Why $\lim_{n\to \infty} \left(1+ \frac 1n \right)^n=e$ doesn't imply $\lim_{n\to \infty} \left(1+\frac 1n \right)≠1?$
Does $1^{\infty}=e$ or $1^{\infty}=1$?
I'd like to be able to search for questions by multiple tags; for example "questions tagged 'nhibernate' and 'web-services'".  I can get close by searching for "nhibernate web-services" but the results tend to be a few questions that relate to both terms--but much more largely just questions that relate to one or the other. How to download a file over HTTP? I have a small utility that I use to download an MP3 file from a website on a schedule and then builds/updates a podcast XML file which I've added to iTunes.  The text processing that creates/updates the XML file is written in Python. However, I use wget inside a Windows .bat file to download the actual MP3 file. I would prefer to have the entire utility written in Python.  I struggled to find a way to actually download the file in Python, thus why I resorted to using wget.  So, how do I download the file using Python? How to tell what method was used to log in (Password vs. Keyfile) from the bashrc Is there a way how you can check what auth method the user which just logged in to an account were using?  I like to print out a warning after login if someone is using a password instead of a keyfile.  Sure one solution is to check the ssh-logs. But is there a nicer way to do this? Since looking up logs could impact performance depending on the log size and method you use to gather this information.  We are using SUSE and Ubuntu. Exact sequence splits? Why can't I transform faces, edges, or vertices without transforming the whole object? My problem is that I sometimes lose the ability to independently translate or otherwise transform any parts of a single mesh. If I try, for example, to just translate several faces, edges, or vertices, then the entire mesh will stretch and displace itself in order to follow the translation. Or, alternatively, if I try to translate just one face then the whole mesh will move as if I'm translating in Object Mode.  I'm not really sure I know how to describe this problem properly. I don't even know how to reliably reproduce it. It seems to happen to any given mesh at random, and it doesn't stop happening to that mesh unless I delete and remake it.  I assume that I must be doing something wrong to cause this to happen. Does anyone have any ideas? Thanks. I have recently installed a custom ROM and cannot find the Play Store. It seems like all apps that belong to Google are missing.  How can I install the Google Apps Package (Play Store, ...) on my Android device? I'm stuck in the College of Winterhold questline because of a glitch between the quests "Good Intentions" and "Revealing the Unseen." After talking to the Augur of Dunlain, I return to the Archmage Savos Aren to finish the quest, and he gives me the Mage's Circlet and finishes "Good Intentions." The problem is, the next quest "Revealing the Unseen" doesn't start. He talks about Mirabelle Irvine and tells me to go talk to her, but since the quest hasn't been started, she doesn't have anything to say about the Staff of Magnus. I've tried reloading from before the quest many times and finishing it but still the same result. I've also tried doing other quests and coming back to try and finish it later, but still the next quest doesn't start. I'm on the PS3.  Anyone have a way of fixing this bug/glitch? Thanks in advance. An inequality for arctan$x$ Why it is true that $|\arctan x-\arctan y|\leq |x-y|$? I have tried to use $\tan x$ but I didn't conclude to something. What is the connection between Poisson brackets and commutators? The Poisson bracket is defined as:  $$\{f,g\} ~:=~ \sum_{i=1}^{N} \left[  \frac{\partial f}{\partial q_{i}} \frac{\partial g}{\partial p_{i}} - \frac{\partial f}{\partial p_{i}} \frac{\partial g}{\partial q_{i}} \right]. $$  The anticommutator is defined as:  $$ \{a,b\} ~:=~ ab + ba. $$  The commutator is defined as:  $$ [a,b] ~:=~ ab - ba. $$  What are the connections between all of them?  Edit: Does the Poisson bracket define some uncertainty principle as well? Proving that $A+A \not\subset 2A $ using a particular definition for sum of sets Let $X$ de a vector space and $A\subset X$. If we define $A+B :=\{a+b|a\in A, b\in B\}$ I am trying to show that    $$ \begin{equation} 2A \subsetneq A+A, \end{equation} $$  i.e., it might happen that $2A \neq A+A$. I was able to show that $2A \subset A+A$, but I am not able to come up with a counterexample to show that the converse is not necessarily true. If I assume $A+A\subset 2A$ and let $x\in(A+A)$, then by its definition we have $x=a_1 + a_2$ for some $a_1,a_2\in A$ I guess I could naively say that $a_1+a_2 = 2(a'_1+a'_2)$ where $a_i=a_i/2$ for $i=1,2$ and I guess $(a'_1+a'_2)$ might not be an element of $A$ in some concrete case but I am not able to come up with anything and I've spent more time than I would like to admit. Any suggestions?  Thank you. How do you detect support for VML or SVG in a browser I'm writing a bit of javascript and need to choose between SVG or VML (or both, or something else, it's a weird world). Whilst I know that for now that only IE supports VML, I'd much rather detect functionality than platform.  