I ordered online for a Lenovo 65W AC adapter for Lenovo G550 laptop.  My original adapter had specifications: 19V 3.42A (64.98W)  While the one I got has specifications: 20V 3.25A (65W)  I want to know if it is safe to use the second adapter with my laptop.  Edit 1: The new adapter is also from Lenovo.
I have a Toshiba Satellite laptop. My charger has stopped working.  I have access to a Lenovo charger. Can I use this charger on my laptop?
Show that a set is dense in $[-1,1]$ Show that $\{\cos\ n:n \in \mathbb{N}\}$ is dense in $[-1,1]$ by using the fact below:      Suppose $x$ is irrational. Then there exists $p_n,q_n \in \mathbb{Z}$   such that $\bigg|x -\frac{p_n}{q_n}\bigg| &lt; \frac{1}{q_n^2}$   I have no idea on how to apply the fact above to show the set is dense in $[-1,1]$. Can anyone help me? What are neutral density filters and how do I use them to create long exposures in daylight? I've seen a few related posts on the site but nothing specifically on this point:  I'd like to be able to take long exposure photos during daylight (like the examples in ). I'm told that you can do this by using a neutral density filter. So my question is: what is a neutral density filter exactly, and how is it used to achieve that smooth long exposure effect? Last seen not updating when using Android app This isn't directly related to the app, but probably more on the APIs it's using. The last seen on the profile page doesn't seem to reflect that I'm actively using the Android app, or taking actions. I was able to vote on items and the last seen property on the profile page said I was last seen 50 minutes ago, when I was using a computer.  I'm assuming it won't count as a visit for the Enthusiast and Fantic badges either. I don't want someone angrily posting on Meta swearing they used the app for a day, yet they lost the consecutive days and has to prove it by showing they voted for something (we're probably far from this situation since it's alpha...) After the last update of TeXLive 2018 (pretest) I get an error with csquotes' macro MakeAutoQuote:  \setcounter{errorcontextlines}{100} \listfiles \documentclass[fontsize=11pt,paper=a4,pagesize,ngerman]{scrartcl} \usepackage[utf8]{inputenc} \usepackage{babel} \usepackage[T1]{fontenc} \usepackage{csquotes} \MakeAutoQuote{»}{«}  \begin{document} ABC \end{document}   The error:  ! Package csquotes Error: Invalid argument.   My versions:  inputenc.sty    2018/04/06 v1.3b Input encoding file babel.sty    2018/02/14 3.18 The Babel package csquotes.sty    2018/02/11 v5.2c context-sensitive quotations (JAW)   I use pdfLaTeX. What is wrong here? Is GNU's Java Compiler (GCJ) dead? Extend a language with additional keywords? How should we handle downvote retaliation? I have a situation where I'm trying to figure out what the right thing to do is on SO.    I see a question.  I answer the question.  I see there are a couple other answers.  One answers the question well, though with less explanation than my answer.  The other answer seems both wrong and irrelevant to the question (doesn't answer the question at all).  I comment to that effect.  The "wrong" part is edited out, but the author of the answer doesn't respond to how their answer actually answers the question.  In fact, they seem offended that I don't "get" it.  After giving them several chances to explain how their answer is relevant to the question and seeing their attitude, I decide to downvote their answer as I don't see how it addresses the question at all and the author won't explain.  They retaliate and downvote my answer and admit in their comments that their downvote of my answer has nothing to do with the content of my answer and only because they don't like me disputing their answer.  Did I do the right thing by downvoting their answer?  Do I just have to live with their downvote retaliation?  Anything I should have done differently?  I also have no way of knowing this for sure, but the next question I answered was upvoted, then downvoted so perhaps this same person is stalking my answers and downvoting other answers of mine too with no comment.  As long as this doesn't continue, I'm not losing sleep over a couple downvotes, but I do wonder if I should have done anything differently.  Followup Later After I Posted This Question: After thinking about it for a little while, the person who disagreed with me decided to delete their post.  So, eventually the message did get through to them.  I don't know if they rescinded their downvote or not (or if they even could). Does the hom-tensor adjunction hold for $O_X$ modules also? With sheaf hom and sheaf tensor product, the statement would consist of a natural transformation $Hom_O (M \otimes_O N, K)\cong_{nat} Hom_O(M, Hom_O(N, K))$, $O = O_X$ is the structure sheaf and $M,N,K$ are sheaves of $O_X$ modules.  If true I think I can check this by hand, by describing sheaves in terms of compatible germs, defining this adjunction on the germs and checking that they glue together. It is easier in the quasi-coherent sheaves on a scheme case because then one can just work in an affine cover and the distinguished base.  I am little bit concerned that one might need a finite presentation hypothesis somewhere, in order for $Hom$ to localize well. ($Hom_{R[S^{-1}]}(M[S^{-1}], N[S^{-1}]) \cong Hom_R(M,N)[S^{-1}]$ needs $M$ finitely presented.) ionice without effect Reading order for Cosmere series by Brandon Sanderson My entry into Brandon Sanderson's works is Mistborn Trilogy, I finished and loved it. Then I got to know that many of his series are connected and happen in the same universe - Cosmere. Next I started with the Way of Kings, but am now kind of worried if I might read the series in the wrong order. So what is the right order to read them? is it the publication order..?   