Why $\sup_{\substack{x\in E,\\ \|x\|=1}}\|Ax\|\geq\sup_{\substack{x\in E,\\ \|x\|\leq1}}\|Ax\|?$
Equivalent Definitions of the Operator Norm
HTML favicon won't show on google chrome Passing multiple commands to gnome-terminal from a script My bash-script is not run in a terminal, but opens a terminal at runtime to ask for user input (sudo password). I would like to tell the user in this terminal what the script is trying to do. First, here is my script:  #!/bin/bash #This should install: Qt Linguist, lrelease  #for Qt Linguist dpkg-query -l qt4-dev-tools if echo $? == 0; then  check1=1 fi  #for lrelease dpkg-query -l qt4-default if echo $? == 0; then  check2=1 fi  echo $check1 echo $check2  if [ $check1 = 1 ] &amp;&amp; [ $check2 = 1 ];then  gnome-terminal -x sudo apt-get install qt4-dev-tools qt4-default fi $SHELL   This opens a terminal with this:  [sudo] password for "username":    But I would like to have:  qt4-dev-tools and qt4-default are missing. Now trying to install. [sudo] password for "username":    How do I get this when starting the terminal with gnome-terminal -x? Make Blender usable on high resolution screen The Blender UI elements are incredibly small by default on high resolution screens on Windows (15" UHD screen).  I found the Preferences -> System -> DPI setting which can be set up to 144.  This makes Blender usable, but still uncomfortable and difficult on the eyes.  Is there a way to make the UI elements even larger? options for appearance of links in hyperref Sorry for asking such a basic question - but is there an actual term for the numbers that appear before and after the decimal point?  Example:  25.18  I know the 1 is in the tenths position, the 8 is in the hundredths position. are there singular terms which apply to all of the numbers that appear both before and after the decimal point?  I'm building a billing system, storing dollars and cents as integers (in separate columns), but for other currencies "dollars" and "cents" are not the correct terms = ).  Thanks! For what real values of $a$ does $\sum_{n=1}^{\infty}{(\frac{an}{n +1})^n}$ converge? For what real values of $a$ does the series $$\sum_{n=1}^{\infty}\left(\frac{an}{n +1}\right)^n$$ converge?  At first, I wanted to do the root test, but the problem is that $a$ could be negative.  If I take it out of the fraction to get $$\left(\frac{a}{n+1}\right)^n$$ it doesn't meet the criteria of either the Dirichlet or the Abel tests. Does Exchange support disposable e-mail addresses? Sometimes it is useful to have e-mail address like foo-randomnumber@example.org, where randomnumber identifies the conversation between a robot such as a mailing list server and a user. Is this possible with Microsoft Exchange? introduces  which will allow the introduction of new literal syntax based on existing literals (int, hex, string, float) so that any type will be able to have a literal presentation.  Examples:  // imaginary numbers std::complex&lt;long double&gt; operator "" _i(long double d) // cooked form {      return std::complex&lt;long double&gt;(0, d);  } auto val = 3.14_i; // val = complex&lt;long double&gt;(0, 3.14)  // binary values int operator "" _B(const char*); // raw form int answer = 101010_B; // answer = 42  // std::string std::string operator "" _s(const char* str, size_t /*length*/)  {      return std::string(str);  }  auto hi = "hello"_s + " world"; // + works, "hello"_s is a string not a pointer  // units assert(1_kg == 2.2_lb); // give or take 0.00462262 pounds   At first glance this looks very cool but I'm wondering how applicable it really is, when I tried to think of having the suffixes _AD and _BC create dates I found that it's problematic due to operator order. 1974/01/06_AD would first evaluate 1974/01 (as plain ints) and only later the 06_AD (to say nothing of August and September having to be written without the 0 for octal reasons). This can be worked around by having the syntax be 1974-1/6_AD so that the operator evaluation order works but it's clunky.   So what my question boils down to is this, do you feel this feature will justify itself? What other literals would you like to define that will make your C++ code more readable?    Updated syntax to fit the final draft on June 2011 TeX Live 2016: minted doesn't work with LuaLaTeX (bug fixed in June 2016) I've installed TeX Live 2016 as it was released today (thanks to the developers for that).  