SVG appears to have a few properties which you can go for: window.SVGAngle for example.  Is this the best way to check for SVG support?  Is there any equivalent for VML?  Unfortuntaly - in firefox I can quite happily do all the rendering in VML without error - just nothing happens on screen. It's quite hard to detect that situation from script. Sign of Work and potential energy in electrostatics Conceptual question:  Suppose we have a configuration of point charges. If the potential of the energy of the system is negative, this means work is positive.   I'm kind of rusty with my mechanics, does the fact that the work is positive mean that to arrange the configuration you have to do work against the electric field? I.e. supply energy via some external force?  In terms of electrostatics, is there a general way of interpreting the sign of potential energy and work? Maybe this question is too obvious to everyone.      In Noetherian ring $R$, ideal $I\subset R$, $P\in\mathrm{Ass}(I)$, then $P=I:a$ for some $a\in R$ where $\mathrm{Ass}(I)$ denotes associated primes of $I$.   This is an exercise 8.29 in Gathmann's Commutative Algebra notes. I am supposed to find this statement obvious. However, up to now, I still did not find this statement obvious. Can someone explain intuitively why noetherianness here allows me removing radical $\sqrt{I:a}$ without going into details?  If $Q$ is a primary ideal of $I$, then certainly $\sqrt{Q:a}=P$ for $a\not\in P$. It seems taking $(p_1,\dots, p_n)=P$, $p_i^{n_i}a\in Q$. Since $Q$ primary, I must have $p_i\in Q$ and $p_i^{n_i}\in Q$. (This argument seems very wrong as this deduces the same conclusion without noetherian property.) Prove that $\sum_{k=0}^n a_k x^k = 0$ has at least $1$ real root if $\sum_{k=0}^n \frac{a_k}{k+1} = 0$ Knowing that $$ \frac{a_0}{1} + \frac{a_1}{2} + \frac{a_2}{3} +\cdots + \frac{a_n}{n+1} =0$$ Prove that  $$ a_0 + a_1x + a_2x^2 + \cdots + a_nx^n = 0$$ has at least one real solution.  I suspect that it's proven with the intermediate value theorem. But can't find two numbers that satisfy it. I don't quite understand the difference between /a/ and /æ/. Google gives the transcription for 'add' as /ad/, while Wiktionary returns /æd/.  Are these sounds actually distinct or is this just two different ways of writing the same one? Get last n lines of a file, similar to tail I'm writing a log file viewer for a web application and for that I want to paginate through the lines of the log file.  The items in the file are line based with the newest item at the bottom. So I need a tail() method that can read n lines from the bottom and support an offset.  This is hat I came up with: def tail(f, n, offset=0):     &quot;&quot;&quot;Reads a n lines from f with an offset of offset lines.&quot;&quot;&quot;     avg_line_length = 74     to_read = n + offset     while 1:         try:             f.seek(-(avg_line_length * to_read), 2)         except IOError:             # woops.  apparently file is smaller than what we want             # to step back, go to the beginning instead             f.seek(0)         pos = f.tell()         lines = f.read().splitlines()         if len(lines) &gt;= to_read or pos == 0:             return lines[-to_read:offset and -offset or None]         avg_line_length *= 1.3  Is this a reasonable approach?  What is the recommended way to tail log files with offsets? Leave the door open vs Leave the door opened Is there any subtle difference between:   We need to carry in some stuff so open the door and leave it open. We need to carry in some stuff so open the door and leave it opened.   I mean "leave it like that (in that state)". In normal line integration, from what I understand, you are measuring the area underneath $f(x,y)$ along a curve in the $x\text{-}y$ plane from point $a$ to point $b$.  But what is being measured with complex line integration, when you go from a point $z_1$ to a point $z_2$ in the complex plane?  With regular line integration I can see $f(x,y)$ maps $(x,y)$ to a point on the $z$ axis directly above above/below $(x,y)$.  But in the complex case, when you map from the domain $Z$ to the image $W$, you are mapping from $\mathbb{R^2}$ to $\mathbb{R^2}$ ...it is not mapping a point to 'directly above/below'...so I don't have any intuition of what is happening with complex line integration. Suppose every subsequence of X converges to 0. Show that lim(X)=0 Question: Suppose that every subsequences of $X = (x_n)$ has a subsequence that converges to $0$. Show that $\lim(X) = 0$   My attempt:   Suppose that $\lim(X) =L \neq 0$  Let $\epsilon &gt; 0$, and let $K(\epsilon)$ be s.t. $n \ge K(\epsilon)$   then $|x_n-L| &lt; \epsilon$  let $n_k \ge k$, and then $k \ge K(\epsilon)$ and $n_k \ge k \ge K(\epsilon)$ s.t. $|x_{n_{k}}-L| &lt; \epsilon$, which is a contradiction. therefore $\lim(x) =0$ How to add programs to the Unity Launcher or Ubuntu Dock? How can I add new programs to the launcher (or the dock in Ubuntu 17.10 and later) in Ubuntu?