How to custom file formats work, encryption, packing etc So say I take an example from Telltale games, they pack all their file assets into ttarch files, now I guess this is a custom file format that allows many file assets such as dds, jpg, bik, wav, 3ds etc to be packed into one file.  So someone has worked out how to explore these ttarch files and inside as you would imagine there are hundreds of files each with non standard file extensions(apart from the  lua files) such as d3dtx, d3dmesh, vers, spline, style, scene, there are also lua files which we all know.  The d3dtx files will be dds, jpg, bmp etc, so do you actually encrypt a dds file in this way, can someone enlighten me on the process of file encryption/packing files together?
How to pack the game files into one without using any file compressor? Well, one example is this file of the game The Sims 2 for PS2: quickdat.arc. The file contains this .arc extension, but it's no one an archive file and it contains some data of the game inside. How can I do this? Put so many files in one?  How to do something like this? All the game files inside one without using a file compressor?
Is there are rule when to use opened vs open?  I always get confused even though I've been speaking English as the dominant language for more than half my life.  E.g.         Is the door open(ed)?   Which file do you have open(ed) in your editor? Isomorphism equivalence implies fundamental group is abelian I'm working on the following problem set.  Let $\mathcal{H}$ be a Hilbert space and $A$ and $B$ orthogonal subspaces of $\mathcal{H}$.  Prove or disprove:  1) $A \oplus B$ is closed, then $A$ and $B$ are closed.  2) $A$ and $B$ are closed, then $A \oplus B$ is closed.  I could prove 1) and if my proof is correct, it even holds if $\mathcal{H}$ is just an inner product space.  Unfortunately, I can't manage to prove 2). Since $\mathcal{H}$ is by assumption a Hilbert space and I didn't use that fact to prove 1), I should probably use it here.  It means that $A$ and $B$ are also complete. Given some convergent sequence in $A \oplus B$, I want to show that the limit is also in  $A \oplus B$. Here I'm stuck. I want to use the completeness of $A$ and $B$, but I don't see how to obtain suitable Cauchy sequences.  Can anyone drop me a hint? Or is my approach all wrong? Compute the limit $\lim_{n \to \infty} \frac{n!}{n^n}$ Triggered send status queued, need to get an alert What happens in electron-electron collisions? Inheriting non-implicit constructors on Apex classes If I have an abstract parent class like this:  abstract class Vehicle {     public Vehicle(Person driver) {         //     } }   and then I create a child class like this:  public class MagicCarpet extends Vehicle {     //this won't compile }   I encounter the following Compile Error:     Error: Parent class has no 0-argument constructor for implicit construction at line ... column ...   Obviously I can explicitly re-declare a constructor on the child class toget it to compile:  public class MagicCarpet extends Vehicle {     public MagicCarpet(Person driver) {         super(driver);     } }   But I feel this isn't DRY. Not sure what's actually going on under the covers here.  How can I get a constructor (other than the implicit 0-argument one) to be inherited by a child class? Solving of a seperable differential equation How to apply a macro to each column of a table Convert a string to an enum in C# What is the purpose of a serial number? Below is a visual proof (!) that $32.5 = 31.5$. How could that be?    (As noted in a comment and answer, this is known as .) Why do C# and Java bother with the "new" operator? Why does the  exist in modern languages such as C# and Java? Is it purely a self documenting code feature, or does it serve any actual purpose?  For instance the following example:  Class1 obj = new Class1();  Class1 foo() {     return new Class1(); }   Is as easy to read as the more Pythonesque way of writing it:  Class1 obj = Class1();  Class1 foo() {     return Class1(); }   EDIT:  hit the nail on the head with the clarification of the question: Why did they choose this syntax? Prove $p_n(x) \rightarrow \sqrt{x}$ uniformly as $n \rightarrow \infty$ Define $(p_n)_n$ recursively by $p_0(x) = 0$ and $p_{n+1}(x) = p_n(x) + \frac{1}{2}(x - p_n(x)^2)$.  Prove that $p_n(x) \rightarrow \sqrt{x}$ uniformly for $0 \leq x \leq 1$ as $n \rightarrow \infty$.  