Refactoring switch statement to enum
Convert a string to an enum in C#
First, this question is motivated by the imprecise question: Is there a sensible notion of parity (evenness and oddness) for real numbers?   Here are some properties a notion of parity for $\mathbb{R}$ should have:    It should be an equivalence relation on $\mathbb{R}$ with exactly two equivalence classes.  Each equivalence class should be dense in $\mathbb{R}$. There should be some kind of symmetry between the two equivalence classes. (This is intentionally imprecise.)   If we divide $\mathbb{R}$ into rationals and irrationals, this lacks symmetry, since the rationals have measure zero and are countable, while the rationals have infinite measure and are uncountable.   So we could require that each equivalence class be uncountable and/or have positive (or infinite) measure. Then take one equivalence class to be the rationals, union with countably many fat cantor sets with positive measure, and the other class its complement. Then both classes are now dense, uncountable, and have infinite measure. But again, symmetry is lacking. One of these classes is "uncountable everywhere" and has "positive measure everywhere" while the other does not.   I propose some definitions: A subset $A \subset \mathbb{R}$ is uncountable everywhere if for any open interval $(a,b)$, the intersection $A \cap (a,b)$ is uncountable. A subset $A \subset \mathbb{R}$ has positive measure everywhere if for every open interval $(a,b)$, the intersection $A \cap (a,b)$ has positive measure. We can see immediately that having positive measure everywhere implies being uncountable everywhere, since a positive measure set must be uncountable.   Finally, my questions:    Is there a partition of $\mathbb{R}$ into two sets that are both uncountable everywhere?  Is there a partition of $\mathbb{R}$ into two sets that both have positive measure everywhere?  Is there a partition of $\mathbb{R}$ into two sets that split each interval $(a,b)$ into two parts of equal measure?   Potential generalizations for extra credit: What about partitions of $\mathbb{R}$ with $n$ equivalence classes, where $n \in \mathbb{N}$, or even with countably many, or even uncountably many equivalence classes?  Note: If you've seen these definitions of uncountable everywhere or positive measure everywhere somewhere under a different name, please let me know. I've never found anything where other people were thinking about these notions.  EDIT: By "measure," I mean Lebesgue outer measure, so we don't have to worry about anything being measurable. Raster generalization - buffers in rasters, expand pixels? Is it possible to create buffers for pixels of raster files? Actually I need to expand the pixels classified as 1 (in white in the figure) with a spatial range of 1 or 2 pixels, in order to perform some generalization.  I'm using QGIS, is this possible with gdal or something? Prime dividing the binomial coefficients It is quite easy to show that for every prime $p$ and $0&lt;i&lt;p$ we have that $p$ divides the binomial coefficient $\large p\choose i$; one simply notes that in $\large \frac{p!}{i!(p-i)!}$ the numerator is divisible by $p$ whereas the denominator is not (since it is a product of numbers smaller than $p$ and $p$ is prime).  My problem is with generalizing this argument for $q=p^n$. I'm looking for the most elegant and simple way to prove that $p$ still divides $\large q\choose i$. How Conditional Random Fields and Logistic Regression could be the same? If you have read  tutorial about CRF, on page 4 under the section Classification, it wants to relate CRF to Logistic Regression (or Maximum Entropy, as it is known by this name in NLP community).   The formulation of Logistic Regression is said to be  $ p(y|x) = \frac{1}{Z(X)}exp \{ \lambda_y + \sum_{j=1}^{K}\lambda_{y,j}x_{j}\} $.  On the other hand, on the Wikipedia  for logistic regression, the formulation is  $ f(t) = \frac{1}{1+e^{-t}} $  and the classifier's formulation is the explanation of this formulation which is derived from Logistic Function.  My question is, first, how Logistic Regression and Maximum Entropy Classifier are related to each other and are identical?   