help you do (or) to do something - difference I know that generally native speakers say it usually like this (without the to):     These exercises will help you get better at math.   Can you help me move these boxes outside?   But sometimes, though very rarely, I see it used with the to. Like in this example:     This is just so that you won’t forget that you shouldn’t change these values after you first create them. It’s purely optional, but in the pages ahead you’ll see how useful all-capped constants can be to help you to better read and understand your programs.   I still don't really understand the deference between the two usages and don't know when we should use one over the other. Could you please help me get this straight once and for all?
Help to do something or help do something? I wrote:      I will help you to acquire Russian.    A native English speaker corrected me saying that 'to' is unnecessary here. Is it correct to say      "I will help you acquire Russian"
Rendered image doesn't show what Rendered Viewport shows... (pictures below) Make all new files in a directory accessible to a group Suppose I have two users Alice and Bob and a group GROUPNAME and a folder foo, both users are members of GROUPNAME (using Linux and ext3).   If I save as user Alice a file under foo, the permissions are: -rw-r--r-- Alice Alice. However, is it possible to achieve that every file saved under some subdirectory of foo has permissions -rwxrwx--- Alice GROUPNAME (i.e. owner Alice, group GROUPNAME)? How to find infinite sum How to find infinite sum $$1+\dfrac13+\dfrac{1\cdot3}{3\cdot6}+\dfrac{1\cdot3\cdot5}{3\cdot6\cdot9}+\dfrac{1\cdot3\cdot5\cdot7}{3\cdot6\cdot9\cdot12}+\dots? $$   I can see that 3 cancels out after 1/3, but what next? I can't go further. Examples of provably${}^n$ unprovable statements Given any statement $A$ and a classical theory $T$ which we assume is at least as strong as Peano Arithmetic ($\sf PA$), we have that $T\vdash A$ implies $T\vdash T\vdash A$ (that is, if a statement is provable, then it is provably provable). Let $T_1=T$ and $T_{n+1}=T_n+{\sf Con}(T_n)$. (We need stronger theories if we want to prove unprovability.) Given this, simply by considering the truth values of the relevant statements, we get the following classification of statements by unprovability:   $T\vdash A$ ($A$ is provable) $T_2\vdash T\not\vdash A$ ($A$ is provably unprovable) $T_3\vdash T_2\not\vdash T\not\vdash A$ ($A$ is provably unprovably unprovable)   &nbsp;&nbsp;&nbsp;&nbsp;...  &nbsp;&nbsp;&nbsp;&nbsp;$\omega$. For all $n$, $T_n\not\vdash\dots \not\vdash T_2\not\vdash T\not\vdash A$ (we can't say anything about $A$'s provability)  We can refine this hierarchy by also considering the status of $\lnot A$. Let's call a class $m,n$ statement one such that $A$ is at level $m$ above and $\lnot A$ is level $n$ in the list. Since $T\vdash\lnot A$ implies $T_2\vdash T\not\vdash A$, the only nonempty classes at level $1$ are the class $1,2$ statements (provable statements) and the class $2,1$ statements (refutable statements). Independent statements are in class $2,2$. The class $1,1$ is nonempty iff the theory is inconsistent.  My question is: Are there any (preferably "natural") statements that fall further into this hierarchy? I know many examples of independent statements, like the continuum hypothesis or the axiom of choice relative to $\sf ZF$, or the Paris–Harrington theorem relative to $\sf PA$. But I know no examples of even any class $2,3$ statements. I expect there may also be natural examples of $\omega,\omega$ statements. My guess is that all the classes $m,n$ with $m,n\ne1$ are nonempty, but examples elude me. Is there a word for happiness made possible by a tragic situation? What word/phrase can I use to describe the activity of hiding a stupid mistake/incident, such as quickly cleaning up tea spilled by accident before anyone could notice? 17.10 Super key to open applications Gravitational waves as dark energy? We had in our lecture on numerical analysis the following: Let $\mathrm{Lin}(X,Y)$ be the set of all linear maps $X\rightarrow Y$. Let $A\in\mathrm{Lin}(\mathbb R^l,\mathbb R^n)$ and $B\in\mathrm{Lin}(\mathbb R^n,\mathbb R^m)$ and $\|C\|_{op}:=\max_{\|x\|\leq1}\|C(x)\|$. Then our lecturer followed $\|A\circ B\|_{op}\leq\|A\|_{op}\cdot\|B\|_{op}$. So he didn't prove it and so I've tried it by my own. My attempt: $$\begin{aligned} \|A\circ B\|_{\mathrm{op}} &amp;= \max_{\|x\| &lt; 1}\|(A \circ B)(x)\| \\ &amp; \leq \max_{\|x\| &lt; 1} \|A\|_{\mathrm{op}} \|B(x)\| \\ &amp;= \|A\|_{\mathrm{op}} \max_{\|x\|\leq1}\|B(x)\|\\ &amp;= \|A\|_{\mathrm{op}}\|B\|_{\mathrm{op}} \end{aligned}$$ But this seems too easy. I am really interested in a nice proof so anybody could help? Thanks a lot! I am looking for an example such that in a pre-Hilbert space $H$ we have for a subspace $U$ that  (i) $\bar{U} \oplus U^\perp \neq H$  (ii) $ \bar{U} \neq U^{\perp \perp}$  Since finite and closed subspaces will probably not do it, I am not good at inventing nice examples. Does anybody here have a few at hand? I'm going on a vacation from Europe to the US and was planning of bringing along some Xbox360 or PS3 games, but now I'm curious if they will be compatible with my European Xbox.  