In S07E07 "The Dragon and the Wolf" of Game of Thrones, while Jaime is preparing his troops to march to Winterfell, Cersei pulls him aside &amp; tells him she means to double cross the rest. She has no intention of helping Dany &amp; Jon.     Jaime says he made a promise to fight for the living &amp; he intends to keep it &amp; abandons Cersei. She calls it treason &amp; nods to The Mountain to kill Jaime. He draws his sword &amp; blocks Jaime's way.     Jaime calls out this bluff &amp; walks away from her &amp; The Mountain doesn't do anything. How did Mountain interpret Cersei intentions really. Cersei doesn't nod again for him to stop. He's supposed to be an undead mute.     Why didn't The Mountain enforce Cersei's order to kill Jaime?
Spoilers from the Season 7 finale of Game of Thrones, "The Dragon and the Wolf".  In one of the final scenes, Jaime and Cersei are discussing Jaime's future with them, at which point       Cersei nods her head, signaling the kill order for 'The Mountain', yet 'The Mountain' pulled out his sword but why didn't he kill Jaime?
How to prove that $L=${$a^p$: p is prime} isn't regular? I tried using pumping lemma or finding infinite equivalence classes, but I didn't succeed.  It's clear to me that there is no automata that accepts this language, but I just can't formally prove that this language isn't regular.  How can you prove it? What is the most straight forward way to downgrade Firefox 57 to Firefox 56?   This is to have more time to wait for working replacements for legacy extensions. I saw the sentence like     Donald Trump to run for president next month.   in the newspaper on the internet.  But I don't know why we have to use to instead of will.  Is there any rule I don't know?  Can anyone tell me the reason why we should use to in the news? Proving that expression is equivalent to the definition of derivative Let $f$ be differentiable at $x=a$.   Prove that if $x_n \to a^+$ and $y_n \to a^-$ then:  $$\lim_{n\to \infty} \frac{f(x_n)-f(y_n)}{x_n-y_n}=f'(a).$$  Every option that I think about seems to my very trivial, so I believe that I am doing something wrong.  Both numerator and denominator approach zero as $n\to\infty$ as the case of the formal definition of derivative, but it isn't guaranteed that the limits are equal (“$\frac{0}{0}$”).   Any direction? I am auditing a Linear Algebra class, and today we were taught about the rank of a matrix. The definition was given from the row point of view:      "The rank of a matrix A is the number   of non-zero rows in the reduced   row-echelon form of A".   The lecturer then explained that if the matrix $A$ has size $m  \times n$, then $rank(A) \leq m$ and $rank(A) \leq n$.   The way I had been taught about rank was that it was the smallest of    the number of rows bringing new information the number of columns bringing new information.    I don't see how that would change if we transposed the matrix, so I said in the lecture:  "then the rank of a matrix is the same of its transpose, right?"   And the lecturer said:   "oh, not so fast! Hang on, I have to think about it".   As the class has about 100 students and the lecturer was just substituting for the "normal" lecturer, he was probably a bit nervous, so he just went on with the lecture.  I have tested "my theory" with one matrix and it works, but even if I tried with 100 matrices and it worked, I wouldn't have proven that it always works because there might be a case where it doesn't.  So my question is first whether I am right, that is, whether the rank of a matrix is the same as the rank of its transpose, and second, if that is true, how can I prove it?  Thanks  :) Etiquette, rules, or advice on which site to pose a question? (Or, why are there so many StackExchange sites?) Basically: I have a question I want to ask regarding using Apple's AppleScript/Objective-C bridge (Objective C wrapped in AppleScript, basically) to implement an HTML/WebKit-based pager (a drop-in for less, like vimpager) and a HTML-ized manpage writer, which should also be capable of rendering to PDF via pandoc/pdftex, etc.  Is this a:   Stack Overflow question? (C/Objective-C, APIs) Ask Different question? (AppleScript) Unix &amp; Linux question? (implementing a pager which is a drop-in for a *nix utility) TeX question? (PDF rendering) All of the above?   Where and how should I ask this, in order to increase the likelihood of the "right person" seeing it?    Edit: I believe this question was too hastily closed as a duplicate.  While the best answer to this question is indeed identical to answer to the other:     Ask the question on the site you think is most applicable. If ... it does not get any answer,   ask a moderator to migrate the question, or alternatively, delete it and re-ask it.   The so-called "duplicate" in question asks     Is cross-posting permitted on multiple Stack Exchange sites if the question is on topic?   whereas this question asks,     Where and how should I ask this [ question that is on topic on multiple Stack Exchange sites? ]     That is to say, if two similar but materially different questions have identical answers, it does not necessarily follow that the questions are likewise the same.  