What's the easiest way in F# (in a functional/recursive style) to, given a number in words, convert it to it's numeric equivalent?  I'm looking at only English for now. E.g:  let parseNumber (s : string) =     match s with     | "One" -&gt; 1     | _ - failwith "Cannot parse"  let result = parseNumber "One Thousand Two Hundred" // result should be 12000   Is there any way of doing this that doesn't involve a massive look-up table?
Is there an efficient method of converting an integer into the written numbers, for example:  string Written = IntegerToWritten(21);   would return "Twenty One".  Is there any way of doing this that doesn't involve a massive look-up table?
How can I reset my menus? I accidentally opened too many menus (or windows) and I want to reset them to default.  It is really annoying, and effecting my animation.  Thanks Proving the general limit $\lim_{n\to\infty} \frac{an+c}{bn+d} = \frac{a}{b}$ Can I combine extension tubes and macro filters at once to give better macros? How do I recover from the Heartbleed bug in OpenSSL? Prove that $\sum^{n}_{r=0}(-1)^r\cdot \large\frac{\binom{n}{r}}{\binom{r+3}{r}} = \frac{3!}{2(n+3)}$ Prove that $\displaystyle \sum^{n}_{r=0}(-1)^r\cdot \large\frac{\binom{n}{r}}{\binom{r+3}{r}} = \frac{3!}{2(n+3)}$   $\bf{My\; Try::}$ We can write $$\frac{\binom{n}{r}}{\binom{r+3}{r}} = \frac{n!}{r!\times (n-r)!}\times \frac{r!\times 3!}{(r+3)!} = \frac{3!\times n!}{(n-r)!\times (r+3)!}$$  So our sum is $$ 3!\sum^{n}_{r=0}(-1)^r\frac{n!}{(n-r)!\times (r+3)!} = \frac{3!}{(n+1)(n+2)(n+3)}\sum^{n}_{r=0}(-1)^r\frac{(n+3)!}{(r+3)!\times (n-r)!}$$  So we get Sum $$ \frac{3!}{(n+1)(n+2)(n+3)}\sum^{n}_{r=0}(-1)^r\binom{n+3}{r+3} = -\frac{3!}{(n+1)(n+2)}\sum^{n}_{r=0}(-1)^{r+3}\binom{n+3}{r+3}$$  $$  = -\frac{3!}{(n+1)(n+2)(n+3)}\left[-\binom{n+3}{3}+\binom{n+3}{4}-\binom{n+3}{5}--.......+(-1)^{n+3}\binom{n+3}{n+3}\right]$$  $$=-\frac{3!}{(n+1)(n+2)(n+3)}\left[\binom{n+3}{0}-\binom{n+3}{1}+\binom{n+3}{2}-\binom{n+3}{3}+\binom{n+3}{4}-\binom{n+3}{5}--.......+(-1)^{n+3}\binom{n+3}{n+3}\right]+\frac{3!}{(n+1)(n+2)(n+3)}\left[\binom{n+3}{0}-\binom{n+3}{1}+\binom{n+3}{2}\right]$$  So we get $$ = \frac{3!}{(n+1)(n+2)(n+3)}\left[1-(n+3)+\frac{(n+3)(n+2)}{2}\right] = \frac{3!}{(n+1)(n+2)}\times \frac{n^2+3n+2}{2} = \frac{3!}{(n+1)(n+2)(n+3)}\times \frac{(n+1)(n+2)}{2} = \frac{3!}{2(n+3)}$$  Can we prove it Using Combinatorial way,bcz above method is very lengthy  If yes then plz explain here  Thanks Why is $1$ not considered a prime number?  Or, why is the definition of prime numbers given for integers greater than $1$? Find the smallest disk in complex plane containing the eigenvalues of a matrix (NBHM 2012) Consider the given matrix  $$\left[\begin{matrix}1&amp; -2&amp; 3&amp; -2 \\1&amp; 1&amp; 0&amp; 3\\-1&amp; 1&amp; 1&amp; -1\\0&amp; -3&amp; 1&amp; 1&amp;\end{matrix}\right]$$  Find out the smallest disk like ($|z-1| &lt; r$ ) in the complex plane containing the eigenvalues of the given matrix.  One easiest method is to find out the eigenvalues from the characteristic equation of the matrix. I can do it so no problem with it.   I am looking for a method to solve the problem without the above method that can be evaluated in very short time. This type of method is possible, I believe.  Thank you for your help Recently I asked about the  pertaining to Voldemorts new face. However I was corrected by ...     Well, I think the confusion comes with mixing movie canon with book canon. In Philosopher's Stone, here's what Harry sees when Quirrell unwraps his turban:           Harry would have screamed, but he couldn’t make a sound. Where there should have been a back to Quirrell’s head, there was a face, the most terrible face Harry had ever seen. It was chalk white with glaring red eyes and slits for nostrils, like a snake.          Philosopher's Stone - page 212 - UK - chapter 17, The Man With Two Faces      So it seems at some point between leaving school, and sticking his face to the back of Quirrel's head possessing Quirrel he got a new face some how.   