Check many keys in dictionary: optimization
How do I check that multiple keys are in a dict in a single pass?
Assume  $$\lim_{n\to \infty}  (y_{2n} - y_n)=0$$  then  $$\lim_{n\to \infty} y_n$$  exists.  I know it's not true, and I can see a sequence that disprove that $(1,1,2,1,3,2,4,1,5,3,...)$ but I want a sequence that has formula.  hint/help?  thanks Use of 'prototype' vs. 'this' in JavaScript? What's the difference between  var A = function () {     this.x = function () {         //do something     }; };   and  var A = function () { }; A.prototype.x = function () {     //do something }; I'm trying to compute the difference between the output of two awk commands but my simple attempts at it seem to be failing. Here is what I'm trying:  diff $(awk '{print $3}' f1.txt | sort -u) $(awk '{print $2}' f2.txt | sort -u)   This doesn't work for reasons unknown to me. I was under the assumption that $() construct was used to capture the output of another command but my "diff" invocation fails to recognize the two inputs given to it. Is there any way I can make this work.  By the way, I can't use the obvious solution of writing the output of those two commands to separate files given that I'm logged on to a production box with no 'write' privileges. Show that the sequence $a_{n+1}=a_{n}+\dfrac{a^2_{n}}{n^2}$ is upper bounded Let $\{a_{n}\}$ be defined with $a_{1}\in(0,1)$, and  $$a_{n+1}=a_{n}+\dfrac{a^2_{n}}{n^2}$$ for all $n\gt 0$.  Show that the sequence is  upper bounded.  My idea: since  $$a_{n+1}=a_{n}\left(1+\dfrac{a_{n}}{n^2}\right)$$ then $$\dfrac{1}{a_{n+1}}=\dfrac{1}{a_{n}}-\dfrac{1}{a_{n}+n^2}$$ then $$\dfrac{1}{a_{n}}-\dfrac{1}{a_{n+1}}=\dfrac{1}{a_{n}+n^2}$$ so $$\dfrac{1}{a_{1}}-\dfrac{1}{a_{n+1}}=\sum_{i=1}^{n}\dfrac{1}{a_{i}+i^2}$$ since $$a_{n+1}&gt;a_{n}\Longrightarrow \dfrac{1}{a_{i}+i^2}&lt;\dfrac{1}{a_{1}+i^2}$$ so $$\dfrac{1}{a_{n+1}}&gt;\dfrac{1}{a_{1}}-\left(\dfrac{1}{1+a_{1}}+\dfrac{1}{2^2+a_{1}}+\cdots+\dfrac{1}{a_{1}+n^2}\right)$$ But the RHS might be $\lt0$ for a sufficiently large starting value; for instance, with $a_{1}=\dfrac{99}{100}$ then $$\dfrac{1}{a_{1}}-\left(\dfrac{1}{1+a_{1}}+\dfrac{1}{2^2+a_{1}}+\cdots+\dfrac{1}{a_{1}+n^2}\right)&lt;0,n\to\infty$$  see:   so this method won't let me bound the series and I don't know what else to do. What is the difference between \emph{...} and {\em ...}?  When to use each of them? steam fatal error "steam needs to be online to update, but was set to offline movies." I tried re-installing  it but it simply keeps giving me this error in a little window. When I close it, an identical error pops up some 3 seconds later without any new provocation. Why $f(x) = \sqrt{x}$ is a function? Why $f(x) = \sqrt{x}$ is a function (as I found in my textbook) since for example the square root of $25$ has two different outputs ($-5,5$) and a function is defined as "A function from A to B is a rule of corre- spondence that assigns to each element in set A exactly one element in B.", so $f(x) = \sqrt{x}$ is not a function? How would I implement a realistic stock market? One can show that $\mathbb{P}^n\times \mathbb{P}^m$ is birational to $\mathbb{P}^{n+m}$ by making note of the Zariski topologies and the canonical isomorphism between affine spaces $\mathbb{A}^n\times \mathbb{A}^m\to \mathbb{A}^{n+m}$.   Question: Does it follow that there is isomorphism $\mathbb{P}^n\times \mathbb{P}^m\to \mathbb{P}^{n+m}$? If so, what is an example of such an isomorphism?   Unfortunately I am having a hard time coming up with one, and haven't seen too many examples thus far. Is it possible to animate the speed of a strip? I want to accelerate the speed of a video and decelerate some seconds before it ends. I wonder if it's possible to do it into the video editing. I know how to increase the speed of a strip but, what I need is a trasition between normal speed and fast speed. Using the same RSA keypair to sign and encrypt The RSA signature operation is basically the same as encrypting with the private key.  In particular, both operations use the same kind of keys.  Is it safe to use the same RSA keypair both for encryption / decryption and for signing / verification? Trigger for avoid insertion from data loader? i have scenario like write a trigger avoid insertion of records  from  data loader,only manual insertion trigger will fire?on any object     while Entering records from data loader trigger should not fire? How to automaticaly enter sudo's grace period upon login SharePoint People.aspx Page is Visible for All Users The SharePoint People.aspx page is visible for all users by default. Is there any way to restrict this page from certain readers? 8.00GB RAM (3.22GB usable) in Windows 7 x64 I have set up Windows 7 Ultimate 64-bit on my PC. I have 8GB RAM and my BIOS states the correct amount (8192MB), but Windows (System Manager) says I have 8.00GB (3.22GB usable). give me a solution. I'm tried this: Run &gt; MSCONFIG, open the Boot tab &gt; click Advanced Options &gt; make sure that Maximum Memory but this wasn't helpful. My Motherboard Details: CPU Type : DualCore Intel Pentium, 3000 MHz (15 x 200) Motherboard Name : Foxconn G41MXE Motherboard Chipset : Intel Eaglelake G41 System Memory : 3296 MB (DDR3-1333 DDR3 SDRAM) DIMM1: Kingston : 4 GB DDR3-1333 DDR3 DIMM3: Kingston : 4 GB DDR3-1333 DDR3 My BIOS Details: BIOS Type : AMI (03/21/11) Vendor : American Megatrends Inc. Version : 080015 Capabilities : Flash BIOS, Shadow BIOS, Selectable Boot, EDD, BBS System Properties :  Bios File :  What about Bios Update? What is the correct way to edit a crontab file? Who would get the longest road? Imagine the following setup. There are 3 (or more) players with an equally long road. What would happen if the longest road was broken? How is it decided who obtains the longest road from there on? Pre-1972 sci-fi short story or novel: alien(?) tunnel where people try new moves and get destroyed if they're not the correct ones It might be a short story or it might be a novel. It must be before 1972 because I read it in my youth and I am OLD.  The following is very impressionistic.  There is a multidimensional/not of this Earth/alien artifact-like tunnel.   Picture a long, perhaps transparent, storm drain like structure sitting in a field but with an opening on only one end.  It is the subject of a lengthy investigation/exploration that has cost many lives. An instrumented investigator enters the "tunnel" and makes the exact movements that his predecessors have made, advancing until he must do something original at which point he survives and a new "move" is added to the list of correct moves or he is destroyed and a "move" is added to the list of things to be avoided at that point.  I remember absolutely nothing else about the work except that (I hope central) feature. Is the external micro SD card path the same for all devices? I am using a Samsung Tab 2.  There is a path: /mnt/external_sdcard/myfile. Here, I can save, read, or write my file to the external micro SD card.  I'm just wondering if this path is the same for all devices, or if it may be different. Running junit tests in parallel in a Maven build?