Calling them duplicate questions does a disservice to both and the site in general I think. Use (or non-use) of articles before abstract nouns Redirect a portion of a bash script to a file to capture set -x output I need to have one column as the primary key and another to auto increment an order number field. Is this possible?  EDIT: I think I'll just use a composite number as the order number. Thanks anyways. Is it (and if yes how?) possible to define an an binary operation $*$ for an arbitrary set $M$ such that $(M,*)$ is a group?  If $M$ is finite or countable infinite this is trivial, but is it also possible for any other sets? And if yes how can you construct $*$? If no can you provide a counterexample? Prove, in this figure, that $EFGH$ is a parallelogram I've just upgraded from Ubuntu 18.04 to its newest LTS version - 20.04. While it comes with some interesting changes, the Desktop icon system was messed up in my opinion. When you hover the mouse cursor over the icons, you see a huge space marked around them that cannot be violated (as you can see in the image below) so that they need to be placed very far apart from each other.  18.04 allowed you to place icons much closer to each other and didn't have that marked space around them. This new way leaves much less space on the Desktop to organize large amounts of icons - including folders, files and shortcuts. Is there a way I can significantly reduce the size of icons and their "spaces" or go back to the old system of organizing files? On "Settings", there is a tool to change the size of Dock icons, but not of Desktop icons.  Also, every time I move or delete something, the Desktop "flashes" and the icons seem to rearrange themselves automatically, nothing of which happened in 18.04. I also can't move anything directly to the Desktop; I need to move to the Desktop folder on Nautilus. This makes me start to think about downgrading Ubuntu back to 18.04. I know the past tense carries the past tense in every dependent clause, but referring specifically to places or to things that are eternal, like the Earth, seems a bit weird and therefore we sometimes (I believe incorrectly) say     He didn't know that New Jersey was actually on the East Coast.   Because it still is. Or     He thought the Earth was round.   So is it square now?  Logically speaking, would you consider the use of past tense here a bit confusing in a day-to-day speech in these examples? Would you instinctively opt for using the present tense? I am not a native speaker. On a previous question of mine, I thanked for an answer by saying:     So the phrase is not an idiom, since it is applied in its literal sense.   I consciously chose since over because, because — well, I like that usage of since, even though I know that some (native speakers) don't like it. Nonetheless, that choice got me thinking for a while, and it occurred to me that I even could have used more alternatives, namely as or for, without changing the meaning.   So, on a general note, here are the alternatives:        Statement A (is true), because statement B (is true).   Statement A (is true), since statement B (is true).   Statement A (is true), as statement B (is true).   Statement A (is true), for statement B (is true).      Are these completely interchangeable? Or interchangeable in certain situations? Or can you point out any (not-so-)subtle differences between any of them? Are there even more synonyms? Old post apocalyptic cartoon where the main character has red hair and lives with a nomadic group ON an American street, but IN a British one. Do the twain ever meet? Make "axis cs" the default coordinate system in a PGFPlots plot I would like to know if there is a way to specify axis cs to be the default coordinate system inside a plot in PGFPlots, so I don't have to type axis cs: in front of every coordinate pair. Here's a MWE that shows what I mean (the actual plot is irrelevant).  \documentclass{article}  \usepackage{pgfplots}  \begin{document}  \begin{tikzpicture}  \begin{axis}[               xmin=0,               xmax=80,               ymin=0,               ymax=80,               grid=major,              ]   \fill [green, opacity=0.5] (axis cs:14,14) -- (axis cs:80,47) -- (axis cs:80,80) -- (axis cs:47,80) -- cycle;   \fill [red, opacity=0.5] (0,0) -- (axis cs:80,0) -- (axis cs:80,47) -- (axis cs:14,14) -- (axis cs:47,80) -- (axis cs:0,80) -- cycle;   \draw [thick] (axis cs:47,80) -- (axis cs:14,14) -- (axis cs:80,47);  \end{axis} \end{tikzpicture}  \end{document} Windows installer for Ubuntu 14.04 LTS onwards Is there any Windows installer (wubi) for Ubuntu 14.04 LTS?  When I mount the .iso file with Daemon Tools and run wubi.exe, it just asks me if I want to reboot (I think that's useful only when the .iso  is burned on CD), so is there no "real" installation? How can I disable a tab inside a TabControl? Is there a way to disable a tab in a ? If $A^{2n}=I$, then $A^n=\pm I$ where $A\in M_n(\mathbb{R})$ Let $A\in M_n(\mathbb{R})$be a matrix. Then, if we have $A^{2n}=I$, can we say that $A^n=\pm I$?  I think yes, because the annihilating polynomial is $x^{2n}-1$. Therefore the characteristic polynomial should be one of $x^n-1$ or $x^n+1$. Thus, since the matrix consists of real numbers, therefore, the matrix $A^n=\pm I$. Am I wrong?Thanks beforehand.