*I need to practice the piano 'a lot' before the concert.*   Using 'a lot' vs 'much' sounds better, but how do I explain this since 'a lot' and 'much' can be used for uncountable items. Is it incorrect to use 'much' or is it just more common to use 'a lot'?
I found the below in  web-site:     We use much in questions and negative clauses to talk about degrees of something.      We don’t use much in affirmative clauses.   Also, it the same web-site, I found the following:     She runs much faster than he does.    also I noticed that some web-sites use much with affirmative clauses:     May we all be having this much fun and getting this much exercise when we're his age!    Is it Okey to use much in affirmative clauses? If yes, when can we use it? and what is the rules?  Update:  Here is another example on how often the word "much" is used  in informal style:     After much consideration I will NOT be performing at the Inauguration with my improv group Capitol Hill-arious
Short story about a woman that travels to other planets. Read online recently. She just manages to live long enough to embrace new technology Can spells with movable areas of effect be moved out of sight or behind obstacles? With spells like Moonbeam or Flaming Sphere, how should we treat the movement of their areas-of-effect when it comes to passing them behind a thick pillar or around a blind corner?  Should we treat any movement of them as if they are being 're-cast' (and so requiring a clear unobstructed view)? Or could a mage presumably will them somewhere out-of-sight? Can anyone help me out with how to make Bing Picture to my Desktop Wallpaper?    So it works by downloading the highest quality of todays picture. Then storing it ex in the Picture folder of your account. After that automatically changing the picture itself.  It should continue the same everyday without hassle in the background.  Probably something I have to add in the Startup Applications. Any differences between Ubuntu versions?    -Do I have to write a script?  This would be appreciated by many others too! Thank You in Advance :) Can we clarify to the OP that their question is not yet closed and the duplicates are only suggestions? I keep seeing custom flags in the queue from question askers who are incredibly irritated because there is a big, prominent box at the top of their question. It's just a list of other questions which may have the answer they desire, and is only even displayed to them because the question is not closed yet.  This question may already have an answer here: [list]  But to an ordinary user, it is not at all clear that the box is only shown to them, or that it will go away on its own if their question never actually gets closed. Could the text for this notice be altered to make it more clear that:  They are just suggestions for the person to view. Potentially if they agree with one, they should vote to close their own question as a duplicate of it.  Their question is not closed yet. If they disagree with the duplicates suggested, they should clarify their question and explain why it's not a duplicate.   I was thinking of an altered wording such as:  You might be able to find an answer to your question here: [list] If those answers do not fully address your question, please [edit your question] to clarify your exact problem.  I went with a more direct wording for the bolded title. Since the notice is only displayed to the asker, it makes more sense to talk directly to them in the message rather than making it feel like it's supposed to be addressing the entire audience of the site. Emphasize that only that person is seeing it by talking to them. It would also be helpful to append a &quot;More info&quot; link at the end of the message that links them to some further documentation about duplicates, and explains how the notice works - particularly that it will go away eventually or change to a proper duplicate notice if the question does get closed. Fixed points under action of conjugate group elements Lecture notes:  If $g$ and $h$ are conjugate then $fix(g)=fix(h)$. To see this, say $g=k^{-1}hk$  If $g.s=s \iff k^{-1}hk.s=s \iff h.(k.s)=(k.s)$  Me: I understand the last line- I just fail to see how it implies $fix(g)=fix(h)$  EDIT: As Ben S says I think there was a typo in the notes and they forgot modulus signs so- New Aim: show $|fix(g)|=|fix(h)|$ Do we really need polynomials (In contrast to polynomial functions)? I execute quite a lot of sudo commands.  I noticed that if I execute one and then another one within few minutes, the 2nd time I don't get the message:     [sudo] password for my_username:   but I do get it when there is more time between the execution of the two commands.  What's the period of time in which the message is not appearing? How can we check it / update it? What is the difference between 'located in' and 'located on'? $\int_{\frac{1}{3}\pi}^{\frac{2}{3}\pi} {\sin(x)\;dx}$ using Riemann sums? Can Ubuntu use all my 4GB of RAM? I heard the following comment of Mr. Marco Rubio about Mr. Donald Trump on CBS’s “Face the Nation” in a clip in February 29th AP Radio News:  “There is never gonna be a time where the Republican Party rallies around and says you have to get out or anyone has to get out for purposes of rallying around Donald Trump. Donald Trump is not Republican Conservative. Donald Trump is trying to pull off the biggest scam in American political history.”  