Statement:  Let $n$ and $m$ be two irrational numbers. Then $n^m$ is always irrational.  I think this statement is correct, otherwise can someone give me a counterexample?  Thanks!
Can an irrational number raised to an irrational power be rational?  If it can be rational, how can one prove it?
Adjective for "terrified yet calm and capable" What is an adjective to describe the duality of a first responder (such as an EMT responding to a terrorist attack) who is terrified for the wounded, yet simultaneously calm, detached, and capable enough to give aid? I'm using Ubuntu 16.04 and there's no fglrx! I'm using Ubuntu 16.04 and there's no fglrx! What happened? Determine app sending SMS Premium messages I normally have "Block Premium Messaging" set up on the phones in my family. This is a verizon content block the prevents you (or family members) from sending messages to premium services that charge.  Recently, I had to replace a phone that broke and when the new phone was activated the blocks I had set up were cleared. On my bill was a $9.99 charge for a text to one of these premium services.   I know nobody sent the SMS to the service to sign up for this. I suspect some application on the phone sent the SMS message. Is there a way I can find out which app on my phone is sending SMS messages to premium services? Can I view all the apps that have permission to send SMS messages?  -- update -- well, I ran RL Permissions and no downloaded apps have the Send SMS permissions. I must have already deleted the offending app or something else is going on. Have there been any recent attempts to falsify the  hypothesis alternative to the Doppler shift explanation for the red shift, or is it simply ignored like the pilot wave quantum mechanical hypothesis alternative to the Copenhagen hypothesis of quantum mechanics has been? What new evidence would it take to get the tired light hypothesis for the red shift reexamined as the recent fluid dynamics oil drop experiments have done for the pilot wave hypothesis of quantum mechanics? I'm mainly a C# developer, but I'm currently working on a project in Python.  How can I represent the equivalent of an Enum in Python? Onomatopoeia for disgust Let $f$ be a continuous function on a set $E$.  Is it always true that $f^{-1}(A)$ is always measurable if $A$ is measurable?  I say no.  We know that $\bar{\psi(x)}:=\frac{\phi(x)+x}{2}$ where $\phi$ is the Cantor (or Cantor-Lebesgue) function and $\bar{\psi}:[0,1] \rightarrow [0,1]$.  We know this function maps a measurable subset of $C$ (the Cantor set) into a non-measurable set $W$.  A few observations about $\bar{\psi(x)}$.  It is strictly increasing and continuous, so it has a continuous inverse $\bar{\psi(x)}^{-1}$.  Thus $\bar{\psi(x)}^{-1}(W)=c \subset C$; that is, $\bar{\psi(x)}^{-1}(W)$ is non-measurable, but c is.  Is this correct? How can I completely remove all traces of Java on my system?   I already know  in case I need it again. Why are there unwanted white lines appearing in a PDF print proof? I designed a christmas card and I normally print it on vista print.  When I ask for a print proof the outlines show. They don’t show when I print it at home.  Why are there unwanted white lines appearing in this PDF print proof and how can I solve this problem? Which algorithm does the JavaScript Array#sort() function use?  I understand that it can take all manner of arguments and functions to perform different kinds of sorts, I'm simply interested in which algorithm the vanilla sort uses. Sell your home and invest in growth stock mutual fund I purchased a home and I made an agreement with a guy who is living in that home and paying me monthly rent. Since I live with my brother I don't have to live in my purchased home.  The rent I'm getting is only 10% of total cost of home while stock fund industry (mutual fund) is paying 20% minimum i.e. I'm getting 10% loss every year and that is a big amount.  I'm not really sure if my home also increase it's value by 10% every year. But I don't think it will be.  Now I'm thinking of selling that home and investing all of my money in a growth mutual fund. Any advice? Why did the Ministry of Magic choose an ax for carrying out a death sentence? Issue in using longtable within table environment I have an issue making a long list with wrapped text. The table can be several page long. I use longtable and assign the width for each column but as soon as I put it in the \begin{table} \end{table}, it does not work. It clips the table. I want to make a label for the table so I put it in the table environment.  And is there a way to automatically adjust the width so that I don't need to assign the value manually?  Thank you.   Tung  \begin{table} \centering \begin{longtable}{|p{6.5cm}|p{2.5cm}|p{2.5cm}|p{2.5cm}|} \hline Name                                      &amp; Company     &amp;  Catalog Number   &amp;   Comments    \\ \hline Small DNA FRAG Extract Kit-100PR          &amp; VWR         &amp;   97060-558 &amp; \\ \hline Acrylamide 40\% solution 500 mL           &amp; VWR         &amp;   97064-522 &amp;  \\ \hline Bis-acrylamide 2\% (w/v) solution 500 mL  &amp; VWR         &amp;   97063-948 &amp;  \\ \hline GeneRuler 100 bp DNA Ladder, 100-1,000 bp &amp; Fermentas   &amp;   SM0241  &amp;    \\ \hline Mini Vertical PAGE System                 &amp; VWR         &amp;   89032-300  &amp;  \\ \hline \end{longtable} \label{tab:list} \end{table} Entire function $f$ such that $|f(z)| ≤ K |z|^3$ for $|z|\ge1$ and $f(z) = f(iz)$ for every $z∈C$ Let $f(z)$ be an entire function such that for some constant $K$ , $|f(z)| ≤ K$ $|z|^3&lt;$ for $|z|\ge1$ and $f(z) = f(iz)$ $∀z∈C$ , then which of the following are correct ?  (A)$ f(z) = Kz^3$ $∀ z∈\Bbb{C}$ (B) $f(z)$ is a constant function (C) $f(z)$ is quadratic function (D) No such $f$ exists   My attempt : I can deduce that since $f(z) = f(iz)$ and since $i^4=1 \implies f$ must involve only fourth powers of $z$ . Hence $f(z)=a_1z^4+b_1z^8+c_1z^{16}+ \cdots $-------(1)  Also for $|z| \ge 1 $: let C.   Then $|g(z)| = |f(z)|/|z^3| \le k$ => By the Cauchy estimate theorem we can prove that :  $f(z)/z^3$ is a constant function $= c $   $\implies f(z)=cz^3$ for $|z| &gt; 1$     ...........(2)  From (1) and (2) ; we get  there does not exist a function like this ?  My textbook answer says it's a constant function ? I have messed up my sudoers file and I want to change the permission on it.   When I login in recovery mode, I cannot run the command chmod as it is read-only option.  I tried mount -o remount,rw / in recovery mode. Didn't work for me:  Err : Ext4-fs remount. Opts errors=remount-ro    How can I boot into recovery mode and with read-write option? In Book 1, Artemis et al escaped from the time stop by drugging themselves to sleep.  In the same time stop, Julius Root "accidentally" plugged Briar Cudgeon with a tranquilizer dart.  Cudgeon fell asleep, but did not disappear from the time stop.  Why not? Could not load 'vboxdrv' after upgrade to Ubuntu 16.04 (and I want to keep secure boot) Mount USB drive with write permissions for everyone or specific user How to get WordPress' hooks/actions run sequence? In what order add_action hooks execute? i.e. init wp_head wp_footer after_theme_setup  etc... ??? ??? ???     EDIT: I've also posted my solution. java.lang.NoClassDefFoundError: org/apache/xpath/XPathAPI