Proof by contradiction that $\sqrt{2} + \sqrt{6} < \sqrt{15}$
Prove by contradiction (not using a calculator) that $\sqrt6 + \sqrt2 < \sqrt{15}$?
I'm using pdfLatex (with --shell-escape option) and I had a problem of compilation with TexWorks that was successfully solved with the help of other post in this site: .  After correcting that error the code compiles smoothly but just displays the logarithmic grids, not the function. The gnuplot files are created in the right place, but the graphic doesn't come out in the PDF.  Code from :  \documentclass{article}  \usepackage{tikz} \usepackage{bodegraph}  \begin{document}  \begin{tikzpicture}[     gnuplot def/.append style={prefix={}}, % Fixed the issue (prefix was 'gnuplot/\jobname/' before) ] \begin{scope} \UnitedB \semilog{-1}{2}{-50}{60}  \BodeAmp{-1:1.35}{\POAmpAsymp{4}{2.0}+\IntAmp{1}}  \end{scope} \end{tikzpicture} \end{document}   Any clues? We already had multiple questions about unbalanced data when using , , ,  and a number of other similar questions, what makes it a very popular topic! Unfortunately, each of the questions seems to be algorithm-specific and I didn't find any general guidelines for dealing with unbalanced data.  Quoting , dealing with unbalanced data     (...) heavily depends on the learning method. Most general purpose   approaches have one (or several) ways to deal with this.   But when exactly should we worry about unbalanced data? Which algorithms are mostly affected by it and which are able to deal with it? Which algorithms would need us to balance the data? I am aware that discussing each of the algorithms would be impossible on Q&amp;A site like this, I am rather looking for a general guidelines on when it could be a problem. Prove that the $\lim_{(x,y) \to (0,0)}h(x,y)$ Does not Exist using Polar Coordinates Let $h(x,y)=\frac{x^5y}{2x^{10}+y^2}$. How would I prove that the $\lim_{(x,y) \to (0,0)}h(x,y)$ Does Not Exist?  I think that we might use polar coordinates, but I am not sure. Is Java "pass-by-reference" or "pass-by-value"? PostgreSQL CPU 100% after configure Wal log shipping hot standby I have configured Hight Avaliabily WAL Log Shipping Hot Standby (SSL) with one node. But after I configure, both hosts (primary and secondary) take 100% CPU usage. The most strange is because I have only one database called &quot;TESTE&quot; with one table called &quot;EXAMPLE&quot; to check if replication was OK. The replication worked perfectly but I don't understand why my CPU takes 100% usage because I don't have any application connect on my cluster. I ran HTOP command and get this results: Image 1 - Primary Server HTOP Info  Image 2 - Secondary Server HTOP info  S.O. version: No LSB modules are available. Distributor ID: Debian Description:    Debian GNU/Linux 10 (buster) Release:        10 Codename:       buster  PostgreSQL version: postgres (PostgreSQL) 12.3 (Debian 12.3-1.pgdg100+1)  Primary server postgres.conf file: max_connections = 100 SSL = on shared_buffers = 2GB work_mem = 10485kb maintenance_work_mem = 512MB dynamic_shared_memory_type = posix effective_io_concurrency = 200 max_worker_processes = 4 max_parallel_maintenance_workers = 2 max_parallel_workers_per_gather = 2 max_parallel_workers = 4 wal_level = replica wal_buffers = 16MB max_wal_size = 200MB min_wal_size = 80MB checkpoint_completion_target = 0.7 archive_mode = on max_wal_senders = 3 wal_keep_segments = 8 hot_standby = on hot_standby_feedback = on random_page_cost = 1.1 effective_cache_size = 6GB default_statistics_target = 100  pg_stat_activity info:  pg_stat_archiver info:  pg_stat_replication info:  If I stop postgres service in both servers the CPU still has 100% usage. Anyone can help me? I've used a number of different *nix-based systems of the years, and it seems like every flavor of Bash I use has a different algorithm for deciding which startup scripts to run.  For the purposes of tasks like setting up environment variables and aliases and printing startup messages (e.g. MOTDs), which startup script is the appropriate place to do these?  What's the difference between putting things in .bashrc, .bash_profile, and .environment?  I've also seen other files such as .login, .bash_login, and .profile; are these ever relevant?  