What's the difference between "someone" and "somebody"?
Is there a subtle difference between "somebody" and "someone", "anybody" and "anyone"?
Does there exist a continuous function $\: f : \mathbf{R} \to \mathbf{R} \:$ such that for   all  functions $\: g : \mathbf{R} \to \mathbf{R} \:$, for all real numbers $x$,  there exists a real number $y$ such that $\: x &lt; y \:$ and $\: g(y) &lt; f(y) \:$? Example 4.21 in Baby Rudin: Why is the inverse of this function not continuous at this point? Bridge Rectifier Fails When AC Inputs are Shorted Identical coefficients estimated in Poisson vs Quasi-Poisson model During Winterbash 2014, there was a hat called , which was earned by giving an answer scoring 5 or better to question that had a score of −3 or worse at the time of answering and later rose to a score of +3 or better.  I’ve already shared the . Those cases give me a great deal of confidence that this would be a challenging badge trigger that would produce good behavior with a minor tweak. Here are the Red Barons earned on other sites:    (Logan Maingi) Mathematics  (Mike Miller) Mathematics  (Hugo) English Language and Usage  (tchrist) English Language and Usage  (Mr. Shiny and New 安宇) English Language and Usage  (Darth Satan) Science Fiction and Fantasy  (DVK) Science Fiction and Fantasy  (rolfl) Code Review  (Heslacher and Hosch250) Code Review  (Edward) Code Review  (janos and Manny Meng) Code Review  (Mark Mayo, Rory Alsop and MeNoTalk) Travel      (DJClayworth) Christianity  (McMagister) Puzzling   Looking through the timelines, I’m convinced that the answerer’s votes should be excluded from the pre-answer question score calculation. Doing that would have reduced the number of Red Barons to 16 across the network. However, the cost of making a badge harder to obtain is worth the benefit of avoiding giving people an incentive to manipulate question scores¹.  To wrap up, the hat seemed to have encouraged a number of great answers and rescued some questions that would otherwise have been lost to time. My outstanding questions are:   Were there any problems on questions where people were attempting to earn the hat, but failed? (Or any other problems I didn’t observe.) If not, should we  or create a new badge? If we create a new badge, what should it be called?   I’m especially interested in feedback that counters my own bias in favor of this idea. If I’m missing any problems, I’d like to know about them now.    ¹ Several questions were downvoted, answered, edited (sometimes trivially)  and upvoted by the user who earned the hat. How can I get back to Blender's default theme? Protect .NET code from reverse engineering? Obfuscation is one way, but it can't protect from breaking the piracy protection security of the application. How do I make sure that the application is not tampered with, and how do I make sure that the registration mechanism can't be reverse engineered?  Also it is possible to convert a C# application to native code, and  is too costly.  C# provides lot of features, and is the ideal language for my code, so writing the whole codebase again in C++ is out of the question.  Secure certificates can be easily removed from the signed assemblies in .NET. Explaining to laypeople why bootstrapping works I would like to visit Iran as a tourist but I'd also like to visit the USA some time after. I know the relations between the two countries are bad.   Is it likely that I'm not allowed to enter the USA after having been to Iran?   If it matters, I've never been to either of those countries. I'm a Swiss citizen, an atheist from a Christian background. Let's say I launch a bunch of processes from a ssh session. Is it possible to terminate the ssh session while keeping those processes running on the remote machine? I'm learning Neural Networks and I grasped the algebra behind them. I'm now interested in understanding how normalization and centering of the input data affect them. In my personal learning project (Regression with NN) I've transformed my input variables to a range between 0 and 1 using the following function:  normalize &lt;- function(x) {return((x - min(x))/ (max(x) - min(x)))}   The NN model fits well and has an acceptable out-of-sample prediction error.   However, I read in other  that scaling the inputs to have mean 0 and a variance of 1 is advised for NN. I don't fully understand:   how this transformation works better for NN against the min-max normalization between 0 and 1. how can I assess which transformation to apply in my data? Disabled submit button on form vs allow submit then show errors? Create an instance of an object from a String in Dart? Games like Super Metroid and Aquaria present the terrain with the other facing parts having rocks and stuff while deeper behind them (i.e. underground) there's different detail or just black.      I would like to do something similar using polygons. Terrain is created in my current level as a set of overlapping square boxes. I'm not sure if this rendering method will work such a system for creating terrain but if anyone has ideas I'd love to hear them. Otherwise I'd like to know how I should re-write the terrain rendering system so it actually works to draw terrain in this manner... In a bash script what does a dot followed by a space and then a path mean? I came across this example when trying to mount a usb device inside a openvz container and I have never seen the construct in the second line before. Can you explain what it signifies?  #!/bin/bash . /etc/vz/vz.conf CSS Selector that applies to elements with two classes How to set the command prompt's color in Bash? If $\forall x \in R, x^2-x \in Z(G)$, than $R$ is commutative Let $R$ be a ring such that for every $x\in R$ we have $x^2-x \in Z(G)$. Show that $R$ is a commutative ring.    My thoughts  What should I do? I could show that every $y \in R$ could be written in the shape $x^2-x$ but I don't know if that is true. We know that  $y \cdot(x^2-x) \ = \ (x^2-x)\cdot y$ for any $x,y \in R$, but that doesn't mean that $xy = yx$. Please give me a hint $2 \otimes_{R} 2 + x \otimes_{R} x$ is not a simple tensor in $I \otimes_R I$ How to close view windows?