How did he manage that? Is it some dark magic he applies? Is it from possessing snakes in Albania? I try to share my internet connection from my laptop (win7) via virtual wifi to my android phone (Samsung Gio). In an elevated cmd I enter  netsh wlan set hostednetwork mode=allow ssid=VWiFi key=xxx keyUsage=persistent netsh wlan start hostednetwork   The android phone connects to VWifi, but the internet connection is hardly usable on the phone while the internet connection on my laptop is very good at the same time (some Mbps)  What works: I can start WhatsApp, type and receive text messages, so I guess there's no general problem, i.e. config can't be completely wrong - but when I try to send pics or audio or try to receive pics or audio messages then I see from the network monitor on my laptop that the connection doesn't even try to send or receive anything (0 kbps up/down).  What sometimes works: connection to some websites with acceptable speed - but sometimes I don't get a single byte. Also this is not reproducible - the same website sometimes shows up, sometimes android tells my the site was not available.  What never worked so far: connecting to Google Play Store. It always tells me to check my connection and try again.  What I tried so far: I read on problems with IPv6, but no matter if I enable or disable IPv6 in the settings of the virtual Wifi, it doesn't help.  I also read about problems related to static/dynamic IPs, my netsh interface ip show config tells my that dchp isn't enabled on my virtual Wifi connection. If I try to enable it by netsh interface ip set address "myWificonnection" dhcp the android phone won't even connect anymore to the virtual Wifi at all. So there may be a solution here if android would connect with dhcp enabled.  I also read about problems with MAC filters, but this is no router, there's no MAC filter in the virtual Wifi.  When I directly connect to a real WLAN router, everything is fine and working. I have the problems only when trying to get into the internet via the virtual Wifi.  Any ideas what may be configured wrong? Either on laptop or on android? Thanks. Neutron decay and electron anti neutrino $n\to p + e + \bar{\nu}_e$ Why do we need neutrino to explain neutron ? Is there any evidence regarding existence neutrinos in the context of $n\to p + e + \bar{\nu}_e$? Have iPhone 4 with iOS 5.1.1 Trying to update to 6.1.2 (not the latest) via downloaded IPSW but unfortunately getting error:     iphone could not be restored device isn't eligible for the requested   build   After searching for fix all over the internet found some suggestion like putting # in hosts file in line gs.apple.com but not helped.  Have you any idea why I'm getting this error and can't restore iphone? Magnetic Field in the presence of a conductor I am studying for my quals and came across an old question that reads like the following:      There are two regions in space separated by an infinite conducting plane. Region 1 has a magnetic dipole of moment $\vec{\mu}$ located a distance $d$ from the plane. What is the magnetic field $\vec{B}$ everywhere in region 1?   I know that for a perfect conductor (superconductor), the normal component of $\vec{B}$ is zero–although I don't exactly know why–but I don't know if that is the case when the problem involves a "conductor" (not explicitly a perfect conductor).  TL;DR: Can anybody give me some insight about the magnetic boundary conditions of a stationary magnetic field in the presence of a conductor?  Thanks! What makes a photo a good photo? I don't know if this is a stupid question, this just came across my mind.  Imagine a photo of a dog yawning.  Someone could say that is a very good photo as it is taken just at the right moment, from a perfect angle (eg. level with the dog) and it has a shallow depth of field focusing on its face.  Someone else might dislike it because unfortunately the dog is ugly.  So from that example I could say people look at the following elements when judging a photo (but I could be wrong):   The timing (if it's taken at the right moment) The angle it's taken from (composition?) DOF (composition?) The subject (eg. whether the dog is pretty)   I am interested to know what experts think the elements you look at when judging whether a photo is a good photo.  