When do you pronounce 'neither' as [nˈiːð.ə(ɹ)] and when [nˈaɪð.ə(ɹ)]?
Is there a rule in British English about how to pronounce "either"?
Let me add or change edit summary during edit window (grace period) Finding the unique rock with its weight I have 12 rocks, all have the same weight except for one rock, but I don‘t know which rock is. How do I know which rock is different from other, and also know that rock heavier or lighter, with maximum 3 comparating steps. My only tool is just a balance that can only compare the weight between the rocks. TypeError: Element-wise multiplication: not supported between 'Matrix' and 'Vector' A question on $p$-groups, and order of its commutator subgroup. $\textbf{QUESTION-}$ Let $P$ be a p-group with $|P:Z(P)|\leq p^n$. Show that $|P'| \leq p^{n(n-1)/2}$.  If $P=Z(P)$ it is true. Now let $n &gt; 1$, then  If I see $P$ as a nilpotent group and construct its upper central series, it will end , so let it be,  $e=Z_0&lt;Z_1&lt;Z_2&lt;......&lt;Z_r=P$   Now as $Z_{i+1}/Z_i=Z(P/Z_i)$, so if if I take some $x\in Z_2$\ $Z_1$ then $N$={$[x,y]|y\in P$} $\leq Z_1(P)$ and $N \triangleleft P $, so $P/N$ is a group with order $\leq p^{n-1}$.  Now if I let $H=P/N$ then obviously |$H/Z(H)$|$\leq p^{n-1}$.  Now $H'\cong P'N/N \cong P'/(P' \cap N)$ so from here I could finally bring $P'$ atleast into the picture, now |$P'$|=$|H'|.|P'\cap N|$ so $|P'|\leq |H'||N|$.   This is where I am $\textbf{STUCK}$  Now , from here how can I calculate or find some power $p$ bounds on $|H'|$ and $|N|$ so i could get my result. Who should I be damage buffing as Mercy I just started playing Overwatch (played a few games during open beta, but wasn't able to play much). I'm enjoying Mercy, but who (in a group situation) should be getting the damage buff? Additionally, when my team splits up, who should I follow to support? How does "Reputation" work? On Stack Exchange, users may gain a certain level of reputation.  What does reputation do? How can a user gain or lose reputation?   See also   in the Help Center  - Maximum amount of votes a user can use in a day and reputation requirements to vote.  - How to get an exact overview of the actions that got you your reputation.  - A full list of all privileges granted at each reputation level on all sites. Suppose an entire function $f$ is real if and only if $z$ is real. Prove that $f$ has at most $1$ zero. Let $f$ be an entire function. Suppose $f(z)$ is real if and only if $z$ is real. Prove that $f$ has at most $1$ zero. How to prove? Totally I have no idea... Please give the solution in detail since I do not understand. Quicksort vs heapsort Why can't I cd to a quoted tilde ('~')? Writing my first script so I'm sure this is a basic question, but can someone please explain to me why I can:  cd ~ cd bin cd ~/bin cd 'bin'   But not  cd '~' cd '~/bin'   I need to cd to a directory path with a space in one of the directory names, so I need the quotes (it's Windows Program Files under wine). I can get around it with two cd commands, but why can't I put ~ in quotes?  If I type cd '~' (or cd "~") I get:  bash: cd: ~: No such file or directory Initial note: Having read , the answers there do not help in this specific situation, as they rely on having lots space to spare - I have very little.  When I started my city, I designed a simple exit from the default highway that I thought was sustainable: I left enough space around it to upgrade the road as I needed to, which has worked up until now. However, I am now stuck with a six-lane one-way exit from the highway that isn't getting used: since cars seem to pick the most efficient lane to get where they want to go, regardless of traffic, the rightmost lane fills up, then spills over onto the highway. This blocks the highway, my bus routes, and more importantly my planned emergency routes.  My setup looks like this:    The red arrows show road direction, and the orange line is the traffic backed up. Note that in this image, I have replaced the six-lane one-way exit with a highway exit, as this is just about as efficient...  This situation is getting to be pretty bad, and is bringing half my city to a standstill. Its effects compound themselves further down the highway:    In this image, the orange line is the traffic directly caused by this exit not working. This traffic jam then blocks two exits/entrances further down, on the red crosses; the yellow line shows the traffic jam caused by these being blocked. In other words, my inefficient exit design is now blocking itself from moving.  So this is a two part problem.   Considering that I'm constructing a residential district in the space above left of the problem exit, and would like to keep the solution inside the power line, how can I redesign this exit to be more efficient? How do I solve the ring of traffic jams? Is it a simple case of just deleting and replacing a bit of road? Prove a function is constant under certain conditions Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be smooth and such that for every $x$    $$\int_{-\infty}^{\infty}\frac{|f(x)-f(y)|}{|x-y|^2}dy &lt; \infty$$   Prove that $f$ is constant. In Oblivion, I had two favorite money-makers:   Dump all my stuff except some basic armor and potions, and raid an oblivion tower. The armor and weapons was worth lots, and selling it in Anvil made a lot of cash fast. Harvest an entire farm's worth of crops, create 'restore fatigue' potions and sell them.   