Second, the CRF tutorial says Logistic Regression (or Maximum Entropy Classifier) is simple CRF model, how? How does one create a custom application launcher for Wine installed apps? I'm making a Java application with an application-logic-thread and a database-access-thread. Both of them persist for the entire lifetime of the application and both need to be running at the same time (one talks to the server, one talks to the user; when the app is fully started, I need both of them to work).  However, on startup, I need to make sure that initially the app thread waits until the db thread is ready (currently determined by polling a custom method dbthread.isReady()). I wouldn't mind if app thread blocks until the db thread was ready.  Thread.join() doesn't look like a solution - the db thread only exits at app shutdown.  while (!dbthread.isReady()) {} kind of works, but the empty loop consumes a lot of processor cycles.  Any other ideas? Thanks. I don't understand an answer. Should I add a comment, or post a new question? I recently (today) asked a question that received what seems to be a clear, concise answer, but one that's beyond my ability to understand (I'm at the cut-and-paste stage with JavaScript, and the answer seems to assume more knowledge than I actually have).  Is it considered better to ask follow-up questions as comments to the answer given, or should I post "fresh" questions to Stack to help me understand the answer that's been given? Is the axiom of choice used in the proof that every open set is the union of basis elements (Mukres, Lemma 13.1) Resizing an iframe based on content I am working on an iGoogle-like application. Content from other applications (on other domains) is shown using iframes.   How do I resize the iframes to fit the height of the iframes' content?  I've tried to decipher the javascript Google uses but it's obfuscated, and searching the web has been fruitless so far.  Update: Please note that content is loaded from other domains, so the  applies. How to initialize all members of an array to the same value? I have a large array in C (not C++ if that makes a difference). I want to initialize all members of the same value.  I could swear I once knew a simple way to do this. I could use memset() in my case, but isn't there a way to do this that is built right into the C syntax? Can anyone explain how one would convert one voltage range to another? I'm going to need to convert a range of -10 to +10 volts into a range of 0 to +5 volts. How would this be accomplished? Thanks!   Let me say  something more. Inside of a torpedo there are gyroscopes. This gyroscope give -10 volts when the torpedo have 180 degrees of deviation to the west and 10 volts when the deviation is to the east. This signal is DC, so i need to change this range a range: 0 to 5 v DC . Thanks Can someone please explain this weird Pygame importing convention? I've installed Ubuntu 13.04 two times on my PC. Each on a different partition. I would like to delete the one which I'm not using. How would I do that? Todo comments:Not include and left align? Prove：$x^d-1 \mid x^n-1$ iff $d \mid n$. Consider the polynomial ring $F\left[x\right]$ over a field $F$. Let $d$ and $n$ be two nonnegative integers. Prove：$x^d-1 \mid x^n-1$ iff $d \mid n$.  my tries:  necessity, Let $n=d t+r$, $0\le r&lt;d$ since $x^d-1 \mid x^n-1$, so, $x^n-1=\left(x^d-1\right)\left(x^{\text{dt}+r-d}+\dots+1\right)$... so,,, to prove $r=0$? I don't know, and I can't go on. How to do it. Possible Duplicate:          Is it correct to start a sentence with did.     Did my work.   instead of      I did my work.   while answering my emails? How can I encourage Stack Overflow to rein in the 'subjective' vigilantes? Complement property of DES I'm supposed to show the complement property of DES ($c=DES(p,k) =&gt; \bar c = DES(\bar p, \bar k)$).  My idea was to just start the algorithm with $\bar p$ and see what happens (ignoring the initial permutation for now). I looked at it step by step and got the the point where $R1 = \bar L1 \oplus f(\bar k1, \bar R0)$. So I figured I had to show that $f(\bar k1, \bar R0) = \bar f(k1,R0)$. Is that even right so far? Because I got stuck at the point where the S-Boxes are used. Why would $S(\bar x) = \bar S(x)$?  Somewhere else I read something about a formal prove using induction, but I don't know how I would do that either... Failed to Login : Invalid session (Try restarting your game) Minecraft Error Bundling python library with addon