I know Grammarly is not a precise source for finding grammar-related mistakes. But its verdict on the following sentence perplexes me:      It's necessary for offering pleasant shopping experience to your customers.    Grammarly says that I should write 'a pleasant shopping experience'. My cognition says that experience is a mass noun and therefore, does not require any article prior to it.   Even Google  did not help me much.  What should I write here-pleasant shopping experience or a pleasant shopping experience?
Let's have breakfast    Let's have a good breakfast      I've learned that indefinite articles aren't used before uncountable nouns, so why is a used before the adjective "good" here?    Is there an exception to the rules or is it wrong?
Is there a formula for $(1+i)^n+(1-i)^n$? I was just reading Harry Potter and the Deathly Hallows, and I was wondering, when Hermione Granger changed into Bellatrix Lestrange, she should've obtained the Dark Mark, temporarily.  Now, my question is: would the Dark Mark work if pressed? Search for all files with a .sql extension in folders and sub folders Two players, $A$ and $B$, alternately and independently flip a coin and the first player to get a head wins. Assume player $A$ flips first.  If the coin is fair, what is the probability that $A$ wins?   So $A$ only flips on odd tosses. So the probability of winning would be $$ P =\frac{1}{2}+\left(\frac{1}{2} \right)^{2} \frac{1}{2} + \cdots+ \left(\frac{1}{2} \right)^{2n} \frac{1}{2}$$  Is that right? It seems that if $A$ only flips on odd tosses, this shouldn't matter. Either $A$ can win on his first toss, his second toss, ...., or his $n^{th}$ toss. So the third flip of the coin is actually $A$'s second toss. So shouldn't it be $$P = \frac{1}{2} + \left(\frac{1}{2} \right)^{2} + \left(\frac{1}{2} \right)^{3} + \cdots$$ Can we see emission lines in stars? I read that stars show both absorption and emission lines. While how we see absorption lines is clear to me, I don't understand how (and when) we see the emission lines. Based on what I read in several of your threads such as  we should not be seeing emission lines at all, since all the emissions would come from the hotter interior but those can't reach the outside (unless I misunderstood this point), and the only emission we see is blackbody radiation. But then how do we see the few emission lines such as in the spectrum shown ? Graph editor for shape key animation I have animation where object changes his shape using shape keys, and I want to make some animation smoothing with graph editor. Is there a way to use graph editor for shape key animation? Let $\{X_\alpha\}_{\alpha\in J}$ be a family of topological spaces and let $X=\prod_{\alpha\in J}X_\alpha$ be endowed with the product topology. Show that $X$ is path connected if and only if each $X_\alpha$ is path connected.  I know this is true if path coennected is changed by connection but I am very confused with this problem, I have tried to do the following:  $\Rightarrow $ let $x,y \in X_\alpha$ be then $(x_\alpha), (y_\alpha)\in \prod X_\alpha$ where $x_\alpha=x, y_\alpha=y$ and $x_\beta=0, y_\beta=0$ for any $\beta\neq\alpha$, and since P is path connected then there is continuous $f:[0,1]\rightarrow \prod X_\alpha$ such that $f(0)=(x_\alpha)$ and $f(1)=(y_\alpha)$, then if $\pi_\alpha:\prod X_\alpha \rightarrow X_\alpha$ is the projection, which is continuous, we have that $\pi_\alpha f:[0,1]\rightarrow X_\alpha$ is continuous and $\pi_\alpha (f(0))=x$ and $\pi_\alpha (f(1))=y$.  $\Leftarrow$ I do not know how to do this address, could someone help me please? Thank you very much. How can I use the subdivision surface modifier to create more high poly meshes without ruining sharp edges? For example this mesh  The sphere should be subdivided but the rim of the cylinder should stay the same because it is a sharp edge. This is the result of the subdevision  How can I get sharp edges to not be affected by the sub surf mod? ViewPager as a circular queue / wrapping Operator norm. Alternative definition Several lines of formulas to the left of one curly brace pointing to equation number How to make several lines of equations under one curly brace from the left side, such that it point to a reference number.  Now I do something like this:  \begin{align} \left. \begin{array}{ll} a = b + c \\ &amp; \dots  \\ a = b + c \\ &amp; \dots  \\ a = b + c  \end{array} \right\} \label{formulas}\\ \end{align}   But equation number appears in the bottom of curly brace. What is a "slug" in Django? Can I have 2x2 workspaces in GNOME 3? I have just upgraded to Ubuntu 17.10 and found out there is no option to have 2 by 2 workspaces. I was able to configure 4 "static" workspaces using , but I would like to have them in 2 rows by 2. Any ideas? av_acharya@AnoxBotox:/$ wireshark qt.qpa.plugin: Could not find the Qt platform plugin &quot;xcb&quot; in &quot;path/to/plugins&quot; This application failed to start because no Qt platform plugin could be initialized. Reinstalling the application may fix this problem.   