In that past there would be a clear difference between NTSC and PAL games, but is this still the case with the current gen of consoles? Suppose A is a 3*3  symmetric matrix s.t.  $$\begin{pmatrix} x &amp; y &amp; 1 \\   \end{pmatrix} A  \begin{pmatrix} x  \\  y\\ 1\end{pmatrix}  = xy -1 $$  let p be the no. of positive eigen value of A and q = rank(A)-p, then p=? q=?  what matrix A should be I can't find?? Star rating in AJAX with Ruby On Rails How can swapoff be that slow? Somehow I happened to swap out 14 GB of memory. After having killed the culprit, I have tons of free memory again, so I thought I could  again. So with 5 GB out of 32 GB used and 14 GB of swap space used, I ran swapoff -a.... and 4 hours later about half of the work was finished.  This means less that 1 MB/s, while I can easily copy 200 MB/s. My swap is encrypted but so are all normal partitions and with  it leads to no noticeable CPU load (and filling the swap space took only a few minutes). I see that there's no special reason to optimize swapoff, however I wonder how it could get that slow?    Just adding some more data: My main memory is 32 GB and I have 32 GB swap space on each of 4 harddisks (surely an overkill, but who cares?). The whole swap space can be  (decrypted and) read in less than 5 minutes:  time -p sudo sh -c 'for i in /dev/mapper/cryptswap?; do md5sum $i &amp; done; wait' 014a2b7ef300e11094134785e1d882af  /dev/mapper/cryptswap1 a6d8ef09203c1d8d459109ff93b6627c  /dev/mapper/cryptswap4 05aff81f8d276ddf07cf26619726a405  /dev/mapper/cryptswap3 e7f606449327b9a016e88d46049c0c9a  /dev/mapper/cryptswap2 real 264.27   Reading a part of a partition can't be slower than reading it all. Yet reading about 1/10th of it takes about 100 times longer.  I observed that during swapoff both the CPU was mostly idle (maybe 10% of one core) and so were the disks ("measured" by the LEDs). I also saw that the swap spaces were turned off one after the other. Output two sided, but only on recto page -- occasional images on verso I am preparing a thesis. In order to reduce the number of physical sheets of paper, I need to print certain figures/tables on the verso side. However the university regs state that, while figs/tables may appear on the verso, the body text must appear on the recto side.  I would like to therefore output the vast bulk of the work on the recto page, but with occasional verso pages. Ideally they would be numbered as a "subpage" of the preceeding recto page (e.g. 131, 131a, 132...) or similar.  The approach which I will tentatively adopt is to use a "twoside" flag, then have "empty" and non-numbered verso pages until a page with content is required.   I'm sure I'm not the first person to have had a similar issue, but am unable to imagine other ways of posing the question. Evaluating $\int \sqrt{1 + t^2} dt$? How do we solve (i.e. get the closed form of) $\int \sqrt{1 + t^2} dt$ ?   shows the closed form of it but not the steps in solving it.  I think I need some algebraic trick..   I thought of some hyperbolic functions and their derivatives and equalities:  If I make $ t = \sinh x$, then I can reduce the integral to  $$ \int \cosh ^2 x dx $$ though I'm not sure if this is valid. But from here, I cannot go on evaluating the integral... During the movie, we learned that Ego tried to reproduce the Celestial gene by having a lot of children and then having them delivered to him. I am not sure if Yondu was contracted for all of them but he definitely delivered at least a few of them since he broke the ravager code and got banned for dealing in kids.  My question is: why did he stop with Peter? Was Peter the last one on the contract or did he keep on delivering some but just not Peter?  Also, why didn't Ego seek out Yondu to get his kid back?  I don't think this was touched on in the movie. This was slightly mentioned here () but that is not answering my question.  I think Yondu said it was because he could get to places where the Ravagers could not since he was a kid but that would have been true with all the others kids he abducted for Ego. Cycles final render pitch black? In solid mode with Material or Texture, it is shown fine.   But in the Render mode, everything is pitch black. I have a sun, and the Opacity of the scene is set to 100%.    I am new to using Blender, so I have no idea what is wrong. If you could help, I would appreciate it. If you need more information to help me, I would be glad to give it. How to parse hex values into a uint? uint color;  bool parsedhex = uint.TryParse(TextBox1.Text, out color);  //where Text is of the form 0xFF0000 if(parsedhex)    //...   doesn't work. What am i doing wrong? I am trying to solve the following question which is Ex3 from Arthur Engel, Problem Solving strategies. Here is the question: $\sum_{k=1}^n k^3 {n \choose k}$ and asks to find the sum. I am sincerely having a hard time trying to figure out how to solve it and get $n^2 (n+3)(2)^{n-3}$. I would really appreciate if someone could show the step-by-step process. Thank you!