Is it possible to echo the two-character string -n using just the echo command built into the bash shell? I know I can do printf '%s\n' -n but was just wondering if the echo built-in is capable of outputting the string -n at all.
I can't figure how to print the string "-n" with the over 30 years-old command echo.  I tried these:  Michaels:Scripts$ echo -n Michaels:Scripts$ echo "-n" Michaels:Scripts$ echo -e "-n" Michaels:Scripts$ echo -- -n -- -n Michaels:Script$ echo -- "-n" -- -n Michaels:Script$ echo "\-n" \-n   I use Mac OS X ML. I consider this behaviour very weird and unexpected.
I am trying to prove the following by Mathematical Induction:  $$\sum_{i=1}^n i\cdot i! = (n+1)!-1\quad\text{for all integers $n\ge 1$}$$   My proof by Induction follows: First prove $P(1)$ is true,  $$\sum_{i=1}^1 i\cdot i! = (1+1)! - 1$$  Then, for all integers $k &gt;= 1$, if $P(k)$ is true then $P(k+1)$ is also true,  $$ \sum_{i=1}^k i\cdot i! = (k+1)! - 1$$ Then, we must show that $P(k+1)$ is true   $$ \sum_{i=1}^{k+1} i\cdot i! = ((k+1)+1)! - 1\\ \sum_{i=1}^{k+1} i\cdot i! = (k+2)! - 1$$  I am currently struggling with the next step to show that $P(k)$ is equal to $P(k+1)$. How would I finish this prove by induction? Which versions of C++ redistributables can I remove? I have a number of Microsoft Visual C++ 2005 and 2008 Redistributable and I would like to know which ones are safe to remove, because there are actually more than 10 installed on my computers.   Microsoft Visual C++ 2005 ATL Update kb973923 - x64 8.0.50727.4053 Microsoft Visual C++ 2005 Redistributable Microsoft Visual C++ 2005 (x64) Microsoft Visual C++ 2008 ATL Update kb973924 - x64 9.0.30729.4148 Microsoft Visual C++ 2008 Redistributable - x64 9.0.30729.17 Microsoft Visual C++ 2008 Redistributable - x86 9.0.30729.17 Microsoft Visual C++ 2008 Redistributable - x86 9.0.30729.4148 Microsoft Visual C++ 2008 Redistributable - x86 9.0.30729.4974 Microsoft Visual C++ 2010 x64 Runtime - 10.0.30319   It could be that these versions are all different, but a confirmation of that is fine for me as well. Thanks in advance.  PS. I'm using an x64 machine one windows 7. Exercise 12 from SEC. 82 of Finite-Dimensional Vector Spaces - 2nd Edition by Paul R. Halmos.  If $A$ and $B$ are linear transformations on a finite-dimensional inner product space, and if $\textbf{0} \le A \leq B$, then $\det A \leq \det B$.  Notation: $0 \le A$ means that $A$ is positive.  If $\det B = 0$, choose $x \in \ker B$, then $0 \le ((B-A)x,x) = (Bx, x) - (Ax, x) = -(Ax, x) \le 0$. Therefore $\ker B \subseteq \ker A$ and $0 = det A \le det B = 0$. How to prove for the case when $B$ is invertible? Intuitively, I feel that since both $A$ and $B$ are positive their proper values are also positive and $B$'s proper values should be greater the $A$'s and same for determinants. I've found strange behavior when closing this  - I definitely see that there are 3 closing votes and 2 of them are at "Off-topic" section:   -but there are no explanations on section itself:   -while, normally, it's expected that it will appear. In custom comments section there are also no closing-votes displayed.   Perhaps it's just my browser (which is FF 26 x64 under Win) - so marking this as a "possible bug". Thank you for your attention. Why do files sometimes change but not the inode or vice versa? When a file is updated then the corresponding inode gets updated. But sometimes the following condition occurs    file is same and inode is new  file gets changed but corresponding inode is older   Why ? The Wikipedia  has a derivation of the Klein-Gordon equation.  It gets to this step:  $$\sqrt{\textbf{p}^2 c^2 + m^2 c^4} = E$$  and inserts the QM operators to get  $$\left( \sqrt{ (-i \hbar \nabla)^2 c^2 + m^2 c^4 } \right) \psi = i\hbar\frac{\partial}{\partial t} \psi$$  The article then says     This, however, is a cumbersome expression to work with because the differential operator cannot be evaluated while under the square root sign. In addition, this equation, as it stands, is nonlocal.   