Elantris (2005)  Mistborn Trilogy Warbreaker (2009) The Stormlight Archive: The Way of Kings (2010) Mistborn: The Alloy of Law (2011) The Emperor's Soul (2012, novella) Shadows for Silence in the Forests of Hell (2013, short story published in Dangerous Women) The Stormlight Archive: Words of Radiance (2014)    or I have seen people suggest the following order too,   Mistborn Trilogy Elantris and the Emperor's Soul The Way of Kings Warbreaker Words of Radiance The Alloy of Law Shadows of Self   I have also read posts where they say it doesn't matter which order you read it in. So am confused, since I have already started the Way Of Kings (Only a few chapters in), should I stop it and go back to Elantris, and follow an order, or should I just continue finish this and pick other books in an order. How to quotient $\mathbb Z [\sqrt{-11}] / (1+\sqrt{-11})$? That's it. I want to do this quotient,  $\mathbb Z [\sqrt{-11}] / (1+\sqrt{-11})$. My first idea was to see which elements are in the ideal:  $(a+b\sqrt{-11})(1+\sqrt{-11}) = a+ a\sqrt{-11} + b\sqrt{-11} -11b$  So I want to make and application who send this elements to $0$, and then see the Kernel of the application and apply the Isomorphism Theorem.  Any ideas? Windows 7 sleeping during operations I've got Windows 7 set up on my media box.  It's set to sleep after 30 mins of inactivity, but it doesn't seem to work as advertised. In the last two weeks it's gone to sleep during a file copy operation and again while encoding an MP4 file.  Is there any way to get Windows to realise that it's actually busy? Does eating infected flesh have an effect? I don't remember what actually happends when people eat infected flesh. I have in mind :  Gareth and the cannibals eating bitten Bob's leg in . It seems that the cannibals survive for a while after eating Bob's flesh and they seem OK.  The Saviors eating pigs that ate walkers in . We don't know for how long this process has been on, but  has his routine and looks used to doing that. Can we assume that Saviors are eating infected pig flesh for a while now ?  Does it have negative effect in long term ? Suppose we have two short exact sequences in an abelian category $$0 \to A \mathrel{\overset{f}{\to}} B \mathrel{\overset{g}{\to}} C \to 0 $$ $$0 \to A&#39; \mathrel{\overset{f&#39;}{\to}} B&#39; \mathrel{\overset{g&#39;}{\to}} C&#39; \to 0 $$ and morphisms $a : A \to A&#39;, b : B \to B&#39;, c : C \to C&#39;$ making the obvious diagram commute. The snake lemma states that there is then an exact sequence $$0 \to \ker a \to \ker b \to \ker c \to \operatorname{coker} a \to \operatorname{coker} b \to \operatorname{coker} c \to 0$$ where the morphisms between the kernels are induced by $f$ and $g$ while the maps between the cokernels are induced by $f&#39;$ and $g&#39;$.  It is not hard to show that the morphisms induced by $f, g, f&#39;, g&#39;$ exist, are unique, and that the sequence is exact at $\ker a, \ker b, \operatorname{coker} b, \operatorname{coker} c$. With the use of a somewhat large diagram shown , we can even construct the connecting morphism $d : \ker c \to \operatorname{coker} a$. However, I'm stuck showing exactness at $\ker c$ and $\operatorname{coker} a$. I thought Freyd might have had an element-free proof in his book, but it turns out he proves it by diagram chasing and invoking the Mitchell embedding theorem [pp. 98–99]. Is there a direct proof? What are nodes, and how do I use them? I'm a bit new to Blender, and in trying to learn more, I've stumbled across nodes.  What are nodes, and how do I use them? How to prove $\vdash\neg P\to (P\to Q)$? I am trying to prove,  $$\vdash\neg P\to (P\to Q)$$  where $P$ and $Q$ are arbitrary but otherwise fixed formulas. The only axioms and rule of inference that I can use are,  $\color{crimson}{\text{Axiom 1.}}\  P\to (Q\to P)$ $\color{crimson}{\text{Axiom 2.}}\  (S\to (P\to Q))\to((S\to P)\to (S\to Q))$ $\color{crimson}{\text{Axiom 3.}}\  (\neg Q\to\neg P)\to(P\to Q)$ $\color{crimson}{\text{Rule of Inference.}}$ .  I know that in Angelo Margaris's book First Order Mathematical Logic there is a proof (page 53) but as I have mentioned , the dot notation seems very confusing and translating them to the nested parentheses notation seems very difficult to me. So, I am trying on my own to prove the result. Can anyone help? Can I draw something on my card and play tournaments with it? Just out of curiosity, what can I do to the card, so it's still legal to play it in official tournaments?   Can I draw something over ruling texts?  Can I draw something over artwork? Can I draw something over mana cost? Can I draw something over its name?   I'll be glad to see some official rulings about it. :) Wiki-tag edit error is non-descriptive I've been editing some wiki entries on the new Expatriates site, and started to get the following error:    When I go to a normal post, I see what is presumably the proper explanation:    Can the Wiki Tag edit error be updated to show a more meaningful error message? Is there anyway to sync Outlook's calendar with Google's calendar? I've tried  before but it doesn't work properly. I'm using Windows 7 and Outlook 2010.  The thing is, it's really easy to check my Google Calendar on my phone since I have an Android terminal, but on my computer I prefer just opening Outlook instead of opening a web browser and logging into Gmail. Finding centrelines from polygons in QGIS? I was wondering if there is a way to create centre lines from polygons in QGIS? I have a polygon layer, but ideally need the centrelines as a separate file.