Prove there are no sets $x,y$ such that $x\in y$ and $y\in x$
From axiom of regularity, how can I prove $x \notin y \lor y \notin x$
Rufus nor any other software can fix my 16GB usb drive after using RUFUS I wanted to make a bootable USB drive using Rufus. I opened the program went with all the default options and I clicked start BUT what I forgot to do is to select an iso because I thought it would just make the disk bootable without selecting anything. Unfortunately it did not. It gave me an error. I do not remember it because this was about 6 months ago after I gave up in fixing it. Anyway I tried to reformat it again using diskpart and it fails. With Rufus it says "ERROR while partitioning drive" and I think that was the initial error as well. Also during the struggle I got messages from windows saying that the disk is write protected and NO, there is no switch for that on the USB pendrive.   More info:     Transcend 16 GB     Rufus 1.4.9,     Frustrated student :/ Limit of $\prod\limits_{k=2}^n\frac{k^3-1}{k^3+1}$ Calculate $$\lim_{n \to \infty} \frac{2^3-1}{2^3+1}\times \frac{3^3-1}{3^3+1}\times \cdots \times\frac{n^3-1}{n^3+1}$$ No idea how to even start. Suppose Alice publishes a book with a public key in it, and later wants to prove that she wrote the book. She could sign challenge messages with her private key, and others could verify those signed messages. Alice is proving she knows a private key without revealing anything about it.  Is this an example of an interactive zero knowledge proof?   Or does this example somehow not apply to zero knowledge proofs? How can I set the maximum draw type for multiple objects? Deploying Qt 5 App on Windows Does the condition $\lim\limits_{n\to\infty}\frac{a_{n+1}}{a_n}=1$ imply that $a_n$ convergent?  When I say convergent I mean to $L\in \mathbb{R}$ or to $\infty$ or to $-\infty$  I have a gut feeling this statement is false, just can't find a series which contradicts it.  Thanks a lot How do I get %LocalAppData% in c#? How to install h.264 decoder? We all know very well how to make an angle of 15 and 45 degree and its multiple using compass. Can anybody tell me how to make an angle of 10 degree and its multiple using compass? Bibliography in Texmaker Determine Whether Two Date Ranges Overlap Title says it all, I don't see confirmation in  and a cursory google search seemed to say assume no and speculate about the pokemon bank. My keyboard has no "media" keys; can I control media without them? My intuition tells me it's a trade off between speed and security, but how did the standardisation process select these three seemingly arbitrary key lengths (namely, AES-128, AES-192, AES-256). How to get back sudo on Ubuntu? How does a fork bomb work? WARNING DO NOT ATTEMPT TO RUN THIS ON A PRODUCTION MACHINE   In reading the  I generally follow what's going on with the following code:  :(){ :|:&amp; };:   excerpt of description     The following fork bomb was presented as art in 2002;   its exact origin is unknown, but it existed on Usenet prior to 2002.   The bomb is executed by pasting the following 13 characters into a    shell such as  or . It operates by defining   a function called ':', which calls itself twice, once in the   foreground and once in the background.   However the last bit isn't entirely clear to me. I see the function definition:  :(){ ... }   But what else is going on?  Also do other shells such as ksh, csh, and tcsh also suffer the same fate of being able to construct something similar? How to insert pipe symbol in (La)TeX? How to insert pipe symbol | in TeX (LaTeX)?  I have tried this sample with pdflatex tmp.tex  \documentclass{extarticle} \begin{document} \textpipe \end{document}   And it give undefined control sequence error  This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian) restricted \write18 enabled. entering extended mode (./tmp.tex LaTeX2e &lt;2009/09/24&gt; Babel &lt;v3.8l&gt; and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, loaded. (/usr/share/texmf-texlive/tex/latex/extsizes/extarticle.cls Document Class: extarticle 1996/10/08 v1.0 Non Standard LaTeX document class (/usr/share/texmf-texlive/tex/latex/base/size10.clo) (/usr/share/texmf-texlive/tex/latex/base/exscale.sty)) No file tmp.aux. ! Undefined control sequence. l.3 \textpipe Do the parent directory's permissions matter when accessing a subdirectory? If I have a root folder with some restrictive permission, let's say 600, and if the child folders/files have 777 permission will everybody be able to read/write/execute the child file even though the root folder has 600? GNOME 3.26 - Clicking one window brings another in the foreground (Ubuntu 17.10) I'm on Ubuntu 17.10 with GNOME 3.26.  Often I have windows tiled on the left and right side of the screen. A typical setup is to have a browser and text editor on the left, a PDF reader and terminal on the right.  Something I've seen happen very often: I'm reading the PDF on the right, having the window in focus. The text editor on the left. When I click on the text editor to write something, it brings forward another window on the right (say the file browser), covering the PDF reader.  This seems to have something to do with the Alt-Tab view history.  My question is: Is it possible to remove the automatic bring-to-front of windows? I don't understand why unrelated windows are brought to the front when I click on another application. I keep going around in circles with this problem:  Given the functions $f:X\to Y$ and $g:Y\to Z$, if $g\circ f:X\to Z$ is bijective, then prove $f$ must be one-to-one and $g$ must be onto. I was able to prove this without difficulty. However the second part of the problem has me stumped:  a) Find functions $f,g$ where $g\circ f$ is bijective but $f$ fails to be onto.  b) Find functions $f,g$ where $g\circ f$ is bijective but $g$ fails to be one-to-one.  My attempt for (a): Let $f:\mathbb{R}\to \mathbb{R}^+$ be defined by $f(x)=e^x$ and $g:\mathbb{R}^+\to \mathbb{R}$ be defined by $g(x)=\ln(x)$. Then $g\circ f(x)=g(f(x))=g(e^x)=\ln(e^x)=x$ which is bijective, $g$ is onto and $f$ fails to be onto... or so I thought. Upon closer inspection $f$ $\underline{is}$ onto for the given codomain $\mathbb{R}^+$.  And now I'm stuck in a rut. Anyone out there have any hints?