Proving a limit as x approaches positive infinity
How to prove that exponential grows faster than polynomial?
I use the scroll function with my mouse and it works fine. But either in script, or in terminal sections of Spyder, I can't use the touchpad for scrolling. I do not experience any problems with my touchpad in other programs like Word, Chrome etc. Is there any option for this in Spyder, specific for touchpad?  I am using Lenovo Legion Y520, Windows 10. Are there fields and ordered fields of every infinite cardinality? On the top of my head, I cannot think of any fields of cardinality more than that of the reals. (It is known that the process of algebraic closure does not increase the cardinality of an infinite field.)  What is the simplest way to give an example of a field (and an ordered field) of a specific cardinality $\alpha$?  I see there is the "Field" of surreal numbers, but it is a proper class rather than a set (and hence do not have a cardinality as such). However, there seems to be some modified construction which gives proper fields with the cardinality of some strongly inaccessible cardinal. Should I defragment my SSD? Free UML drawing library for .NET Give each site a parallel site for polling, recommendations and subjective-ish stuff Affiliation for a retiree This question is similar to   and  except that I am a retiree.  I intend to submit a paper to a journal without mentioning any affiliation because I am no longer employeed. I have been thinking about a footnote in the paper indicating I am a retiree from my former employer for two reasons: I am receiving pension from the company pension fund and it is a well-known company in U.S. Using their name may make me look good. On the other hand, I feel like it's cheating because I am not their employee anymore. Herstein Topics in Algebra, $\pi \mid a$ or $(\pi,a) = 1$ How do you change the size of figures drawn with Matplotlib? How do you change the size of figure drawn with Matplotlib? On found exact duplicates, should these be voted to close directly against a preferred, or ultimate, canonical question?   Or is a chain of possible duplicates (where one question is closed as duplicate of another, which itself is a duplicate of another, and so on and so on) allowable or OK?  One example of this situation can be found . My computer no longer boots Windows or the installed operating system. Instead, I may get this error:  PXE-E61: Media test failure, check cable -or- Check cable connection!  PXE-M0F: Exiting PXE ROM.   and/or one of the following messages or similar:  Operating System not found  No boot device available- No bootable devices--strike F1 to retry boot, F2 for setup utility  No bootable device -- insert boot disk and press any key  No Boot Device Found. Press any key to reboot the machine  Default Boot Device Missing or Boot Failed  Reboot and Select proper Boot device or Insert Boot Media in selected Boot device   What does this mean and what can I do?     This question comes up often and the answers are usually the same. This post is meant to provide a definitive, canonical answer for this problem. Feel free to edit the answer to add additional details. Get Absolute Position of element within the window in wpf I would like to get the absolute position of an element in relation to the window/root element when it is double clicked. The element's relative position within it's parent is all I can seem to get to, and what I'm trying to get to is the point relative to the window.  I've seen solutions of how to get a the point of an element on the screen, but not in the window. Proof by induction that $2 + 4 + 6 + \cdots + 2n = n(n+1)$ How can I permanently enable cheating? I'm giving Deus Ex a quick playthrough as a refresher before jumping into Human Revolution. In the interest of expediency, I've decided to cheat. ^.^  Normally, cheats must be re-enabled for each level when playing the original DX. I've encountered instructions on several sites (word-for-word identical instructions, so clearly copy/pasted) for permanently enabling cheats, but they aren't working for me:     Because you will need to redo this for every level, you can open up 'user.ini' and add 'bCheatsEnabled True' in the [DeusEx.DeusExGameInfo] section of the file to allow cheats to be activated forever.   Not only is that not working for me, it doesn't even look right compared to the rest of the file (space instead of =). With increasing desperation, I've tried adding that line (both verbatim and switching to an equal sign) to every section of both User.ini and DeusEx.ini which looks even remotely plausible — even creating a [DeusEx.JCDentonMale] section, just in case.  Does anyone know how to get this working? I'm running DX:GOTY version 1.112fm from Steam on Windows 7. A Variation of the even-town odd-town problem Let assume facebook has $n$ users. Mark Zuckerberg decided that people are allowed to open groups under the following restrictions:      1) No two different groups can exactly the same participants.      2) The number of users in each group is even.      3) Every two group has an odd number of common users.      Denote by $m$ the maximal number of groups that can be formed in facebook under the restrictions mentioned above. Prove $m \leq n$.   I tried solving this by defined a matrix, multiplying it by its transpose and using some rank considerations I thought I could derive the bound, but I didn't succeed. Could you please give me a hint?  The question had anther subsection : prove that in the case that $n$ is even than we have stron inequality I am in the process of creating a LaTeX template for a conference submission, and up until now I've been working only with the anonymous submissions. Now I need to create the "camera-ready" version, which means I need to add authors to the document.   The template is based on article.cls, with some tweaks to meet the font and formatting specifications. The following image contains the examples from the Word template for the conference:    Basically, I need to be able to bold the author's name (which could I suppose be done manually in the document rather than in the template) and more importantly: divide the authors into two columns, with an optional centered last column with an odd number of authors. The font size of the author block corresponds to my \LARGE defined in the class file.  Are there any packages that facilitate this type of conditional formatting, either in a document, or in a .cls file? How can I use those packages to achieve the formatting I require? SSH remote user need to be logged in? I opened the PC in the morning, and this is what I got:      As is visible the icons of the UWA apps were no affected and the start menu also is unaffected.    When Control Panel is in category view the entire page is empty and in large/small icons the name is visible, no icons.  I deleted the iconcache.db in %USERPROFILE%\AppData\Local folder. Following the instructions here: . But to no avail and now windows is not rebuilding the cache.   I also ran sfc /scannow but no changes took place.  What should I do?  (01/01/2016 8:00PM GMT +5:30) Edit: I tried opening the system properties and I got 0x8000ffff error and this:        Then I closed the popup and pressed the OK button on the System Properties Windows and I got 0x8007057A error:      Opening the Image Backup Control Panel page I again got an 0x8007000E error:        I tried using system restore via advanced startup but once again I got 0x800FFFF error.  P.S.: I did try restarting, didn't work. Disable ssh password authentication by user Is it possible to enable ssh password authentication for one user on a system and disable it for an other.  If you add  ChallengeResponseAuthentication no PasswordAuthentication no UsePAM no   to /etc/ssh/sshd_config you disable it for all users  Adding it to ~/.ssh/config doesn't seem to work \includegraphics optional argument not resolved if macro In the 70's I had a stack of old Amateur Radio magazines (50s-60s), and for a long time I saved an article about using the  to combine a number of resistors to achieve a specific value. Does anyone recall and have a copy of this article, or know how the Euclidean algorithm is applied to solve this problem?