sudo apt-get install --reinstall qt5-default Reading package lists... Done Building dependency tree        Reading state information... Done The following NEW packages will be installed:   qt5-default 0 upgraded, 1 newly installed, 0 to remove and 23 not upgraded. Need to get 0 B/24.4 kB of archives. After this operation, 170 kB of additional disk space will be used. Selecting previously unselected package qt5-default:amd64. (Reading database ... 241279 files and directories currently installed.) Preparing to unpack .../qt5-default_5.12.8+dfsg-0ubuntu1_amd64.deb ... Unpacking qt5-default:amd64 (5.12.8+dfsg-0ubuntu1) ... Predicting the number of decimal digits needed to express a rational number The number $1/6$ can be expressed with only two digits (and a repeat sign denoted as $^\overline{}$), $$ \frac{1}{6} = \,.1\overline{6}$$  Meanwhile, it takes 49 digits to express the number $1/221$, since a string of 49 digits repeats: $$\frac{1}{221} = .\overline{004524886877828054298642533936651583710407239819}$$ Yet for $1/223$, 222 digits repeat, giving a total of 224 digits needed to express the number.  If $f:\mathbb{Q}\rightarrow\mathbb{N}$ is a function that gives the smallest number of digits needed to express a rational number in decimal notation, what can we say about $f$?  For example, if we do not consider the negative sign to be a digit, then $f$ is an odd function.  Other than that, is there any pattern to it at all? I'm talking about this nonsense:   Now, I'm aware that there are problems with the practicalities (or possibilities) of methods involving exotic matter with negative mass, and that kind of thing has been addressed here:   But in this case my question is different and more specific. Sweeping all the other problems of constructing such a beast under the rug, wouldn't this violate causality?  SR says that the simultaneity and relative ordering of events is dependent on the relative motion of the observer, but that no matter how it works out, if event A causes event B, no observer will see B first. One of the many problems with FTL travel (or signals) is that if any information is sent faster than light, there will exist an inertial frame in which the signal arrives before it is sent, a blatant violation of causality. (I think we can all agree, can we not, that the threshold should be extremely high before breaking assumptions that we're in a causal universe?)  So how is any scheme to travel faster than light, even if it may locally satisfy the equations of GR, not a blatant violation causality according to SR?  Is my understanding of GR incomplete and there's something in it that obviates the causality implications of SR? Or am I correct that FTL claims should be dismissed with extreme prejudice on this basis alone? (Pending a serious replicable experiment showing causality to be breakable.) Execute command in remote active terminal Suppose you have a terminal emulator (T1) open with a PID of 6350.  From another terminal, type this command (C1):  echo "ls\n" &gt; /proc/6350/fd/0   This writes ls and the new line in T1 but does not execute it. Why?  I also tried using cat|bash with echo "ls\n" &gt; /proc/catid/fd/0 but it is still not executed.  How can I echo the command into another terminal and have the command executed?  possible answer :  $ mkfifo toto; $ bash &lt; toto; $ echo "ls" &gt; toto;   In this case you cannot write anymore directly in the terminal (everything is displayed the same way the command (C1) displayed thing in this terminal. As the title suggests, I'd like to prove that the sum $$ \sum_{n=2}^\infty (\ln n)^{- \ln n} $$ is finite.  The root and ratio test both fail here, but  suggests that there is a comparison that can be used to show convergence.  The only thought I have is that it may help to write the terms as $e^{-\ln(n)\ln(\ln(n))}$, but this has not led me to any particular insight.  Any ideas are appreciated. Different methods of evaluating $\int\sqrt{a^2-x^2}dx$: Is there a simple and nice way to solve $\int\sqrt{a^2-x^2}dx$:  PS:I am not looking for a substitution like $x=a\sin p$, Connect iPhone to Mac Without Charging I am developing iOS apps and I hate, that always when I connect my iPhone to my Mac to install and test an app, the iPhone gets charged. Is there any possibility to connect my iPhone to my Mac without charging the phone?    My Environment: -  iPhone 4S (No Jailbreak) -  MacBook Air3,2 (Late 2010)