Do "who" questions not get auxiliary verb?
Do I have to use “do” in any “wh-” question?
Please excuse the selfishness of the following question:     Let $G$ be a group and $H \le G$ such that $|G:H|=2$. Show that $H$ is normal.   Proof:  Because $|G:H|=2$, $G = H \cup aH$ for some $a \in G \setminus H$.   Let $x\in G$. Then $x \in H$ or $x \in aH$.  Suppose $x \in H$. Then $xhx^{-1} \in H$ because $H$ is a group.  Suppose $x \in aH$. Then $ahH(ah)^{-1} = ahHh^{-1}a^{-1} = a(hHh^{-1})a^{-1}$ ***1  ***1: Can I say now that $x \in H$, based on the that $hHh^{-1} \in H$ and that $aa^{-1} = e$ ?  Thank you for the time you spent reading my doubts. Set "this" variable easily? Assigning Float Pointers in C Using the properties of real numbers, verify commutativity on complex numbers. I have just started self-studying Linear Algebra after a 3 year hiatus from mathematics (in an extended neuroscience foray), and I want to ensure that I am sufficiently verifying commutativity of complex numbers by using the properties of real numbers.  My attempts...  (1) Commutativity of Addition:   Verify that $w + z = z + w$ for all $w, z \in \mathbb{C}$.  $$w + z = (a + bi) + (c + di) \hspace{10mm}\text{by definition of }\mathbb{C}$$ $$\hspace{13mm} = a + (bi + c) + di \hspace{10mm}\text{by associativity in }\mathbb{R}$$ $$\hspace{17mm} = a + (c + bi) + di \hspace{10mm}\text{by commutativity in }\mathbb{R}$$ $$\hspace{16mm} = (a + c) + (bi + di) \hspace{10mm}\text{by associativity in }\mathbb{R}$$ $$\hspace{19mm} = (c + a) + (di + bi) \hspace{10mm}\text{by commutativity in }\mathbb{R}$$ $$\hspace{13mm} = c + (a + di) + bi \hspace{10mm}\text{by associativity in }\mathbb{R}$$ $$\hspace{17mm} = c + (di + a) + bi \hspace{10mm}\text{by commutativity in }\mathbb{R}$$ $$\hspace{17mm} = (c + di) + (a + bi) \hspace{11mm}\text{by associativity in }\mathbb{R}$$ $$\hspace{13mm} = z + w \hspace{34mm}\text{by definition of }\mathbb{C}$$  $$\blacksquare$$  This seems a bit verbose to me - is it acceptable to combine steps? For example, rather than:  $$w + z = (a + bi) + (c + di) \hspace{10mm}\text{by definition of }\mathbb{C}$$ $$\hspace{13mm} = a + (bi + c) + di \hspace{10mm}\text{by associativity in }\mathbb{R}$$ $$\hspace{17mm} = a + (c + bi) + di \hspace{10mm}\text{by commutativity in }\mathbb{R}$$ can I instead write: $$w + z = (a + bi) + (c + di) \hspace{10mm}\text{by definition of }\mathbb{C}$$ $$\hspace{48mm} = a + (c + bi) + di \hspace{10mm}\text{by associativity and commutativity in }\mathbb{R}$$?  (2) Commutativity of Multiplication:  Verify that $wz = zw$ for all $w, z \in \mathbb{C}$.  $$\hspace{-14mm}wz = (a + bi)(c + di) \hspace{24mm}\text{by definition of }\mathbb{C}$$ $$\hspace{4mm} = a \cdot c + a \cdot di + bi \cdot c + bi \cdot di \hspace{10mm}\text{by distribution in }\mathbb{R}$$ $$\hspace{9mm} = a \cdot c + bi \cdot c + a \cdot di + bi \cdot di \hspace{10mm}\text{by commutativity in }\mathbb{R}$$ $$\hspace{35mm} = c \cdot a + c \cdot bi + di \cdot a + di \cdot bi \hspace{10mm}\text{by multiplicative commutativity in }\mathbb{R}$$ $$\hspace{1mm} = c(a + bi) + di(a + bi) \hspace{20mm}\text{by distribution in }\mathbb{R}$$ $$\hspace{5mm} = (c + di)(a + bi)\hspace{34mm}\text{by distribution in }\mathbb{R}$$ $$\hspace{4mm} = zw \hspace{55mm}\text{by distribution in }\mathbb{R}$$ $$\blacksquare$$  This also seems a bit wonky to me. Any and all suggestions on clearing up my verification, reasoning, etc. would be greatly appreciated! Is there a way to create synchronization profiles for Google Chrome? For example I want to tag some of my browsers as "home browser"s and others as "work browser"s and I want:   my bookmarks to be synced with all browsers, my extensions to be synced only within browsers of the same type (home with home, work with work) Better way of saying "those who are curious"? I am writing a note in which I want to ask (curious) readers to refer another paper. The phrase curious minded comes to mind, but it seems somewhat awkward.  Is there a better way to convey similar import? Are global variables thread-safe in Flask? How do I share data between requests? When I run LaTeX file its gives error as  "! Package minted Error: You must have pygmentize installed to use this package", you must have pygments installed. when I go through minted documentation minted itself required pygments, so Tex friend How do I install this pygment, I don't know the procedure to install. Please guid me or any link pygement.exe file What is the difference between "INNER JOIN" and "OUTER JOIN"? Also how do LEFT JOIN, RIGHT JOIN and FULL JOIN fit in? Software center disappeared [19.10] I have had trouble with sound (now fixed) since upgrading to 19.10, and in the middle of trying the common solutions, the Software Center "disappeared". I got aware of quite late, so I don't know what caused it.  Anyway, would you know how to reinstall it ? Trying sudo apt-get install software-center doesn't work. Is it possible to set the GPU fan speed using the default free ati driver?  My card (X1900) was deprecated in the fglrx drivers a while back.  