That is a simple question and I can't start a simple desenveloment.  Just $k=5$ we have $4^5 = 1024 &gt; 5^4 = 625$  for $k+1$: $4^{k+1} &gt; (k+1)^4\Rightarrow 4^k &gt; (k+1)^4/4$  And How can i proceed after that?  Best,
I know that it holds for $n=5$, so the first step is done.  For the second step, my IH is: $4^n &gt; n^4$, and I must show that $4^{n+1} &gt; (n+1)^4$. I did as follows:  $4^{n+1} = 4*4^n &gt; 4n^4$, and if I show that $4n^4 &gt; (n+1)^4$ holds for $n\geq 5$ I'm done, so I expand the right hand side and arrive to:  $$4n^4 &gt; n^4 + 4n^3 + 6n^2 + 4n + 1$$  And this holds iff: $$3n^4 - 4n^3 - 6n^2 - 4n - 1 &gt;0$$ And here I'm stuck, I don't really know how to show that the given inequality holds. Any hints?
Changing permissions on serial port Are Stack Overflow people *still* nice? The title is a reference to . We had the good fortune, to start this experiment with a really positive culture and have managed to hang onto it through vast growth and several fairly bitter internal arguments. But that does not guarantee we'll keep it forever. Lately I've had a unscientific feeling that Stack Overflow has been a bit rougher on newbie mistakes. The actual composition of this question was triggered by the comment thread on  (now with pending delete votes, so it is in danger of being 10k only). The  currently has 3 reputation points and has been a member for all of two days. The question bear the obvious (to me, at least) hallmarks of being written by a non-native English speaker with a shaky grasp of the tongue, and it is a rather simplistic question that could be answered fairly easily by Google. Question body:  Sir, I am mc student, I have knowledge in c,c++,J2EE. I want to ask you should I command in Linux with J2EE. Is it worth?  Instead of trying to improve the question, to discern exactly what the OP meant, or explaining how the question should be improved we get this comment thread instead (without wanting to call out these posters in particular, this was just the thread that got be off my duff):  2 Can you elaborate? – Dave McClelland 21 hours ago 1 Absolutely yes! If it can run on your Blu-Ray player, imagine the possibilities it can do on Linux. – The Elite Gentleman 21 hours ago 1 Basically, it's as worth as running Java on any other platform. – Alexander Gessler 21 hours ago 1 @The Elite Gentleman, You can try run it on your sim-card too) – Stas Kurilin 21 hours ago 1 @STas Kurilin, really? What heapspace size must I give? sarcastic laugh – The Elite Gentleman 21 hours ago 1 @The Elite Gentleman I don't know. But there are some) See for details oracle.com/technetwork/java/javacard/overview/… – Stas Kurilin 21 hours ago @The Elite Gentleman, you're absolutely right given a full fledged desktop machine with Linux, Java would run so fast his program could go back in time and rescue whales from extinction. – Quaternion 21 hours ago @Stas Kurlin, if you have a program that runs on a sim-card isn't it hard to get output? I've always found processorless environments problematic. – Quaternion 21 hours ago @Quaternion - It was a joke) I've newer wrote such programs. But, I think there should be some processor. – Stas Kurilin 20 hours ago @Stas Kurlin, I was joking too, but I have to apologize after reading that page you liked to. You can run Java off a smart card... that's crazy and cool. +1 on account of good learning for the day. – Quaternion 20 hours ago @Quaternion Thanks. I heard about this stuff several weeks ago. Java at a sim card is a really cool argument) – Stas Kurilin 20 hours ago @Quaternion, lol, without having to worry about Segmentation Faults along the way. – The Elite Gentleman 19 hours ago  I've been leaving comments on threads like this from time to time, asking them to be a little more forgiving, but that is a drop in the bucket. Nothing flag-worthy here, but not a &quot;nice&quot; as things once were. There is very little effort to understand what the question may really be, nor why to explain why the question has been closed, what other resources exist, or how that decision could be reversed. With a brand new user who probably has a hard time with English. Ouch. Do we need an official re-iteration of &quot;Be nice.