To fix this, the first equation is squared instead to get  $$\textbf{p}^2 c^2 + m^2 c^4 = E^2$$  after which the QM operators are inserted and the expression is simplified to get  $$-\hbar^2 c^2 \nabla^2 \psi + m^2 c^4 \psi = -\hbar^2 \frac{\partial^2}{\partial t^2} \psi$$  A couple things I don't understand.  First, are the solutions to this differential equation not exactly the same as the solutions to the first differential equation?  Both sides of the starting equation were squared, so it seems to me that regardless of the particular form of the resulting differential equation, both of them should have the exact same set of solutions.  Secondly, why is the first differential equation cumbersome to work with?  It seems like it would in fact be easier to work with, since the operator under the square root could be expanded in terms of a Taylor series and then you have an equation that is first order in time.  And finally, can someone elaborate on what nonlocal means? The linked article on the Wikipedia page didn't entirely help me understand it. To whom was Yoda referring when he said, "There is another?" In the original trilogy Yoda refers to another hope:     Obi-Wan: "That boy is our last hope."   Yoda: "No...there is another..."   The assumption being after seeing Return of the Jedi (Episode VI) that the other was Leia.  If, however, you consider the prequel trilogy canon, then this assumption depends greatly on your point of view*. Obi Wan knows about Leia (and for unknown reasons has discounted her as a hope), so Yoda must be referring to someone or something else.  Is there any canonical source as to what Yoda meant, or was uncle George setting us up for Episode VII?  *as a wise man once said      you will find that many of the truths we cling to depend greatly on   our own point of view.   Just to add a bit of clarity: I was thinking about who Yoda was referring to when he was talking to Obi-Wan. When talking to Luke, it is obvious that Leia is the other (as he talks about a 'Skywalker'). It is not so obvious (after watching the prequel trilogy) that he means it when talking to Obi-Wan. Finding a formula to sum natural numbers up to $n$ Possible Duplicate:          I got this question in homework:  Find an expression for the sum ‫‪     $\sum k = 1 +\cdots + n‬‬$.    and prove it using an induction.   I'm not even near finding the expression. What I did notice is that if $n$ is (for example) 5 then the sum would be   $5^2 - 4^2 + 3^2 - 2^2 + 1^2$  So the first number is always positive and from there on the sign changes.  Any tips on how do I contintue from this point on, assuming I'm in the right direction?  Thanks! What translation occurs when writing to a file that was opened in text mode that does not occur in binary mode? Specifically in MS Visual C.  unsigned char buffer[256]; for (int i = 0; i &lt; 256; i++) buffer[i]=i; int size  = 1; int count = 256;   Binary mode:  FILE *fp_binary = fopen(filename, "wb"); fwrite(buffer, size, count, fp_binary);   Versus text mode:  FILE *fp_text = fopen(filename, "wt"); fwrite(buffer, size, count, fp_text); How to develop a SharePoint Designer Workflow Action for use in SharePoint (2013) online Expected prediction error - derivation found a 1994 uncashed profit sharing retirement plan check I found an old un-cashed check dated 1994 for $487 from my Xerox Retirement plan with no expiration date. Can I still cash it? how to pass value like 100,102,103 to view params I am trying to zoom plot numbers.Plot numbers like 1 10-12 13/P road 20(A) 100&amp;102 and etc.I am able to zoom to all combination plot numbers except 1,2,3.when I pass such value its trowing error:  1 feature types requested, but found 2 view params specified  geoserver sql view is:  select * from plotboundary where nmindar='%nmindar%' and plno='%plno%'   default values and validation are  Name  | Default Value   | validation  nmidar| Hanagawadi I A  | ^[\w\d\s]+$  plno  |  100,102&amp;103    | ^[ A-Za-z0-9_ *@.