The free drivers seem to work with 3D, Compiz and such, but running graphics intensive programs makes my GPU heat up and produce artifacts, while the GPU fan never seems to increase. (When set to 100% in Windows it makes a massively louder noise.) the least possible value for :$ \lfloor \frac{a+b}{c}\rfloor +\lfloor \frac{b+c}{a} \rfloor+\lfloor \frac{c+a}{b} \rfloor $ If we know that for every $a,b,c&gt;0$ ,how we can find  the least possible value for :  $$ \lfloor \frac{a+b}{c}\rfloor +\lfloor \frac{b+c}{a} \rfloor+\lfloor \frac{c+a}{b} \rfloor $$ Why doesn't saturation current in the photoelectric effect depend on the frequency of light absorbed ny the metal emitter? I'm trying to recall the title of a young adult-targeted book. It was probably published by Scholastic, or at least sold through their take-home pamphlets, which means it was probably published before I started high school in 1996. It's about a group of teenagers who receive invitations to play a game at an invitation-only arcade. When they go there, they are put in an immersive VR game in which they must learn to survive on an alien planet. I believe the game ends and they wake up back in the real world after they fall asleep on the alien one. They are invited back the the game a couple times, and then it turns out…      …they go to play the game again, but they are unable to exit it. Eventually they realize that they actually are on an alien planet now, and that the previous game-playing sessions were just training for the real thing. I believe the epilogue states that all of the players have coupled up and the females have become pregnant, and they are optimistic about populating the new planet.   I think it was told in the first-person perspective of a female player. I don't think there was a real protagonist or strong conflict; just the group of players learning how to survive in the game. One of the other players had a photographic memory and used it to map the planet's surface. I think the cover art featured of a girl wearing a VR headset over her eyes, with her hair being blown back and her mouth open in surprise. What are the fundamental differences between the mainstream *NIX shells? What are the fundamental differences between the mainstream *NIX shells and what scenarios might prompt you to use one over the other?  I understand that some of it probably comes down to user preference but I've only ever used Bash and I'm interested to hear where another shell might be useful. Also, is there an impact on user-written shell scripts when running under one shell or another or is it simply a matter of changing the shell at the top of the file?  My instinct says it's not that easy. The runtime arguments are as follows: $1 is the path to the file containing the list of files $2 is the path to the directory containing the files What I want to do is check that each file listed in $1 exists in the $2 directory  I'm thinking something like:  for f in 'cat $1' do if (FILEEXISTSIN$2DIRECTORY) then echo '$f exists in $2' else echo '$f is missing in $2' sleep 5 exit fi done   As you can see, I want it so that if any of the files listed in $1 don't exist in the directory $2, the script states this then closes. The only part I can't get my head around is the (FILEEXISTSIN$2DIRECTORY) part. I know that you can do [ -e $f ] but I don't know how you can make sure its checking that it exists in the $2 directory. IF/ELSE script in sender profile I'm trying to create a dynamic sender profile where the from name and from email change if a value is present in a specific field of the data extension. I want the Lead First Name value and Lead Last Name values to appear. I'm trying to keep all the logic in the sender profile. %%=IIF(EMPTY(AttributeValue(&quot;X&quot;)), &quot;Bill&quot;, AttributeValue(&quot;LeadFirstName&quot;) AttributeValue(&quot;LeadLastName&quot;))=%%  Not sure why, but doing the test, the script shows up as the sender and isn't resolving. Show that any prime ideal from such a ring is maximal. Let R be a commutative ring with an identity such that for all $r\in$ R, there exists some $n&gt;1$ such that $r^n = r$. Show that any prime ideal is  maximal. (Atiyah and MacDonald, Introduction to Commutative Algebra, Chapter 1, Exercise 7.)    Any hints? Delete with Join in MySQL Here is the script to create my tables:   CREATE TABLE clients (    client_i INT(11),    PRIMARY KEY (client_id) ); CREATE TABLE projects (    project_id INT(11) UNSIGNED,    client_id INT(11) UNSIGNED,    PRIMARY KEY (project_id) ); CREATE TABLE posts (    post_id INT(11) UNSIGNED,    project_id INT(11) UNSIGNED,    PRIMARY KEY (post_id) );   In my PHP code, when deleting a client, I want to delete all projects posts:  DELETE  FROM posts INNER JOIN projects ON projects.project_id = posts.project_id WHERE projects.client_id = :client_id;   The posts table does not have a foreign key client_id, only project_id. I want to delete the posts in projects that have the passed client_id.  This is not working right now because no posts are deleted. "(" or "\left(" parentheses? What is the difference between ( and \left( in LaTeX? Sometimes, when the content is small, it does not seem to matter which pair I use.  What is the best practice when it comes to which parentheses use?