I thought I misheard “There is never gonna be a time where –“ for “There is never gonna be a time when –“ at first, because I was in understanding that time should be trailed by “when” as a relative noun or adverb. An English Japanese dictionary at hand (Readers English Japanese Dictionary published by Kenkyusha) provides “where” singly as a relative to refer the ‘place.’ However, my lookup of the following two sources endorsed that I heard it right:  Here is what is never going to happen in this race. There's never going to be a time where the Republican Party rallies around and says you have to get out or anyone has to get out for purposes of rallying around Donald..  “Here is what is never going to happen,” Rubio continued. “There's never going to be a time where the Republican Party rallies around and says you have to get out or anyone has to ...   Is it common, at least not uncommon to use “where” after “time” as a relative? Origins of Tension First of all, I have a confusion about the definition and idea of Tension. For example, in my Physics Textbook, the idea of tension is written like this: &quot;Let's say there is a wire with a cross-section area of A and its length is $L_o$. If I hang the wire from a point and hang a weight of W on the other end of the wire, it will generate a repulsive force of T. This T is called the Tension Force.&quot; For me, this only explains to me what force will we call tension force, but it doesn't quite explain to me what is exactly this Tension force or where it originates from. Also, I have been doing pulley problems (Figuring out the acceleration of weights hanging from pulleys)  by first labeling all of the tension forces by $T_1$, $T_2$, and then doing some math with them to get my answer. But It bugs me that I am using these tension force values without even knowing where they came from or what they are. My idea was, maybe Tension force comes from the intermolecular bonds between the molecules of the rope, rubber or wire, etc. But even then, I have some different situational questions. For example:  Why you can't push a rope, copper wire against a wall?  What happens when I pull on two ends of a wire with 2 different forces?  Does the force increase proportionally to the applied force? Why does the wire break after a certain amount of force is exceeded.?  Does the idea of tension apply to everyday objects,(for example, a coffee mug, glass pane, etc). If it does, can I use something like a heat map or 3D equation to describe the tension in every point of the object? [Edit: more concisely, is there a mathematical way to show the various amounts of tension forces on a 2D (like a metal sheet) and 3D objects (like a football ) instead of a 1D object(like a string)].  If I take a metallic object like a paperclip or a thin wire. I can bend It multiple times and it eventually breaks into two pieces. I used to do this to pull of capacitors from old circuit boards. But does it happen with things like ropes or paper? If not, why it doesn't happen? ( Maybe it has something to do with intermolecular forces and the various internal stresses?)  Let's say I have an iron bar and I have thrown it out into space. Does that iron bar have equal stress distribution or still uneven or will the stress on all points become zero? (Is there even such thing as zero stress?) I have a problem with using "too" in a sentence. In what situation would you use "too" instead of "so" or "very"? Please include an example to illustrate the difference. Direct product of abelian groups Let $G_1,\dots,G_n$ be groups. Prove that the direct product $G_1\times\cdots\times G_n$ is abelian if, and only if, each of $G_1,\dots,G_n$ is abelian. To prove that the direct product is abelian is straightforward but what I don't understand is the converse. Don't you think people need to know what they did wrong exactly so they can fix it and get unbanned from asking questions or posting answers? Is there a continuous bijection from $[0,1]$ onto $[0,1] \times [0,1]$? That is with $I=[0,1]$ and $S=[0,1] \times [0,1]$, is there a continuous bijection $$ f: I \to S? $$  I know there is a continuous bijection $g:C \to I$ from the Cantor set $C$ to $[0,1]$. The square $S$ is compact so there is a continuous function  $$ h: C \to S. $$ But this leads nowhere. Is there a way to construct such an $f$?  I ask because I have a continuous functional $F:S \to \mathbb R$. For numerical reason, I would like to convert it into the functional $$ G: I \to \mathbb R, \\ G = F \circ f , $$ so that $G$ is continuous. Will my passport number change when I renew it? When writing a book and referring to a female and male aged 18–25, what term would be most appropriate? Boy and girl seem too young, whereas man and woman seem too old.  Example sentence:     A boy/man emerged from the shadows.   Edit: I think the word I am looking for is similar to 'guy' but less American and colloquial. Any thoughts? How do I get a vanilla GNOME after Ubuntu 17.04? Some people (me) would prefer the straight GNOME experience as opposed to the Unity style desktop offered in Ubuntu 17.10.  How can I get the standard GNOME desktop and interface? What is the difference between a field and a property?