"A bed that needs made"
How are "needs to be washed," "needs washing," and the regional variant "needs washed" to be distinguished"?
I need to prove that $\mathbb{R}\backslash\mathbb{Q} \sim \mathbb{R} $  Using Cantor-Bernstein, need to show an injection from $\mathbb{R}\backslash\mathbb{Q}$ to $\mathbb{R}$ and from $\mathbb{R}$ to $\mathbb{R}\backslash\mathbb{Q}$.    $\mathbb{R}\backslash\mathbb{Q}$ is a subset of $\mathbb{R}$ so only need to show injection from $\mathbb{R}$ to $\mathbb{R}\backslash\mathbb{Q}$ to complete the proof.    Possible injection: $f:\mathbb{R}\to \mathbb{R}\backslash\mathbb{Q}$ defined as $f(x) = \pi x$ if $x$ is not a multiple of $\pi$; otherwise $f(x) = \sqrt{2} x$.    Not sure if $f$ actually is an injection... How can the Xenomorph see? If you just look at a picture of one there are no eyes readily apparent but they clearly know where they are going. Could their screeching be some form of echo-location? Proof that a sum of Bernoulli rvs has Binomial distribution Adjective for someone who exaggerates emotions to get sympathy What's the difference between Normalization and Standardization? At work we were discussing this as my boss has never heard of normalization. In Linear Algebra, Normalization seems to refer to the dividing of a vector by its length. And in statistics, Standardization seems to refer to the subtraction of a mean then dividing by its SD. But they seem interchangeable with other possibilities as well.   When creating some kind of universal score, that makes up $2$ different metrics, which have different means and different SD's, would you Normalize, Standardize, or something else? One person told me it's just a matter of taking each metric and dividing them by their SD, individually. Then summing the two. And that will result in a universal score that can be used to judge both metrics.  For instance, say you had the number of people who take the subway to work (in NYC) and the number of people who drove to work (in NYC).   $$\text{Train} \longrightarrow x$$ $$\text{Car} \longrightarrow y$$  If you wanted to create a universal score to quickly report traffic fluctuations, you can't just add $\text{mean}(x)$ and $\text{mean}(y)$ because there will be a LOT more people who ride the train. There's 8 million people living in NYC, plus tourists. That's millions of people taking the train everyday verse hundreds of thousands of people in cars. So they need to be transformed to a similar scale in order to be compared.  If $\text{mean}(x) = 8,000,000$  and $\text{mean}(y) = 800,000$  Would you normalize $x$ &amp; $y$ then sum? Would you standardize $x$ &amp; $y$ then sum? Or would you divide each by their respective SD then sum?  In order to get to a number that when fluctuates, represents total traffic fluctuations.  Any article or chapters of books for reference would be much appreciated. THANKS!  Also here's another example of what I'm trying to do.   Imagine you're a college dean, and you're discussing admission requirements. You may want students with at least a certain GPA and a certain test score. It'd be nice if they were both on the same scale because then you could just add the two together and say, "anyone with at least a 7.0 can get admitted." That way, if a prospective student has a 4.0 GPA, they could get as low as a 3.0 test score and still get admitted.  Inversely, if someone had a 3.0 GPA, they could still get admitted with a 4.0 test score.  But it's not like that. The ACT is on a 36 point scale and most GPA's are on 4.0 (some are 4.3, yes annoying). Since I can't just add an ACT and GPA to get some kind of universal score, how can I transform them so they can be added, thus creating a universal admission score.  And then as a Dean, I could just automatically accept anyone with a score above a certain threshold.  Or even automatically accept everyone whose score is within the top 95%.... those sorts of things.  Would that be normalization? standardization? or just dividing each by their SD then summing? I want to create an effect/color like this image of the cloud in the Parse.com logo. It is not quite white, and seems to have a texture. I am new to illustrator, but have a white "cloud" made thanks to some other tutorials. How do I proceed? How to get my own IP address and save it to a variable in a shell script? What are watched tags and ignored tags? How do they work? What are tag subscriptions? What are interesting tags? On Stack Overflow, the content of the main page question list appears to be influenced by watched and ignored tags. How does that work?   For more information, see &quot;&quot; in the . Which dialects of English consider "would" to be a polite form of "will"? My recent trip to India exposed me to many sentences using &quot;would&quot; as a polite substitute for &quot;will&quot;, as in  Please make sure to leave on time. The last bus would depart at 8PM. Thanks for checking out early. However, there would be no refund.  