Now I have the following MWE:  \documentclass{article} \usepackage{minted} \begin{document}  \begin{minted}{ruby} class Foo   def init     pi = Math::PI     @var = "Pi is approx. #{pi}"   end end \end{minted}  \end{document}   When running pdflatex --shell-escape test.tex it runs through the file and produces the PDF as expected. Doing the same with lualatex --shell-escape test.tex fails with  This is LuaTeX, Version 0.95.0 (TeX Live 2016)   system commands enabled. (./test.tex LaTeX2e &lt;2016/03/31&gt; Babel &lt;3.9r&gt; and hyphenation patterns for 1 language(s) loaded. (/opt/texlive/2016/texmf-dist/tex/latex/base/article.cls Document Class: article 2014/09/29 v1.4h Standard LaTeX document class (/opt/texlive/2016/texmf-dist/tex/latex/base/size10.clo)) (/opt/texlive/2016/texmf-dist/tex/latex/minted/minted.sty (/opt/texlive/2016/texmf-dist/tex/latex/graphics/keyval.sty) (/opt/texlive/2016/texmf-dist/tex/latex/oberdiek/kvoptions.sty (/opt/texlive/2016/texmf-dist/tex/generic/oberdiek/ltxcmds.sty) (/opt/texlive/2016/texmf-dist/tex/generic/oberdiek/kvsetkeys.sty (/opt/texlive/2016/texmf-dist/tex/generic/oberdiek/infwarerr.sty) (/opt/texlive/2016/texmf-dist/tex/generic/oberdiek/etexcmds.sty (/opt/texlive/2016/texmf-dist/tex/generic/oberdiek/ifluatex.sty)))) (/opt/texlive/2016/texmf-dist/tex/latex/fancyvrb/fancyvrb.sty Style option: `fancyvrb' v2.7a, with DG/SPQR fixes, and firstline=lastline fix  &lt;2008/02/07&gt; (tvz)) (/opt/texlive/2016/texmf-dist/tex/latex/float/float.sty) (/opt/texlive/2016/texmf-dist/tex/latex/base/ifthen.sty) (/opt/texlive/2016/texmf-dist/tex/latex/tools/calc.sty) (/opt/texlive/2016/texmf-dist/tex/latex/ifplatform/ifplatform.sty (/opt/texlive/2016/texmf-dist/tex/generic/oberdiek/pdftexcmds.sty (/opt/texlive/2016/texmf-dist/tex/generic/oberdiek/ifpdf.sty) (/opt/texlive/2016/texmf-dist/tex/generic/oberdiek/luatex-loader.sty (/opt/texlive/2016/texmf-dist/scripts/oberdiek/oberdiek.luatex.lua))) (/opt/texlive/2016/texmf-dist/tex/generic/oberdiek/catchfile.sty) uname -s &gt; "test.w18"  ! Package catchfile Error: File `test.w18' not found.  See the catchfile package documentation for explanation. Type  H &lt;return&gt;  for immediate help.  ...                                                l.93     \CatchFileDef\@tempa{\ip@file}{}  ?    As mentioned, it's a freshly installed TeX Live 2016; I've also checked the installed Pygmentize version, which is 2.1.3 (installed via pip). Testing with TeX Live 2015, the above code, however, works without problems with both pdflatex and lualatex.  Does anybody have a hint for me on how to fix this, or is it a bug in lualatex or minted (or whatever other package) that should be reported?  Update: With minted version 2.2 (2016-06-08), the package loads the shellesc package automatically, as mentioned by @David Carlisle and @egreg in the comments; therefore, the problem should not occur any more, if you have this version installed. Show that $K[x,xy,xy^2,\dots]$ is not Noetherian Here is the problem I am stuck on: Fix a field $K$ and consider the subring $A \leq K[x,y]$ generated by $K \cup \{x,xy,\dots,\}$. Show that $A$ is not Noetherian.  I figure that taking ideals $I_n = (x,xy,\dots,xy^n)$ should give an infinite strictly ascending chain, which would establish that $A$ is not Noetherian, but I cannot figure out how to show that each $I_n$ is a proper subset of $I_{n+1}$. Any help here? What was Natsume hiding in her closet in episode 11? In episode 11 of Tokyo Ravens, what was Natsume hiding in her closet? Possible Australianism - netbank = a website + app by which an Aussie can do their banking, including transferring money to other people.  A while ago, I ended up with $1000 transferred into my account, which in the description looked like a netbank transfer, not like a cheque, cash deposit etc, and which looked like it had already cleared and landed in my account. Usually when something is still working through the bank's system it displays as 'pending', but did not in this case.  I received a phone call from someone, saying that they had accidentally typed in the wrong account number, and wanting me to send them the same amount of money back via netbank.   