I'm not sure where to go with this.  I can show inductively that $\forall n,\  0 \leq p_n(x) \leq 1$ for $0 \leq x \leq 1$, and I think that $p_n(x)$ is increasing with $n$, but I have no idea whether this helps me.  I know that I need to show that $\forall \epsilon&gt;0: \exists N \in \mathbb{N}: \forall n \geq N: \forall x\in [0,1]: \big|p_n(x) - \sqrt{x}\big| &lt; \epsilon$ Edit:  I just had a thought.  I'm given a version of Dini's theorem that reads  Let $X$ be a compact metric space, $(f_n)_n$ a sequence of real-valued continuous functions on $X$, $f$ a continuous function on $X$ such that: (i) $f_n \rightarrow f$ pointwise on $X$, and (ii) $f_n(x) \geq f_{n+1}(x) $ for all $x \in X, n \in \mathbb{N}$. Then: $f_n \rightarrow f$ uniformly on $X$.  Obviously, (ii) is not true for my sequence, but what if I took $f_n(x) = -p_n(x)$ and $f(x) = - \sqrt{x}$?  Then I could prove (ii) to be true, I know that $[0,1]$ is compact, and $f_n(x)$ is real-valued.  The only part I would need to prove is (i), which is where I get confused.  Correct me if I'm wrong, but after that I could say that since $(-p_n)_n \rightarrow -\sqrt{x}$, then $(p_n)_n \rightarrow \sqrt{x}$.  Any advice? Rewrite code to make it faster How can I test for POSIX compliance of shell scripts? Considering that POSIX is the closest thing to a common standard among all unices, I'm interested in knowing if there's a shell that supports it exclusively. While most modern shells provide support for POSIX (and will run POSIX compliant scripts without any problem), they don't do a good job at pointing out non compliant features.  Is there any shell that implements POSIX and POSIX only, in such a way that it'd throw an error for any non compliant feature?  EDIT I want to clarify that I'm not asking for general tips for writing portable shell scripts. The related question mentionned in the comments already covered this. I thought of this question when I found out that bash has a --posix option but only to discover that it only affects some intialization behaviors which is not exactly what I'm looking for. Expectation of the Maximum of iid Gumbel Variables I keep reading in economics journals about a particular result used in random utility models. One version of the result is: if $\epsilon_i \sim_{iid}, $ Gumbel($\mu, 1), \forall i$, then:   $$E[\max_i(\delta_i + \epsilon_i)] = \mu + \gamma + \ln\left(\sum_i \exp\left\{\delta_i \right\} \right),  $$  where $\gamma \approx 0.52277$ is the Euler-Mascheroni constant.  I've checked that this makes sense using R, and it does.  The CDF for the Gumbel$(\mu, 1)$ distribution is:  $$G(\epsilon_i) = \exp(-\exp(-(\epsilon_i - \mu)))$$  I'm trying to find a proof of this and I've had no success.  I've tried to prove it myself but I can't get past a particular step.   Can anyone point me to a proof of this?  If not, maybe I can post my attempted proof up to where I get stuck. Story with multiple 'third planet' races Two very closely related questions:  If a card has two different "Sacrifice this creature for X" abilities on it, does sacrificing it give both benefits?  Likewise, if a card requires a creature to be sacrificed, but that creature has a "Sacrifice this creature for X" ability, do you get the sacrifice benefit when you sacrifice it for the other requirement? Is $\lim\limits_{n\rightarrow\infty} n$ comparable to $\aleph_0$? For example, can we say: $\infty=\lim\limits_{n\rightarrow\infty} n &lt; \aleph_0$?  These are two different types of structures. The limit being like the length, extension, or just generic magnitude and the other being cardinality of a set. Can we compare magnitude to cardinality?  Intuitively, we can reach $\aleph_0$ by counting the natural numbers on the number line and in the process will be approaching $\infty$. Which leads me to believe $\infty\leq\aleph_0$. But I can't see why it should be a strict inequality. I feel like they should be of equal magnitude.  I saw on a recent comment that $2^\infty=\infty$, but are those infinities really the same? It seems not to me. Of course we (usually) have that  $2^{\aleph_0}=\aleph_1$ where ${\aleph_0}$ and $\aleph_1$ are clearly two very distinct infinities, countable vs uncountable at least. Maybe one might argue that as far as the concept of magnitude is concerned, all infinities are "equal".