Thanks in advance for your comments. I think the title says it all. I can't see any reason employers have to incentivize employees to contribute to their 401(k) evenly throughout the year. Instead couldn't they use a relatively simple formula that is based on how much of their income the employee has contributed to their 401(k) thus far for the year? If that or their current contribution is over the threshold, they get the match this pay period, even if they didn't contribute anything.  EDIT: To clarify, my employer matches 100% of the first 3% of my contribution and 50% of the next 2%. The match is added every pay period along with my contribution. I am pretty sure there is no "true-up" feature, so if I were to hit the $17.5K limit early, and not be able to contribute at least 5% of my salary, I would not get the full match. So I have to be careful to make my contributions evenly throughout the year to get the maximum match. Just trying to figure out my employer's motivation for requiring this. Maximum Likelihood Estimator for $\theta$ when $X_1,\dots, X_n \sim U(-\theta,\theta)$ Exercise :     Calculate a Maximum Likelihood Estimator for the model $X_1,\dots, X_n \; \sim U(-\theta,\theta)$.   Solution :  The distribution function $f(x)$ for the given Uniform model is :  $$f(x) = \begin{cases} 1/2\theta, \; \; -\theta \leq x \leq \theta \\ 0 \quad \; \; , \quad\text{elsewhere} \end{cases}$$  Thus, we can calculate the likelihood function as :  $$L(\theta)=\bigg(\frac{1}{2\theta}\bigg)^n\prod_{i=1}^n\mathbb I_{[-\theta,\theta]}(x_i)= \bigg(\frac{1}{2\theta}\bigg)^n\prod_{i=1}^n \mathbb I_{[0,\theta]}(|x_i|) $$  $$=$$  $$\bigg(\frac{1}{2\theta}\bigg)^n\prod_{i=1}^n \mathbb I_{[-\infty,\theta]}(|x_i|)\prod_{i=1}^n \mathbb I_{[0, +\infty]}(|x_i|)$$  $$=$$  $$\boxed{\bigg(\frac{1}{2\theta}\bigg)^n\prod_{i=1}^n \mathbb I_{[-\infty,\theta]}(\max|x_i|)}$$  Question : How does one derive the final expression in the box from the previous one ? I can't seem to comprehend how this is equal to the step before.  Other than that, to find the maximum likelihood estimator you need a $\theta$ sufficiently small but also $\max |x_i| \leq \theta$ which means that the MLE is : $\hat{\theta} = \max |x_i|$. How to restrict some websites in Ubuntu 14.04 I would like to restrict some websites to be surfed. I mean I want to prevent access to some websites. Please guide me on how to do the same in Ubuntu 14.04 LTS. Tracker icon is misaligned in activity page $\aleph_1$ is the cardinality of the countable ordinals. It is the least cardinal number greater than $\aleph_0$, and assuming the continuum hypothesis it's equal to $\mathfrak{c}$, the cardinality of the the real numbers.    My question is, is it possible for all $\aleph_1$ subsets of $\Bbb{R}$ to have Lebesgue measure $0$?  This is, of course, impossible assuming the continuum hypothesis, because then all sets of real numbers would have measure $0$, which is absurd.  But is $\mathsf{ZFC}$ + $\lnot\mathsf{CH}$ + "all subset of $\Bbb{R}$ of cardinality $\aleph_1$ have Lebesgue measure $0$" consistent?  If not, what if we replaced Lebesgue measure with some other measure?  It may be worth noting that, although there may be subsets of $\Bbb{R}$ with cardinality $\aleph_1$, there are no subsets of $\Bbb{R}$ which have the order-type $\omega_1$ (the order-type of the countable ordinals) under the usual ordering on $\Bbb{R}$.  Any help would be greatly appreciated.  Thank you in Advance. Travel to US two day before B1 visa expires Sometimes when I write, for example, "the boundaries of segments", I am suggested to use "segments' boundaries" or even "segment boundaries".   Or "the page's content" vs. "the content of the page" vs. "the page content". Then I would like to know is it always preferred to use phrases with apostrophe or adjective?  For example      In our terms, they are mainly textual elements within the page content, which serve as the starting point  of a data region (or a data region's starting point ?)  or a distinctive feature within it