How to assign a word to execute a particular command
shortcut for commands
Do you say "I like apple" or "I like apples"? When stating a general fact/preference on countable nouns, singular or plural is more suitable and natural? Example 1 :  I like apple. or I like apples.  Example 2:  I like eating apple. or I like eating apples. Better yet, are there any Spacewalk-like software packages that work for both RedHat-based and Debian-based systems? Smart Phone's camera socket I just want ask how the socket in the image is called?   I couldn't really find and the closer I could get is only Raspberry's module. Show that $1^{p-1} + 2^{p-1} +\ldots + (p-1)^{p-1} \equiv -1 \mod p$ Show that    $$1^{p-1} + 2^{p-1} +\ldots + (p-1)^{p-1} \equiv -1 \mod p$$   So, I use Fermat's little theorem, that is if $p$ does not divide $a$, then $a^{p-1}$ is congruent to $1$ (mod $p$). But I'm still confused. If $1^{p-1}$ is congruent to $1$ (mod $p$), $2^{p-1}$ is congruent to $1$ (mod $p$), and $p$ does not divide $p-1$, so $(p-1)^{p-1}$ is congruent to $1$ (mod $p$). How does that equal $-1$ (mod $p$)? Comparing and contrasting, p-values, significance levels and type I error I was wondering if anybody could give a concise rundown as to the definitions and uses of p-values, significance level and type I error.  I understand that p-values are defined as "the probability of obtaining a test statistic at least as extreme as the one we actually observed", while a significance level is just an arbitrary cutoff value to gauge if the p-value is significant or not. Type I error is the error of rejected a null hypothesis that was true. However, I am unsure regarding the difference between significance level and the type I error, are they not the same concept?  For example, assume a very simple experiment where I flip a coin 1000 times and count the number of times it lands on 'heads'. My null hypothesis, H0, is that heads = 500 (unbiased coin). I then set my significance level at alpha = 0.05.  I flip the coin 1000 times and then I calculate the p-value, if the p-value is > 0.05 then I fail to reject the null hypothesis and if the p-value is &lt; 0.05 then I reject the null hypothesis.  Now if I did this experiment repeatedly, each time calculating the p-value and either rejecting or failing to reject the null hypothesis and keeping a count of how many I rejected/failed to reject, then I would end up rejecting 5% of null hypotheses which were in actuality true, is that correct? This is the definition of type I error. Therefore, the significance level in Fisher significance testing is essentially the type I error from Neyman-Pearson hypothesis testing if you performed repeated experiments.  Now as for p-values, if I had gotten a p-value of 0.06 from my last experiment and I did multiple experiments and counted all the ones that I got a p-value from 0 to 0.06, then would I also not have a 6% chance of rejecting a true null hypothesis? Can it be proven in $\sf ZF^{\neg\infty}$ that the sets $x_n=\{x_{n+1}\}$ do not exist? There are two directories shown by 'ls'.  Normally directories anywhere are blue on black background.  But the first one is blue on green and impossible to read.  Why is this?  How to make it blue on black, or at least something light on something dark?  This is on Ubuntu 12.04, using bash in Gnome Terminal.  In Konsole, the blue is slightly darker, and possible to read, though could be way better. Automatically detect edit abuse and exclude from badges/flag for mod review has 5 pages of 1 character edits (including an edit to one of my posts), apparently in a massive attempt to earn the Copy Editor badge.  Should Copy Editor, etc., ignore 1 character whitespace-only edits?    If we still want to count minor edits (which may be useful), could we at least detect edit abuse via some secret algorithm? ~20+ one character whitespace-only edits in the course of an hour should at least raise a flag of some sort.    If whitespace character are too hard to count, can we at least assume that 20 non-tag edits in 20 minutes (less than a minute per edit) is a good signal of abuse? The specific algorithm should be secret, obviously, but I think these sorts of edit abuses shouldn't be too difficult to detect. Word for two collections that do not have any elements in common I'm looking for a word for when you have a collection A and a collection B and they have no overlap.  In mathematical terms: the relation between two sets where the intersection is empty. Like in this Venn diagram:    The word that keeps popping up in my mind is disparate sets, but I don't feel that completely covers the meaning when I look at the definition, because that doesn't seem to preclude overlapping sets that are different:     disparate   1. distinct in kind; essentially different; dissimilar:   disparate ideas. Show that any set of 7 distinct integers includes two integers $x$ and $y$, such that either $x-y$ or $x+y$ is divisible by 10 Show that any set of 7 distinct integers includes two integers $x$ and $y$, such that either $x-y$ or $x+y$ is divisible by 10. I'm trying to apply the pigeonhole principle, but haven't been able to come up with a convincing argument.   Though similar to , I think the difference between the two is enough to warrant a second post. I want to bake some displacement maps for Unity Engine. I want to use Cycles renderer. I have read that it's only available in Experimental version of Cycles, but when I changed Cycles to Experimental version there isn't baking type for Displacement map, there are UV, Normals, Shadows etc. but there isn't any Displacement/Depth map choice. I have Blender 2.78a (2016-10-24) downloaded yesterday. Where can I find this option or how can I enable it? General rule for partial fraction decomposition I've used Windows for many years, using Dreamweaver as my editor as it had a file tree which is based on a project (via Local, FTP or SFTP).  I need a web development IDE with the following functionality:   syntax highlighting for PHP, HTML, CSS, JavaScript  file tree - Local, FTP, SFTP, Project-Based (e.g. via the methods of Local/FTP/SFTP) in other words, like Dreamweaver can open multiple files (tabbed)   Additionally, I wouldn't mind features like debugging, class listings, etc, as long as I can hide them away. understanding TTNavigator We have played a 7-team competition, all seven teams met, we eliminated the team with the lowest points. After that the remaining six teams played knock out games and the three winning teams will go direct to semi-finals.  We decided that 4 teams should be picked to go for semi-final and that the best loser will join the other three to make it four teams to battle at the semi-final and final.  During the quarter final games, one team is beaten 2-0, another is beaten 3-0 and the third team is beaten in a penalty shoot-out by 4-0.  Now should you want a best loser to join the other three teams making four teams to play in the semi-final, who among these three teams would be in the best losers position. Substitute for onions and garlic I love the taste of onions and garlic and it seems lots of other people do too.  But they upset my stomach so much that I can't really cook with them.  What can I use in their place to give my food a similar flavour? If asking a question or giving instruction towards a group of objects where the number is unknown (and possibly could be one) what is the correct way to phrase the sentence? Which of the following sentences are more correct:     Has there been any studies regarding this and if so what has been the   conclusion?   OR     Has there been any studies regarding this and if so what have been the   conclusions? Prove that if $V$ is an inner product space, then $|\langle x,y\rangle| = \Vert x \Vert\Vert y\Vert$ if and only if one of the vectors $x$ or $y$ is a multiple of the other.  I am given a hint to let $a= \frac{\langle x,y\rangle}{\|y\|^2}$, and let $z = x - ay$, then prove $y$ and $z$ are orthogonal and $|a|= \frac{\|x\|}{\|y\|}$. I don't know how they come up with this, what was the original idea? Identify $P(2014)$ if $P(i)=1/i$ for every positive integer $1\le i\le2013$ Suppose $P(x)$ is a polynomial of degree $2012$ and $P(x) = 1/x$ when $x$ takes the integer values $1\cdots2013$ (inclusive). What is the value of $P(2014)$?   I get $1/1007$ but I'm not sure if it's right, and my method is very inelegant. How do you disable browser autocomplete on web form field / input tags?