? How Does Kylo Ren not stop Chewbacca's blaster? How does Kylo Ren stop the blaster shot in the beginning when being shot at by Poe, only to be unaware of the coming blaster shot from Chewbacca, which seems much more predictable.   I am sure he knew Chewbacca, Rey and Finn where there as Chewbacca turns with the opening of the doors when Rey and Finn come in.  EDIT in regards to Richards Answer: I just want to expand a little more on question. What I don't understand is that Kylo Ren uses the force, so it is just not a matter him not hearing. When Poe shoots him from behind, he makes no sound, but yet he turns and stops the blaster and Poe. That has to be due to the power he commands in the Force.  And this is from Obi-Wan Kenobi:     "Well, the Force is what gives a Jedi his power. It's an energy field   created by all living things. It surrounds us and penetrates us; it   binds the galaxy together."―Obi-Wan Kenobi —   So it seems to me that it would be very hard for him even in a weakened state to not even notice that he was being shot at by virtue of the force being a part of Sith and Jedi's alike. Even if he was too weak to actually stop the blaster, the Force should have been able to warn him. How does one show that $$\sum_{k=0}^{n}\binom{n+k}{k}\frac{1}{2^k}=2^{n}$$ for each nonnegative integer $n$?  I tried using the  but I guess I am applying it incorrectly. With the snake oil technique we have $$F(x)= \sum_{n=0}^{\infty}\left\{\sum_{k=0}^{n}\binom{n+k}{k}\frac{1}{2^k}\right\}x^{n}.$$ I think I have to interchage the summation and do something. But I am not quite comfortable in interchanging the summation. Like after interchaging the summation will $$F(x)=\sum_{k=0}^{n}\sum_{n=0}^{\infty}\binom{n+k}{k}\frac{1}{2^k}x^{n}?$$ Even if I continue with this I am unable to get the correct answer.  How does one prove this using the Snake oil technique?  A combinatorial proof is also welcome, as are other kinds of proofs. Evaluate $\int_0^\infty \frac{(\log x)^2}{1+x^2} dx$ using complex analysis How do I compute      $$\int_0^\infty \frac{(\log x)^2}{1+x^2} dx$$   What I am doing is take   $$f(z)=\frac{(\log z)^2}{1+z^2}$$  and calculating   $\text{Res}(f,z=i) = \dfrac{d}{dz} \dfrac{(\log z)^2}{1+z^2}$ which came out to be $\dfrac{\pi}{2}-\dfrac{i\pi^2}{8}+\dfrac{i\pi}{2}$  Im not too sure how to move on from here. the given answer is $\dfrac{\pi^3}{8}$  Any help will be appreciated. thank you in advanced. When Ron broke his wand, why didn't he apply for Hogwarts financial aid? We know, from Book Six, that Hogwarts has a financial aid for students in need. It's supposed to cover all expenses regarding materials and school supplies, so it certainly covers wands. So why didn't Ron simply apply for this fund when he broke his wand in Book Two, since his family could not afford a new one?  Seems absurd that no teacher would notice that Ron had a broken wand and inform him there's a school fund. Plot hole?  Obs.: Even if Ron could afford a new wand, one could ask how we would purchase it (you must experiment personally to find a wand that chooses you). It turns out that there's a local branch of Ollivander in Hogsmeade. I'm sure that, under those circumstances, a second-year student like Ron would be allowed to visit Hogsmeade to purchase a new wand. I'm having problems using the UV mapping in blender 2.67. Specifically, I am trying to unwrap a really simple mesh, but the UV map is still giving me a net where some of the boxes are completely out of proportion to the others, which causes the texture to stretch horribly. Here is a picture to illustrate:    The mesh only has those three faces you can see in the picture, and the single seam on the front corner. It's a trivially simple mesh, so I really don't understand why the two side faces are being stretched in the UV map to be the same size as the top face. I've tried clicking the average islands scale button as suggested by some of the answers to other questions but that has no effect. It's frustrating because it seems so simple.  Hopefully someone can show me the presumably simple mistake I am making!  Edit: Just to make this clearer, I have already added a seam as the first answer suggests i do. Hopefully this picture will make that clearer, the yellow arrow is pointing to the edge i seamed. The mesh is only three faces so should only need this single seam. The image shows the mesh from infront and behind/underneath so it should make more sense.    Double Edit: One more picture for clarity on the seam issue. The mesh is unfolding correctly, it is just the scale of the unfolded map that is incorrect (in relation to one another) How can I assign a Func conditionally between lambdas using the conditional ternary operator? Generally, when using the conditional operator, here's the syntax:  int x = 6; int y = x == 6 ? 