Is $1=0.\overline{9}$?
Is it true that $0.999999999\ldots=1$?
How to do power series expansion What is the coefficient of $x^{11}$ in the power series expansion of $\frac 1{1-x-x^4}$?    How do I do power series expansions? Is it possible to create an iron door which responds to levers on both sides If $f:D\to D’$ is analytic and $u: D'\to R$ is harmonic then the composition of $u$ and $f$ is harmonic in $D$ If $f:D\to D’$ is analytic and $u: D'\to R$ is harmonic then the composition of $u$ and $f$ is harmonic in $D$.  How can I show that the above statement is true/false? Can anyone help me? How do I find packages to install via apt-get I have 16GB RAM. Do I need 32GB swap? I read many places that the rule of thumb for swap space is to double the amount of physical RAM. However, 32 GB does seem a LOT. Do I need that much? Do I need it at all with this high amount of physical RAM? Can anyone help me with a solution? Geomagnetic reversal? I have always been told that the geomagnetic field acts "as if" there were a bar magnet inside the Earth. I now this is not true, but I feel that knowing what is actually going on would help me understand the answer to the question that I'm about to ask:  Why does geomagnetic reversal happen? Is it something gradual or relatively fast?  (What is the origin of the geomagnetic field? Can we answer my questions starting from this mechanism? Area enclosed between the curves $y=x^2$ and $y=60-7x$ Find the area enclosed between the curves $y=x^2$ and $y=60-7x$.  I am completely new at this but I have tried and I believe that it should be between the numbers $0$ and $60$ is this right? Why do I get a segmentation fault when writing to a "char *s" initialized with a string literal, but not "char s[]"? I see stuff like command 1&gt; out or with 2&gt;&amp;1 to redirect stderr, but sometimes I also see &amp;&gt; by itself, etc.  What is the best way to understand &amp; and what it means exactly? Multiplicative order and powers Let's consider two number $a$ and $b$ such as $gcd(a,b)=1$. Can you explain me intuitively why there exist $n&gt;0$ such as $a^{n} \equiv 1 \space (mod \space b)$  ? How to modify the system default background image I am about to ship a new 10.04 installed system to a customer. This is the 1st system that we are shipping with our preinstalled software and an additional hardware test platform, so I thought it would be a nice idea to have the desktop wallpaper include our company's logo.  What I want to do is just to add the logo to the default background image. the questions are:   Where are the set of backgrounds stored? What are the rules for creating a custom background from scratch? If I create a background from scratch, how do I add it to the system's background set (i.e., not just save it in the user's Pictures directory - I want it to be available to all future users of the machine)? Validity of work-energy theorem in presence of non-conservative forces? Does the VBA "And" operator evaluate the second argument when the first is false? I am having trouble understanding what defines Entailment operator. On Mathoverflow I posted this question on what I perceive to be .  Consider: :     P therefore Q  P            Therefore, Q   My question is could we have arbitrarily defined it such as:     P therefore Q  P            Therefore, P   However, if an advanced civilization receives information in the form of following nested structures/containers or packets, how will they interpret Modus Ponens if in an alien land Modus Ponens is not defined?    Therefore, it raises the validity of MP. How do we define the implication or entailment operator? Because if we use an argument that relies on implication or entailment operator ipso facto, then it is trivial that logic is circular.  Is there a flaw in my rationale? Get the client IP address using PHP 2D collision detection Let's assume I'm using this character.  (source: ) How would you implement collision detection for it? Using a bounding box doesn't seem to be a good approximation, because the bird's shape is nowhere near a square. I was thinking of having a sort of quad tree data structure inside the object that represents portions of the image. Each leaf could be either false (in case it covers the white/transparent space outside the bird) or true (in case it represents an area of the bird i.e. beak, eye etc). Then somehow test the only obstacle in the scene for collision with the bird. But my problems in my approach are:  I don't know how to initialize the quad tree. Once the quad tree is initialized, I'm not sure how to traverse &amp; use it once the obstacle is within the coordinates of the image.  How would you do collision detection with non-squarish characters? LE: The other approach I've seen was to use multiple bounding boxes. For example I'd have one or a few bounding boxes for the beak, then a few of them for the hair or the tail. But it can get tedious. If this is a valid approach in my case, how would I generate those bounding boxes? I doubt I'd have to have them hardcoded in my program. LE2: I care about fairly precise collisions. I can't imagine how a single bounding box or circle can at least approximate decently that shape, so this approach won't work. NSArray becomes NSCFArray when passed Convergence of $\sum_{n=1}^\infty (-1)^n(\sqrt{n+1}-\sqrt n)$ Please suggest some hint to test the convergence of the following series $$\sum_{n=1}^\infty (-1)^n(\sqrt{n+1}-\sqrt n)$$ Is everything in the physical world composite? In philosophy there is a principle that anything composite cannot have existed eternally, since it is preceded by its parts and whatever forces assembled it.  Is everything in the physical world composite in one sense or another or is there something not composite?