For e.g   "All Muslims are terrorists, that muslim guy knifed that girl in London last month"  "All white men have privilege, just look at any senior level boardroom"  (not the same as the fallacy for associating a group with the actions of a few)
What is the technical term for when people thinks the actions of the few represent the many.  Like when people thinks everyone in a specific group behaves a certain way cause of how a few people in the group behave, including non stereotypical behaviours. I thought it was "generalisation" but I couldn't find any articles using that term.
I am reading through Folland's Real Analysis: Modern Techniques and Their Applications, and they have the following proposition and proof:     Proposition: If $\{f_{j}\}$ is a sequence of $\bar{\mathbb{R}}$- valued measurable functions on $(X, \mathcal{M})$, then the functions:      $$g_{1}(x)=\sup_{j} f_{j}(x)$$ $$g_{2}(x)=\inf_{j} f_{j}(x)$$ are   measurable.       Proof:      We have       $$g_{1}^{-1}((a,\infty])= \bigcup_{j=1}^{\infty}  f_{j}^{-1}((a,\infty])$$ $$g_{2}^{-1}([-\infty,a))=  \bigcup_{j=1}^{\infty} f_{j}^{-1}([-\infty,a))$$      Where the result follows from the fact that $g_{1}^{-1}((a,\infty])\in  \mathcal{M}$ for all $a \in \mathbb{R} \iff g$ is measurable, and   $g_{2}^{-1}([-\infty,a))\in \mathcal{M}$ for all $a \in \mathbb{R}  \iff g$ is measurable.   I understand the last part of the proof, but how do we know $g_{1}^{-1}((a,\infty])= \bigcup_{j=1}^{\infty}f_{j}^{-1}((a,\infty])$ and $g_{2}^{-1}([-\infty,a))=\bigcup_{j=1}^{\infty} f_{j}^{-1}([-\infty,a))$? I would appreciate any help with this. Story on quantum indeterminacy: protagonist has to “quantum select” a portable computer’s state How to use resistors? I have a power supply of 5 volts @ 1A. I want to reduce the current from 1A to 250mA. Which resistor should be use?   I tried this equation(Ohm's Law):  R = V / I  = 5/(0.75)  = 6.66 Ohms.  I tried the 6.66 Ohm resistor but it only reduce few mili Amps. Pass by Reference / Value in C++ I would like to clarify the differences between by value and by reference.  I drew a picture     So, for passing by value,  a copy of an identical object is created with a different reference, and the local variable is assigned the new reference, so to point to the new copy  How to understand the words: " If the function modifies that value, the modifications appear also within the scope of the calling function for both passing by value and by reference "  Thanks! Why use "need not" instead of "do not need to"? I recently read that:     What our current level of thermodynamics does tell us though is that if there is such a thing as a Big Crunch, the universe will look a lot different as it heads towards collapse than it did when expanding – the universe started in a state of low entropy and high order and will end in a state of high entropy and   low order.   But shouldn't the order be in a high state and hence entropy becomes a low state in the Big Crunch (assuming a closed universe)?  The reason I write this is because the gravitational forces in a closed universe are so strong they will cause gravitational collapse so the universe will shrink and go backwards, eventually through all the stages of the big bang and become a singularity once more.   It was my understanding that a singularity has a state of high order and low entropy. Have I got this the wrong way round?   If so; Can someone please explain why? pgfplots external with large dataset (lualatex?) I have fairly large datasets with densely strucutred data that i cant downsampe much without loosing structure. I use TexMaker on Ubuntu 14.04LTS. I use   \usepackage{tikz,pgfplots,pgfplotstable} \pgfplotsset{compat=1.9} \usepgfplotslibrary{external} \tikzexternalize   and   \tikzsetnextfilename{figs/test1}   to externalize the figures. This works good compiling with pdflatex -shell-escape. But as the data becomes to large I am out of memory. I am trying to compile using LuaLaTeX -shell-escape instead of pdfLatex but get the following error message:   ! Package tikz Error: Sorry, the system call 'pdflatex -halt-on-error -interact ion=batchmode -jobname "figs/test1" "\def\tikzexternalrealjob{article}\input{ar ticle}"' did NOT result in a usable output file 'figs/test1' (expected one of . pdf:.jpg:.jpeg:.png:). Please verify that you have enabled system calls. For pd flatex, this is 'pdflatex -shell-escape'. Sometimes it is also named 'write 18' or something like that. Or maybe the command simply failed?   so pgfPlots seem to call pdfLatex without the appropriate -shell-escape flag and without me specifying it. How can i get this to compile in LuaLatex? or can i compile only the figures in LuaLatex and the rest in pdfLatex (the opposite of what is happening now)? I found  and  example but neither helped me...  Thankfull for help and i am also thankful for any general advice that can help me resolve the problem of ploting larger data sets in pgfplots.   Cheers /J Should the first word after a colon be capitalized? Which of the following is correct?   