5 : 9;   Nothing fancy, pretty straight forward.  Now, let's try to use this when assigning a Lambda to a Func type. Let me explain:  Func&lt;Order, bool&gt; predicate = id == null     ? p =&gt; p.EmployeeID == null     : p =&gt; p.EmployeeID == id;   That's the same syntax, and should work? Right? For some reason that doesn't. The compiler gives this nice cryptic message:     Error  1   Type of conditional expression cannot be determined because there is no implicit conversion between 'lambda expression' and 'lambda expression'   I then went ahead and changed the syntax and this way it did work:  Func&lt;Order, bool&gt; predicate = id == null     ? predicate = p =&gt; p.EmployeeID == null     : predicate = p =&gt; p.EmployeeID == id;   I'm just curious as to why it doesn't work the first way?  (Side note: I ended up not needing this code, as I found out that when comparing an int value against null, you just use object.Equals) How to see python symbolic names of objects on cursor hover of menu items in Blender 2.8 in Blender 2.79 one could hover over a UI element and see the symbolic python name of said element. How would one accomplish the same with Blender >= 2.8? How do I deal with a runaway bride? I killed my first wife once I found out there is a mercenary you can marry who gives you up to 300 gold a day (in Whiterun). The only requirement, of course, being that I had to hire her first. So I hired her, and then I popped the question, to which she replied the usual: tell the priest to arrange the wedding.   When we reached Riften I told her to wait, just outside the bee and barb, and arranged the wedding. I went through the process, and the second it finished she left, I followed but as I left she was nowhere to be seen. I have tried going back to my house, the pub where I hired her and that same spot in Riften about 6 times each now, some during the day, some during the night and cannot find her at all.   Now this isn't to much of a problem because I can re-marry...oh wait, to remarry, my spouse has to die, so I can't claim gold off her and can't remarry, and the autosaves have been used up fast travelling to the places I thought she might've been. My last save is something like 6 levels ago, and I don't want to have to load it.   What should I do about this situation? Is list::size() really O(n)? Recently, I noticed some people mentioning that std::list::size() has a linear complexity. According to  , this is in fact implementation dependent as the standard doesn't say what the complexity has to be. The comment  says:     Actually, it depends on which STL you   are using. Microsoft Visual Studio V6   implements size() as {return (_Size);   } whereas gcc (at least in versions   3.3.2 and 4.1.0) do it as { return std::distance(begin(), end()); } The   first has constant speed, the second   has o(N) speed    So my guess is that for the VC++ crowd size() has constant complexity as Dinkumware probably won't have changed that fact since VC6. Am I right there? What does it look like currently in gcc? If it is really O(n), why did the developers choose to do so? Biometrika journal style file not getting along with TeXLive-2020 I cannot compile styleguide.tex in biometrika.zip (see ). Here is a MWE which leads to the same error message, though not sure yet that I've not tossed baby out with bath water. \documentclass{article} \RequirePackage[thmmarks]{ntheorem}  \makeatletter \def\arabic#1{{\rm\expandafter\@arabic\csname c@#1\endcsname}} \theoremnumbering{arabic} \newtheorem{definition}{Definition} \makeatother  \begin{document}  \begin{definition} This is a definition. \end{definition}  \end{document}  Here is the output of pdflatex: % pdflatex styleguide This is pdfTeX, Version 3.14159265-2.6-1.40.21 (TeX Live 2020) (preloaded format=pdflatex)  restricted \write18 enabled. entering extended mode (./styleguide.tex LaTeX2e &lt;2020-02-02&gt; patch level 5 L3 programming layer &lt;2020-03-06&gt; (/usr/local/texlive/2020/texmf-dist/tex/latex/base/article.cls Document Class: article 2019/12/20 v1.4l Standard LaTeX document class (/usr/local/texlive/2020/texmf-dist/tex/latex/base/size10.clo)) (./ntheorem.sty  Style `ntheorem', Version 1.24 &lt;2004/09/20&gt; ) (/usr/local/texlive/2020/texmf-dist/tex/latex/l3backend/l3backend-pdfmode.def ) (./styleguide.aux) ! Use of \@item doesn't match its definition. \update@series@target@value #1-&gt;\def \reserved@a {                                                   #1}\ifx \target@meta@famil... l.13 T       his is a definition. ? q OK, entering \batchmode I have a shapefile with contours and their heights.   