Surely bank account numbers have a checksum, which make it relatively difficult for a typo to result in a payment going to the wrong person? What are likely sources of them being able to find my phone number to call me? Obviously, the bank either being hacked, or giving it out in response to a query from this person (but surely the bank is unlikely to tell me my own mobile number if I claim to have forgotten it?). Presumably either my phone, or the phone of someone I have sent money to/received money from could be compromised. Has anyone heard of any instances of this happening?  I then went to my bank, explained the situation and said that I did want to refund the money through the officially sanctioned methodology. After the laughter died down, the bank told me to ask the person to fill out a form, then they would get me to fill out a form that would authorize undoing that exact payment.  I rang up the person to tell them this, and over the course of about a week received an increasingly elaborate story about how that wasn't working, they needed the money immediately, there was a fee to fill out that form and they couldn't afford to pay it etc.  After that, I never heard back from them again. I check my netbank for several weeks after, expecting the money to magically disappear, but it did not. This was probably a year ago, and I'm pretty vague with money so may not have noticed if it disappeared more recently. How were they expecting to benefit?  Were they hoping to get the transfer from me, and undo the transfer to me, to leave them $1k up? If so, how can an internet banking transfer be 'undone' once it has already shown as 'received'. Or was this to do with money laundering? The account they requested me to send money to was the same as the one that the money appeared to come from. This was a scam, right? How to mount an ISO file? I'm running into trouble trying to mount a large iso:  dev@dev-OptiPlex-745:~$ sudo mount -o loop /home/dev/Hämtningar/matlab2011a_64.iso /cdrom mount: warning: /cdrom seems to be mounted read-only. dev@dev-OptiPlex-745:~$    Can you tell me how I should do it? Cannot truncate table because it is being referenced by a FOREIGN KEY constraint? Using MSSQL2005, can I truncate a table with a foreign key constraint if I first truncate the child table (the table with the primary key of the FK relationship)?  I know that I can either   Use a DELETE without a where clause and then RESEED the identity (or) Remove the FK, truncate the table, and recreate the FK.   I thought that as long as I truncated the child table before the parent, I'd be okay without doing either of the options above, but I'm getting this error:     Cannot truncate table 'TableName' because it is being referenced by a FOREIGN KEY constraint. Image, pre-image, and injection proof verification Just wanted to verify this proof was correct. Trying to make sure I have a handle on these subjects before the exam. Any style comments also more than welcome.    Statement: Let $f : A \mapsto B$ be a function. $f$ is injective if and only if for all $X \subseteq A$, $f^{-1}(f(X)) \subseteq X$.  Proof:  $\Rightarrow$ Suppose that $f$ is injective. Let $X \subseteq A$, and let $x \in X$. Since $f$ is injective, $f^{-1}(f(X)) = \{x\} \in X$, so $f^{-1}(f(X)) \subseteq X$.   $\Leftarrow$ Suppose that for all $X \subseteq A$, $f^{-1}(f(X)) \subseteq X$. Let $a_1, a_2 \in A$ and $X = \{a_1\}$. Suppose $f(a_1) = f(a_2)$. If $a_1 \neq a_2$, then $f^{-1}(f(X)) = \{a_1, a_2\} \not \subseteq X$, a contradiction. Thus $a_1 = a_2$, so $f$ is injective. Nikkor f/1.8G 35mm or 50mm? I'm new to photography. I got a Nikon D3100 with the 18-55 kit lens.  I was looking to buy a f/1.8 prime lens, and I found two options:   AF-S DX NIKKOR 35mm f/1.8G   AF-S DX NIKKOR 50mm f/1.8G   How should I go for choosing one or the other? Going into a directory linked by a link Send values from one form to another form Update query cancelled by user A function such that $f:\mathbb C \to \mathbb C$ such that $f(z)f(iz)=z^2$ satisfies $f(z)+f(-z)=0$.(MADHAVA-2020) Suppose $f$ is a function such that $f:\mathbb C \to \mathbb C$ such that $f(z)f(iz)=z^2$, then we have to show that $\forall z\in \mathbb C f(z)+f(-z)=0 $.   Actually I have solved this problem and have no doubt about it but actually this question came in MADHAVA-2020. So I posted it on this site.   I am not answering the question and inviting all users to answer it.  It is a nice problem.   I will answer it within a week, but I am letting everyone try.