&quot;? Is there something else we can do to encourage our big city to keep the small-town feel we grew up with? Universal extractors With an  of archive/compression file formats, is there a single free/open-source command line tool to rule them all? Perhaps something with a consistent / unified set of flags? (note my  friendly )  I once run into a set of aliases meant to largely simplify the task of compressing/de-compressing files with bindings to tar and other utils, but I can't find this anymore.  Update: How can I configure something like atool to not use unzip to extract zip files (which apparently can't handle files larger than 4GB) and to use gunzip instead?  $ aunpack large_file.zip error:  Zip file too big (greater than 4294959102 bytes) Archive:  large_file.zip warning [large_file.zip]:  1491344848 extra bytes at beginning or within zipfile   (attempting to process anyway) error [large_file.zip]:  start of central directory not found;   zipfile corrupt.   (please check that you have transferred or created the zipfile in the   appropriate BINARY mode and that you have compiled UnZip properly) aunpack: unzip ...: non-zero return-code Converting HTML to plain text in PHP for e-mail C# HttpWebRequest with XML Structured Data Imagine a standard machine-learning scenario:     You are confronted with a large multivariate dataset and you have a   pretty blurry understanding of it. What you need to do is to make   predictions about some variable based on what you have. As usual, you   clean the data, look at descriptive statistics, run some models,   cross-validate them etc., but after several attempts, going back and   forth and trying multiple models nothing seems to work and your   results are miserable. You can spend hours, days, or weeks on such a   problem...   The question is: when to stop? How do you know that your data actually is hopeless and all the fancy models wouldn't do you any more good than predicting the average outcome for all cases or some other trivial solution?  Of course, this is a forecastability issue, but as far as I know, it is hard to assess forecastability for multivariate data before trying something on it. Or am I wrong?   Disclaimer: this question was inspired by this one  that did not attract much attention. It would be nice to have detailed answer to such question for reference. I have noticed after deleting an original page in WordPress with lets say a permalink of your_domain.com/contact/ and then trying to recreate the same page with the same name/slug, my WP is generating a "-2" at the end of the link, like: your_domain.com/contact-2/.  I don't understand why, since the original page was deleted. Why is WordPress treating new pages as if the original still exists? How to I clean WP caches, if such a thing even exists?Thank you ahead of time for clearing this up for me. On every other site on Stack Exchange I can click on the site's title and be taken directly to the questions...     Except Meta.stackexchange.com   Here I actually have to click on the word "Questions" as there is no link active on the Meta title and logo.  Now I agree this isn't a big deal, however as I typically visit stack exchange pages up to a couple of hundred times a day, this one that doesn't fit spoils my flow. I am pretty certain it used to work.  It works for me in Firefox, and Safari on iPad, but even closing and reopening Chrome doesn't fix the issue.  Chrome is on Version 53.0.2785.116 Bind application to a specific network interface Where does gravitational waves' energy go? Following the measurement of gravitational waves, many sources described them and explained they carry energy away. What I don't get is how this energy will get transfered back to anything else.  If the fabric of space-time itself is vibrating, it would seem to be in impossible for any physical object to gain this energy.    What am I missing?  How would one hypothetically get energy out of gravitational waves?  If impossible, does the universe end up with nothing but GW? Is there a gender-neutral pronoun that can replace “his” or “her”? This post has two parts: (a) a question and (b) a proposal.   (a) Often, particularly while writing technical papers or user's manuals, I have come across a situation where I need to say:      A user of this software may not need to use it from his personal computer. He can use it from a phone or even from his tablet.   