I am not familiar with such patterns in AmE or BE. Are they common in particular settings that I'm not aware of? How common are they in India? Note: the following query seems to return a bunch of other examples (among conditional uses of course) inurl:.co.in &quot;would&quot; Combinatorial proofs: having a difficult time understanding how to write them out Can someone explain how combinatorial proofs work?  I've included an example questions that's been giving me a hard time.  Any insight on the topic would be great.  $$\sum_{k=1}^{n}k{n \choose k} = n2^{n-1}$$  Another one:  $${2n \choose 2} = 2{n \choose 2} + n^2$$  The solution says:  LHS: Pick two people from a pool of n men and n women. RHS: Pick two women, pick two men, and pick one of each.  But I don't see how this applies.  How does $n^2$ show that we're picking "one of each?"  Thanks for the help :) List all my drafts In GMAIL you can list all your boss-tell-off and wife-cuss-out emails by clicking Drafts    I'd like to see my started-but-never-finished responses, possibly between x Answers and y Votes in /&lt;&lt;user&gt;&gt;/Stats/? won't instead of using' wouldn't' is possible? I have asked many questions about "would" both in ELL and ELU. But I still have a question about the use of "would". I have recently asked a question which @Jay also answered. He used "wouldn't" in the following sentences: 1. Here, you wouldn't say, "May I ask you what is your name?" Though we break this rule for questions sometimes 2. Well, someone might say that in informal speech, but you wouldn't write it or use it in formal speech. 3. "May I ask you what's your name?" is awkward; a fluent speaker wouldn't say that.  I had asked  question in ELL and I have received answers for it. But there is one thing that I'm still confused about.  Do the meanings of the sentences above change if we use 'won't' instead of using 'wouldn't' ? can we use 'won't' in the place of 'wouldn't' without changing the meanings of the sentences above? After upgrading to Ubuntu 14.04 from 12.04 I have duplicate entries in dash.    How can I get rid of them? Probability to choose specific item in a "weighted sampling without replacement" experiment Given $n$ items with weight $w_n$ each -- what is the probability that item $i$ is chosen in a $k$-out-of-$n$ "weighted random sampling without replacement" experiment? Can a closed-form solution that depends only on $w_i / w_\cdot$ be derived ($w_\cdot = \sum_j w_j$.)?   EDIT: A solution that depends only on $w_i / w_\cdot$ is impossible. Assume $n=3$, $i=1$, $w_1 = 1$, and two cases: (1) $w_2 = 1, w_3 = 1 + \varepsilon$, (2) $w_2 = 2, w_3 = \varepsilon &gt; 0$. In case (1) the probability is almost $2/3$, in case (2) it is almost $1$, but in both cases $w_1 = 1$ and $w_\cdot = 3 + \varepsilon$.  What I have tried so far to solve the problem:  Let $P^n_k(w, i)$ be the probability that item $i$ is chosen in an $k$-out-of-$n$ experiment with weight vector $w$. In the first draw, the item is chosen with probability $w_i / w_\cdot$. Otherwise, we are looking for the probability to choose this item in a $k-1$-out-of-$n-1$ experiment, with the same weight vector except for the item that has been selected. Hence:  $$ P^n_k(w, i) = w_i / w_\cdot + \sum_{j \neq i} w_j / w_\cdot \cdot P^{n-1}_{k-1}(w - j, i) $$ $$ = w_\cdot^{-1} \left( w_i + \sum_{j \neq i} w_j \cdot P^{n-1}_{k-1}(w - j, i) \right) $$  with $w-j$ being "the vector $w$ without the $j$th element".  How to solve this recurrence relation? (If it is correct at all...) I have an Ubuntu 14.04 server that has no external monitor connected.  I use NoMachine to remote control the machine.  When I do so, the Unity/Gnome interface doesn't see any monitors connected, so I can only use 800x600 when connecting with NoMachine.  If I plug in a monitor, I can set the resolution to whatever size the NoMachine window is on the remote computer.  Is there a way to create a "fake" monitor device on Ubuntu so I can set a desktop resolution in Unity/Gnome? static_assert fails compilation even though template function is called nowhere How to find sum of the infinite series $\sum_{n=1}^{\infty} \frac{1}{ n(2n+1)}$ $$\frac{1}{1 \times3} + \frac{1}{2\times5}+\frac{1}{3\times7} + \frac{1}{4\times9}+\cdots $$  How to find sum of this series?  I tried this: its $n$th term will be = $\frac{1}{n}-\frac{2}{2n+1}$; after that  I am not able to solve this. Kant introduces the notion of the noumenon in his critical philosophy; he also later demonstrates in his system that solipsism isn't possible.   Is the introduction of the noumenon essential to this demonstration, and thus justifies it's introduction? How can I enable Ctrl+Alt+Backspace? Ctrl+Alt+← can usually be set to restart X, however I can't find the option to allow this (it is disabled by default).  I have looked in System-&gt;Preferences-&gt;Keyboard and System-&gt;Preferences-&gt;Keyboard Shortcuts but I can't find an option to enable it.  Where can I change this setting? Let $m,n$ be positive integers bigger than $1$. Show that $\mathbb{Z}_m \times \mathbb Z_n$ is cyclic if and only if $\gcd(m,n)=1$.    I have no idea on how to start. Anyone hints are much helpful.