What are the differences in which ones get run when logging in physically, logging in remotely via ssh, and opening a new terminal window?  Are there any significant differences across platforms (including Mac OS X (and its Terminal.app) and Cygwin Bash)? Font size setting is missed in iPhone application Can you add a setting for choosing font size in iPhone mobile app?   It's hard to read questions. How do I get a list of all files (and directories) in a given directory in Python? Do opposite categories always exist? How can I add mp3 files as podcasts to my iPhone using iTunes? I am using iTunes 12.5 on Windows 10 with an iPhone 5s.  Sometimes I download hour-long .mp3 files that I want to put onto my iPhone as podcasts, so that it automatically remembers where I am in my listening if I have to stop in the middle.  I know how to transfer .mp3 files to my iPhone, where they show up as Music.  I also know that I can right click on any song, choose 'Get Info' and under Options change the media kind to 'Podcast.'  But when I change the file to a podcast, it disappears from iTunes, though it does show up on my device when I open the Podcasts app.  How can I transfer an .mp3 file to my iPhone as a podcast, and still have that podcast show up in iTunes when I look there to see what podcasts are on my device? Gibbs free energy intuition What is ? As my book explains:     Gibbs energy is the energy of a system available for work.   So, what does it want to tell? Why is it free? Energy means ability to do work. What is so special about this energy? Can anyone simply explain?   I just want a math-free intuition. In Xubuntu 16.04.3 (and several previous versions aswell) it is not possible to have no power icon in the notification area.  A power icon is displayed even though 'Show system tray icon' is unchecked in Xfce Power Manager.  When 'Show system tray icon' is checked, there are two power icons displayed.  (See screenshots)  I've searched and I can't find any information related to this in Xubuntu/Xfce.  Is there a way to fix or work around this bug? What was the first version of Ubuntu and where can I find it? lists Ubuntu 4.10 (Warty Warthog) as the first Ubuntu released by Canonical Ltd.  But I wanted to know whether there ever was an Ubuntu 1.x, as in Windows or Mac OS. If yes, is it available somewhere? Let , $\Delta = B(0,1)$.  If $f:\Delta \rightarrow \Delta$ is holomorphic, and $f(0)=0$, prove that $|f(z)+f(-z)| \leq 2|z|^2$.  My attempt so far:  $\displaystyle f(z) = \sum_{n=0}^{+\infty} a_n z^n = \sum_{n=0}^{+\infty} a_{2n} z^{2n} + \sum_{n=0}^{+\infty} a_{2n+1} z^{2n+1}$  $\displaystyle f(-z) = \sum_{n=0}^{+\infty} a_n (-z)^n = \sum_{n=0}^{+\infty} a_{2n} z^{2n} - \sum_{n=0}^{+\infty} a_{2n+1} z^{2n+1}$  Then, $\displaystyle f(z)+f(-z) = 2  \sum_{n=0}^{+\infty} a_{2n} (z^2)^n =: 2 g(z^2)$  If $g(\Delta) \subset \Delta$, as $g(0) = 0$, I can invoke Schwarz Lemma and I win. However, I don't know how to prove this. Could anyone help me? Thanks! How to print the full NumPy array, without truncation? It is given $23!=2585201xy38884976640000$. Now it is required to find the value of $x$ and $y$. I know I could find it by using divisibility rules and solving simultaneous equations. Is there any other way to solve it (without computing it by a calculator)? This question is just out of curiosity. If the electric field is the gradient of the potential, then can we say that whenever potential is zero, the electric field is zero? For example, in a dipole, at the center of the two charges making up the dipole, the potential is zero but the electric field is non-zero. But if $E = -\operatorname{grad}V$, then why is $E$ not zero?  Another example: In the case of two positive charges, the electric field is zero at the mid-point of line joining them, but potential is non-zero. What am I misunderstanding here? Open maps which are not continuous My Bash Prompt is currently setting the xterm titlebar using the following sequence:  PS1='\033]0;\u@\h&gt;\w\007'   Is there an easy way to display the current command in the titlebar. For example, if I am tailing a file using tail -f foo.log, I want my titlebar to say tail -f foo.log. what operation repeated $n$ times results in the addition operator?