For example: This. For example: this. What autofocus zone selection mode should I use for action/event shooting? I have a Canon 7D, and typically shoot everything I do in its single-point autofocus zone select mode, because I usually want fine control over exactly what the camera is focusing on and I often find that its two automatic focus zone select modes don't focus on what I want in focus.  For most of the photography I do, this is fine -- I have enough time that I can compose the shot the way I want, use the joystick on the back to select the right focus point, and take the shot at my leisure.  However, recently I've been doing more event/action photography, and I've been running into issues with this mode of operation.  Too often, I will see a person start to do something interesting, but my autofocus point is not in the right place -- so by the time I get the camera up, adjust the settings, and move the autofocus point, the opportunity to take the shot has passed.  My question is, what autofocus zone selection mode and workflow should I use for this type of photography?  I could use the 5-zone partial-auto mode (which gives me a choice of top, middle, bottom, left, or right, and then the camera chooses the points within my selected region), but I find that the time needed to switch in between that mode and the single-point mode is similarly prohibitive, and I have to hope that the camera chooses the right thing to focus on. How do I solve $$x'=e^{it}\overline{x}?$$  This is a complex differential equation, but I don't see how to solve it.  Edit: the original ODE is given by $$(x', y')=\begin{pmatrix}\cos t&amp; \sin t\\ \sin t&amp;-\cos t\end{pmatrix}(x,y)$$ I want to show that solutions of this ODE do not remain bounded for all $t$, and the idea was to solve the complex equation. How do I disable this:    after taking screenshot? How do I run Command & Conquer Gold on Windows 7 64-bit (in XP mode)? I downloaded the first Command &amp; Conquer game  and burnt some CDs. I couldn't get the Setup.exe program to run in Windows 7 64-bit, as it must need some old DLLs. So I ran up the Windows XP Mode virtual machine, and was able to install it fine.   However, when I try to run the program, I just get an empty message box with an "OK" button. I've set the compatibility to Windows 95, and checked all of the options in the Compatibility tab, but it's not running. I also downloaded the patch suggested by EA, which is an updated version of the THIPX32.DLL file (copied into the C&amp;C installation folder).  Has anyone managed to get this working? How do I install OpenStack? Prove that $\sup \{-x \mid x \in A\} = -\inf\{x\mid x \in A\}$ I need to prove that $\sup \{-x \mid x \in A\} = -\inf\{x \mid x \in A\}$ and am having trouble moving the $-x$ out of the $\sup$ to $\inf$. Another thing is that I don't quite know how to prove $b = \inf$ (see below). Any help would be appreciated! Here my attempt:  Let $a = \sup\{-x \mid x \in A\}$  Then by definition $a \geq -x$ for $x \in A \implies -a\leq x$ for $x \in A$  Thus $-a$ is a lower bound of $A$. Assume $b$ is a lower bound of $A$  Then $b \leq -a \implies  a \geq -b$ and $a = \sup \{−x \mid x\in A\} = -\inf(A)$ singular/ plural in the attributive A doll house or a dolls house? Which is correct for the toy? ... There's that thing called Same Sex Couples Act; how about calling it Same Sex Couple Act?  The question is - when should I put attributives in plural? As far as I remember, Bill Bryson claimed in his Dictionary of Troublesome Words that - and that's what I vaguely recall from my classes - attributives should be in singular. Except for some exceptions. If so, what are they? I'm looking for some rule of thumb here other than "when in doubt, JFGI", of course.  NOTE: I leave out forms like a doll's house/dolls' house as they're pretty clear to me, as well as cases like The 'Big Boys and Their Motors' Club in which attributives are separate entities. When should I use "when" and "while"? But you can't find anything while you're crying.   But you can't find anything when you're crying.   I'll tell you about it while Frank saddles the horse.   I'll tell you about it when Frank saddles the horse.     When should I use when, and when while? Are these sentences correct? I've found conflicting sources over who initiated the idea of Marvel's Multiverse having numbered universes.  Some say Alan Moore's Captain Britain was the first to use Earth-616, whereas others indicate it was fan-created from Fanzines: with Mark Gruenwald's Omniverse being the frontrunner.  Who is responsible for creating the universe designations? Is there any credible information on their development? Installing AMD & Intel dual graphics Labelled spanning trees of $K_n-e$ Let $e$ be an edge of $K_n$- the complete graph on $n$ vertices. Prove that the number of labelled spanning trees of $K_n-e$ is $(n-2)n^{n-3}$.  I think the answer lies in using some modified form of Prüfer's sequence but I can't quite nail it. What are the various units (ex, em, in, pt, bp, dd, pc) expressed in mm? How can one determine the length of the different units (measured 1ex, 1em, 1in, 1pt, 1bp, 1dd, 1pc) in mm?