\/#&amp;+-\,()-_]*$   ajax function:   $.ajax({             url: 'http://XX.168.1.XX:8089/geoserver/XX/ows?service=WFS&amp;version=1.0.0&amp;request=GetFeature&amp;typeName=XX:vwplot&amp;maxFeatures=5000&amp;outputFormat=text/javascript',             contentType: 'application/json',             dataType: 'jsonp',             jsonpCallback: "parseResponse",             data: {                 viewparams: "nmindar:" + nmindar + ";plno:" + plno             }   Can any one tell me how to pass value to viewparams in geoserver, value includes comma. For example as mentioned above "100,102&amp;103" is a single value(plot number).Here   comma is not a separator. How is the no-cloning theorem compatible with the fact that fan-out gates work? I have some difficulty with understanding no-cloning theorem. Simply speaking, according to the theorem, it is not possible to copy a quantum state.  On the other hand, CNOT gate can be used as so-called fan-out gate which purpose is to copy one qubit to another one, previously in state $|0\rangle$.  It seems that these two facts negate each other.   My question: How is no-cloning theorem compatible with the fact that fan-out gate works? Let $X$ be a random variable and let $g,f$ be real-valued, nondecreasing, and bounded.   Show that $\mathbb{E}[f(X)g(X)]\geq \mathbb{E}[f(X)]\mathbb{E}[g(X)]$  Having a hard time seeing where to start for some reasons, any hints?  I managed to write:  $\mathbb{E}[f(X)g(X)] = \frac{1}{4}\mathbb{E}[(f(X)+g(X))^2 - (f(X)-g(X))^2]$  But I'm not sure if this is in the right direction or not. Can we have a way to access Area 51 on the iOS and android app?  More sites would flourish due to more traffic. Disable Tabbing in Firefox 3, Chrome 4 and IE8? Tabbed Browsing may be nice for reading news sites in one sitting, but I still think they are a usability nightmare if you need to keep the page open for a long time, e.g., for testing it while developing or as a reference for something.  The nice thing about the Windows Taskbar (before Windows 7 ) is that it's easy and natural to remember where things are. I can have 30 tabs in it, but because I know what each one is, I know where I have to click to open something - it's the most efficient way of working I've encountered so far.  Sadly, Tabbed Browsing completely breaks this efficiency because it is not possible to specifically click on a tab in the taskbar, I have to click on the browser, search the tab and then click it, which means at least 2 clicks.  Long story, short question: Is there an extension or setting to completely disable tabbing on Firefox 3, Chrome 4 and Internet Explorer 8 and have one Window/Taskbar entry for each open page? I know that in Chrome I can just drag a tab out of a Window to create a new one, but if there is a general way, that would be easier.  Edit: IE8 conveniently offers an option for that: Tools - Options - Tabs - Enable Tabbed Browsing. The annihilator of a module is an ideal Let $R$ be a ring and let $M$ be an $R$-module. Define the annihilator of $M$ to be the following subset of $R$:  $Ann_R(M) =\{r\in R \mid rm = 0_M  \text{ for all } m\in M \}$  Prove that $Ann_R(M)$ is an ideal of $R$.  please help as much as you can a full answer is greatly appreciated   Thanks Dark Souls 2 coop/invading problem I was playing Dark Souls II on my pc a lot. After about 200 hours of ingame time I found that I cant summon or invade anybody. I tried new characters and reinstalling but it didn't help. So any tips, and reasons. P.S. I didn't used any cheats. I've just set up a new machine with Ubuntu Oneiric 11.10 and then run  apt-get update apt-get upgrade apt-get install git   Now if I run git --version it tells me I have git version 1.7.5.4 but on my local machine I have the much newer git version 1.7.9.2  I know I can install from source to get the newest version, but I thought that it was a good idea to use the package manager as much as possible to keep everything standardized.  So is it possible to use apt-get to get a newer version of git, and what is the right way to do it?