Skyrim seems to spoil this:   Merchants have a max-amount per day/QOD/... instead of per item You can't carry as much (or maybe I have yet to discover the strength/feather spells) Alchemy is a lot harder (most common items go into food recipes now, which don't sell for those prices) On top of that, once a dungeon is cleared, it doesn't respawn - so no 'farming' familiar dungeons?   What are some easy/repeatable money making methods in Skyrim? Which are most efficient effortwise/real-life-time wise? Is it possible to scale specific apps on Windows 10? Just read this which basically says you can freeze and thaw food in the fridge any number of times.    I'm still unclear on one point. If I had food which would be good in the fridge for 4 days and i put it in the freezer after 3 days, when I put it back in the fridge is my food good after its thawed for another 4 days or 1 more day? How can I find out which process is locking a file or folder in Windows?  For instance, when trying to delete a folder, Windows reports this:     The action can't be completed because the folder is open in another program   Happens the same with a file, but how do I find out what program or application is currently using it and preventing me from deleting the file or folder? Remove Meta Privilege for MSE (only) What is a more efficient way to draw this tree? I have drawn the following tree in TikZ. What I don't like about it is   that I have to manually adjust the sibling distance for each level; and the syntax is too cumbersome.   It has been suggested to me by @percusse and @AlanMunn that using tikz-qtree and/or forest may be a more efficient way to produce the same result. But I don't have experience in using either package.   It would be nice if someone can reproduce my example using either of these packages, so that I can have quick example to learn from instead of reading a 150-page manual trying to find an answer.    \documentclass{standalone} \usepackage{tikz} \usepackage{amsmath}  \begin{document}  \tikzset{   % Two node styles for game trees: solid and hollow   solid node/.style={circle,draw,inner sep=1.2,fill=black},   hollow node/.style={circle,draw,inner sep=1.2}, }  % macro for entering payoffs \newcommand\payoff[1]{   $\begin{pmatrix} #1 \end{pmatrix}$ }  \begin{tikzpicture}[font=\footnotesize]   \tikzset{     level 1/.style={level distance=15mm,sibling distance=65mm},     level 2/.style={level distance=15mm,sibling distance=30mm},     level 3/.style={level distance=15mm,sibling distance=15mm},     level 4/.style={level distance=15mm,sibling distance=10mm},   }    \node[hollow node,label=above:{Nature}]{}     child{node[solid node,label=left:{P1}]{}       child{node(l1)[solid node]{}         child{node[solid node,label=below:{\payoff{1\\-1}}]{}edge from parent node[left]{L}}         child{node[solid node,label=below:{\payoff{0\\0}}]{}edge from parent node[right]{R}}         edge from parent node[left]{U}       }       child{node(l2)[solid node]{}         child{node[solid node,label=below:{\payoff{0\\0}}]{}edge from parent node[left]{L}}         child{node[solid node,label=below:{\payoff{2\\-2}}]{}edge from parent node[right]{R}}         edge from parent node[right]{D}       }       edge from parent node[left,xshift=-10]{A}     }     child{node[solid node,label=right:{P1}]{}       child{node(r1)[solid node]{}         child{node[solid node,label=below:{\payoff{-2\\2}}]{}edge from parent node[left]{L}}         child{node[solid node,label=below:{\payoff{0\\0}}]{}edge from parent node[right]{R}}         edge from parent node[left]{U}       }       child{node(r2)[solid node]{}         child{node[solid node,label=below:{\payoff{0\\0}}]{}edge from parent node[left]{L}}         child{node[solid node,label=below:{\payoff{-1\\1}}]{}edge from parent node[right]{R}}         edge from parent node[right]{D}       }       edge from parent node[right,xshift=10]{B}     }   ;    \draw[dashed](l1)--(l2)--node[midway,above]{P2}(r1)--(r2); \end{tikzpicture}  \end{document} Do you have to take the second leg of a domestic flight? How can I get admin access to a Mac without knowing the current password? My Father died last year and I inherited his Mac Mini. My wife has retired and we are trying to set up the mini for her use but the changes we want to make require admin access and we do not have the information my father used to set up the machine.  Is it possible to reset the admin information without having the old information? If so, how would I go about it?   I am not a Mac user usually so any guidance will have to be pretty simple! Similar to , what's the best way to stay up to date with the latest stable releases of Thunderbird?