when i run my application on android emulator it crashed though there is no error in my code.it shows the following error
What is a NullPointerException, and how do I fix it?
I've never really understood why math induction is supposed to work.  You have these 3 steps:   Prove true for base case (n=0 or 1 or whatever) Assume true for n=k.  Call this the induction hypothesis. Prove true for n=k+1, somewhere using the induction hypothesis in your proof.   In my experience the proof is usually algebraic, and you just manipulate the problem until you get the induction hypothesis to appear.  If you can do that and it works out, then you say the proof holds.  Here's one I just worked out,  Show $\displaystyle\lim_{x\to\infty} \frac{(\ln x)^n}{x} = 0$  So you go:   Use L'Hospital's rule. $\displaystyle\lim_{x\to\infty} \frac{\ln x}{x} = 0$. Since that's $\displaystyle\lim_{x\to\infty} \frac{1}{x} = 0$. Assume true for $n=k$. $\displaystyle\lim_{x\to\infty} \frac{(\ln x)^k}{x} = 0$. Prove true for $n=k+1$.  You get $\displaystyle\lim_{x\to\infty} \frac{(\ln x)^{k+1}}{x} = 0.$   Use L'Hospital again: $\displaystyle\lim_{x\to\infty} \frac{(k+1)(\ln x)^{k}}{x} = 0$.  Then you see the induction hypothesis appear, and you can say this is equal to $0$.  What I'm not comfortable with is this idea that you can just assume something to be true ($n=k$), then based on that assumption, form a proof for $n=k+1$ case.  I don't see how you can use something you've assumed to be true to prove something else to be true. How do I setup keyboard macros? In my daily life I'm always typing &lt;kbd&gt;Keyboard Character&lt;/kbd&gt; and I'd like to set up a macro in Ubuntu to automatically enter &lt;kbd&gt; &lt;/kbd&gt;.  I'd like to assign it to say Shift+Control+K or whatever keyboard control character combination isn't assigned and already used by Ubuntu.  Back in the day of TSR (Terminate and Stay Resident) MS-DOS programs this was possible. Certainly it must be in Ubuntu too?  Do I have to write a daemon to accomplish this?    I found other questions with no answers: ,   I found a similar question with an answer: . However that question stipulated the answer could not be AutoKey. I encountered an 'errorUnknown graphics extension: .eps.' I tried to load an .eps picture, but an error occured,      errorUnknown graphics extension: .eps. How to get correct scale values? The scale of my map is wrong, no matter what coordinate system I use in my project. The map and all objects show the correct coordinates but the scale of the map shows nonsense and the measurement tool gives wrong dimension.   The map should be like 1:10000 but qgis shows 1:1. Anyone an idea? How do I convert Word smart quotes and em dashes in a string? I am creating a custom form on a Salesforce Marketing Cloud Landing Page. This page will have information such as Email address, first name and last name pre-filled from an email, however there will be some cases where emails can be entered by the customer. What is the best way to validate email addresses on form submit? E.g. a regex to look at overall structure or is there a better way? What kind of ring $R$ makes $\mathcal O(\mathrm{Proj}\,R[x_0,\cdots,x_n])=R$? The set of limit points of the sequence $1,\frac12,\frac14,\frac34,\frac18,\frac38,\frac58,\frac78,\frac1{16},\frac3{16},\ldots$ Alternative proof that $(a^2+b^2)/(ab+1)$ is a square when it's an integer Let $a,b$ be positive integers.  When $$k = \frac{a^2 + b^2}{ab+1}$$ is an integer, it is a square.    Proof 1: (Ngô Bảo Châu): Rearrange to get $a^2-akb+b^2-k=0$, as a quadratic in $a$ this has two values: $a$ and $kb - a = (b^2-k)/a$. (The second root is determined in two different ways from the expansion $(x-r_1)(x-r_2) = x^2 - (r_1 + r_2)x + r_1 r_2$.)  Now suppose we have $a,b$ such that $k$ is an integer but not a square, by the investigation about roots we have that the second root is a nonzero integer since $k,b,a$ are integers and $k \not = b^2$, futhermore it is positive which is easily seen from its defining equation.  WLOG assume $a \ge b$ so that the second root is strictly smaller than $a$. This leads to a decent, replacing $a$ with the second root.    Proof 2 (Don Zagier): Apply reduction theory (specifically, Sätze 1 and 2 of Section 13 of my book on quadratic fields) to the quadratic form $x^2 + kxy + y^2$, which is the unique reduced quadratic form in its equivalence class.    