I have seen many authors use female pronouns (i.e. “she” and “her”), but lately this trend seems to have ebbed somewhat.   I, and (I suspect) many other authors, do not want to use passive voice to avoid this.   Is there a gender-neutral way to describe the same situation?   (b) If there is none, I would like to propose using “ze” (for “he” or “she”) and “zir” (for “his” or “her”, rhyming with “fir”) as gender-neutral pronouns. I want to know how you feel about these words. Can you overload controller methods in ASP.NET MVC? I'm curious to see if you can overload controller methods in ASP.NET MVC.  Whenever I try, I get the error below.  The two methods accept different arguments.  Is this something that cannot be done?     The current request for action 'MyMethod' on controller type 'MyController' is ambiguous between the following action methods: Many to Many and Weak Entities I have an entity that cannot exist without being defined by another, and I want this entity to participate in a many-to-many relationship.  Example: An artist has an album (the album cannot exist without an artist), the album also has many tracks, but the same track can exist in many albums.  So we have a many-to-many relationship between the album and the tracks.  If the album is a weak entity, then its primary key is a foreign key referencing the artist, thus it cannot be a foreign key to another table representing a many-to-many relationship.  The question is: is it possible to have this kind of relationship in SQL, and if so, how do I express it? I am flying from New Orleans to Dulles (IAD) on United Express, and from IAD to Frankfurt on United. I have a short connection (45 minutes) in IAD.   I'm trying to figure out how can I make it:  Will I need to go throughout security and border check since I'm leaving the US? How big is IAD airport? and are there different terminals for domestic and international flights? If so, how long would it take to walk between them? Running Synaptic I get the following error message:  E: The package hl1440lpr needs to be reinstalled, but I can't find an archive for it. E: Internal error opening cache (1). Please report.   Upon accepting the message, Synaptic quits. How can I port forward with iptables? I am trying to make a histogram with the fitted curve plotted on it. Here's the mwe:   \documentclass[a4paper]{scrartcl}     \usepackage{tikz}     \usepackage{pgfplots,pgfplotstable}     \usepackage{filecontents}     \pgfplotsset{compat=1.10}     \usepackage[active,tightpage]{preview}     \setlength\PreviewBorder{2pt}     \newcommand{\plots}{0.611201}     \newcommand{\plotm}{2.19882}     \begin{filecontents}{data.dat}     2 0.0629921259843     3 0.0236220472441     4 0.0314960629921     5 0.125984251969     6 0.0629921259843     7 0.102362204724     8 0.110236220472     9 0.0551181102362     10 0.0629921259843     11 0.0314960629921     12 0.0236220472441     13 0.0314960629921     14 0.0629921259843     15 0.0551181102362     16 0.0393700787402     17 0.0472440944882     18 0.00787401574803     19 0.0393700787402     24 0.00787401574803     27 0.00787401574803     33 0.00787401574803     \end{filecontents}     \begin{document}     \begin{preview}      \begin{tikzpicture}     \begin{axis}[     yticklabel style={/pgf/number format/fixed},     scaled y ticks = false,     minor y tick num={1},     xtick pos=left,     legend cell align = left,     legend style={draw=none},     xlabel = {group size},     ylabel = {ratio}     ]     \addplot[blue,ybar,fill, fill opacity=0.3, bar width = 0.8,] table {data.dat};     \addplot[red, line width = 1,domain=1:40,samples=100] {1/(x*sqrt(2*pi)*\plots)*exp(-(ln(x)-\plotm)^2/(2*\plots^2))};     \legend{empirical,lognormal fit}     \end{axis}     \end{tikzpicture}     \end{preview}     \end{document}     As you can see, the legend is not really good. How can I change the legend so it looks more like this? I want to construct a field with $125$ elements. My idea is to consider the polynomial ring $\Bbb F_5[x]$. It is enough to find an irreducible polynomial $f\in \Bbb F_5[x]$ of degree $3$ because then $\Bbb F_5[x]/(f)$ is a field with exactly $5^3=125$ elements.  How do I find an irreducible polynomial of degree $3$ in $\Bbb F_5[x]$? Spartan 6 DCM unstable clock output Mathematica won't give eigenvectors but Wolfram Alpha will? What am I doing wrong?