Is it possible to make a DEM from contours in QGIS without using GRASS?   I found  but the answer is for ArcGIS Desktop. Prove there is an increasing sequence ($s_n$) of points in $S$ such that $\lim s_n = \sup S$. Let $S$ be a bounded set. Prove there is an increasing sequence ($s_n$) of points in $S$ such that $\lim s_n = \sup S$. Note: If $\sup S$ is in $S$, it’s sufficient to define $s_n = \sup S$ for all $n$.  What I have tried so far:  Let $M=\sup S, L = \lim\, s_n,\,|s_n-L|&lt;\epsilon/2$, then $M-\epsilon &lt; L- \epsilon/2 &lt; s_n &lt; M &lt; M+\epsilon$. But I get this based on $M &lt;= \epsilon+L$, because $\epsilon+L$ is an upper bound for $s_n$.   However, as $s_n$ are just points in $S$, so I don't know if it's sufficient to say $M$, which is the $\sup$ of $S$, is smaller than $L+\epsilon$. Approximating $\pi$ with least digits Do you a digit efficient way to approximate $\pi$? I mean representing many digits of $\pi$ using only a few numeric digits and some sort of equation. Maybe mathematical operations also count as penalty.  For example the well known $\frac{355}{113}$ is an approximation, but it gives only 7 correct digits by using 6 digits (113355) in the approximation itself. Can you make a better digit ratio?  EDIT: to clarify the "game" let's assume that each mathematical operation (+, sqrt, power, ...) also counts as one digit. Otherwise one could of course make artifical infinitely nested structures of operations only. And preferably let's stick to basic arithmetics and powers/roots only.  EDIT: true. logarithm of imaginary numbers provides an easy way. let's not use complex numbers since that's what I had in mind. something you can present to non-mathematicians :) Problem storing arrays with update_user_meta I am writing a function that adds an ID number to an array and puts the array in the usermeta. $_GET['auction'] is the post_id.  Below is the function:  $reminders = get_user_meta( $current_user-&gt;ID, "reminders" ); print_r( $reminders ); if( in_array( $_GET['auction'], $reminders ) ) {     echo "Failed: Auction already in list"; } else {     array_push( $reminders, intval( $_GET['auction'] ) );     if ( update_user_meta( $current_user-&gt;ID, "reminders", $reminders ) ) {         echo "Success";     } else {         echo "Failed: Could not update user meta";     } } print_r( $reminders );   Here is the output after adding one auction:  Array ( )  Success Array ( [0] =&gt; 7 )    Here is the output after adding two auctions:  Array ( [0] =&gt; Array ( [0] =&gt; 7 ) )  Success Array ( [0] =&gt; Array ( [0] =&gt; 7 ) [1] =&gt; 73 )   And here is the output after adding three auctions:  Array ( [0] =&gt; Array ( [0] =&gt; Array ( [0] =&gt; 7 ) [1] =&gt; 73 ) )  Success Array ( [0] =&gt; Array ( [0] =&gt; Array ( [0] =&gt; 7 ) [1] =&gt; 73 ) [1] =&gt; 0 )   Notice that adding a new element to the array using array_push works fine. But when the array is stored in the usermeta then retrieved again, the last element in the array has been put into an array of its own, creating an infinitely dimensional array. I'd prefer to keep this array one dimensional.  Is there a way I can run update_user_meta and get_user_meta without it changing the structure of my array? When a person lifts a book while standing on the earth's surface. Why is his force considered external to the book-earth system? Isn't his force internal like the case of the forces that cause the exploson of a bomb. I think the forces the person exerts on both the book and the earth are internal since they are equal but opposite therefore resulting in the position of the centre of mass of the system being maintained and if i'm right is the mechanical energy of the system constant?  Am i wrong? Please correct me. How do I make Chromium use Flash from Google Chrome? Now, that Adobe has stopped issuing new releases for Linux desktops, the only option for users is to use Google Chrome, for those who want to use the latest Flash updates. I use Chromium. Is there any way to get Chromium use the Flash from Google Chrome? The reason I as this question is that I have noticed both these browsers run in the background, so technically, the browsers' plugins are available to use. Determine destination location of apt-get install ? Minecraft looks like a bad texture pack I am playing Minecraft 1.12 but today the in-game textures look much lower quality than usual. I don't have any of the super secret settings turned on, and I'm unsure how to fix this and get the normal textures back.