Note that Proof 2 is pretty much the same as Proof 1 when written out in explicit detail, but I could not read Zagier's book because I cannot read German.  I would like to know more approaches to this and other alternative proofs of this result if possible! Thanks in advance.  I would also be interested in related problems (especially easier ones of a similar nature) and texts which cover the reduction theory in English. Use hostnames to connect to machines on LAN I have just had my broadband upgraded to  which means my router has had to change. Previously I was using a Thomson TG585v7 ADSL thingy provided by my ISP. One nice thing about that router was that it would act as a local DNS and allow me to find my other machines on the network by using &lt;hostname&gt;.lan instead of IP addresses.  I've now switched to a Linksys WRT320N ethernet router which connects to my fibre modem, and which I've updated to the latest firmware (1.0.04). I have 2 machines on the network which I regularly want to connect to each other; one is running Windows 7 and the other is running OS X Lion.  The problem I'm having is that I'm unable to connect to my Win7 machine from the OS X machine using the Win7 machine's name. However, I'm able to ping the OS X machine from my Win7 machine using the hostname. Why is it that scanf() needs the l in "%lf" when reading a double, when printf() can use "%f" regardless of whether its argument is a double or a float?  Example code:  double d; scanf("%lf", &amp;d); printf("%f", d); How Triangle Law and Parallelogram law of addition of Vectors are different?Ain't they.  Please don't tell me the things written in book......give me the appropriate reason.And how do i distinguish between the two while adding vectors,what am i trying to say is i get really confused where to use parallelogram law and where triangle law  P.s:my basics are really weak though!May be the question might not be right Are $10\times 10$ matrices spanned by powers of a single matrix? I don't know how to answer this question:     Is there a $10 \times 10$ matrix $A$ such that $$M_{10}(\mathbb{F})=\text{span}\{I,A,A^2,\ldots, A^{100}\}\textrm{,}$$ where $M_{10}(\mathbb{F})$ is the vector space of $10 \times 10$ matrices over $\mathbb{F}$?   I think there is a connection to Jordan normal form. NRPE unable to read output, but why? How do you test that a Python function throws an exception? How does one write a unittest that fails only if a function doesn't throw an expected exception? .NET How to check if path is a file and not a directory? I have a path and I need to determine if it is a directory or file.    Is this the best way to determine if the path is a file?  string file = @"C:\Test\foo.txt";  bool isFile = !System.IO.Directory.Exists(file) &amp;&amp;                           System.IO.File.Exists(file);   For a directory I would reverse the logic.  string directory = @"C:\Test";  bool isDirectory = System.IO.Directory.Exists(directory) &amp;&amp;                              !System.IO.File.Exists(directory);   If both don't exists that then I won't go do either branch.  So assume they both do exists. Please help me to prove this trigonometric equation.  $\cos \left( 36^\circ \right)-\cos \left( 72^\circ \right) = \frac{1}{2}$  Thank you. As, the above link shows, other countries have similar murder rates but they are not in the radar of international travelers.  For example, as seen in the list, Puerto Rico has similar statistics. But, personally, I never heard of Puerto Rico to be a dangerous place to travel.  Why is it considered so dangerous to travel in South Africa? Is that due to the incompetent law enforcement agencies? Prove: $\gcd(a,b) = \gcd(a, b + at)$. set session - custom variable to store user id I want to store user id in custom session variable and use it (read) in trigger procedures to authorize user actions. I found something like this:  set session "myapp.user" = '12345'; ... SELECT current_setting('myapp.user');   and it seems to work - I thought that "myapp.user" should be declared in .conf file but it seems that I can create session variables on the fly (I didn't change .conf file at all).  Is there any disadvantage of doing like this?