Suppose that $f(y)-f(x) \leq (y-x)^2 $ for all $x\in \mathbb{R}$ and $y\in \mathbb{R}$. Then how can i show $f$ is a constant function.   I encountered this problem reading Calculus book written by Michael Spivak. He said that this would imply that $|f(y)-f(x)| \leq (y-x)^2$ and I could derive this exchanging y and x. And his final hint was Divide the interval from $x$ to $y$ into $n$ equal pieces.
Problem: Let $f$ be defined for all real $x$, and suppose that   $$|f(x)-f(y)|\le (x-y)^2$$  for all real $x$ and $y$. Prove $f$ is constant.  Source: W. Rudin, Principles of Mathematical Analysis, Chapter 5, exercise 1.
Unzipping geoprocessing package (GPK) file? I was under the impression that all ArcGIS package files could have their contents examined and potentially used by renaming them to *.zip and unzipping them.  This impression is supported for map package (*.mpk) files by  to  and I thought I had used it succesfully on geoprocessing package (*.gpk) files in the past.  However, today I am unable to use a  which I think is because it was created using ArcGIS Desktop 10.5.x when I am using 10.2.1.01. When I rename this *.gpk as *.zip and try to examine it in Windows Explorer I get:     Compressed (zipped) Folders Error      Windows cannot open the folder      The Compressed (zipped) Folder ....zip is invalid.     Is it possible to unzip a geoprocessing package (*.gpk) file to see whether it may contain some useful ArcPy code when that *.gpk cannot be unpacked to provide a usable toolbox? Custom post type - posts list - white screen of death i am getting a weird error - white screen in the list of posts for a specific Custom post type (just for that one)   tried deactivating all the plugins tried checking for error (debugging = true)   Still nothing the page just doesnt echos anything... (nothing in source too)  I am talking about such a url in the admin:     Here is register_post_type part i am using:    function register_submodelcpt() {     $labels = array(         'name'                  =&gt; __('Sub Models', THEME_NAME),         'singular_name'         =&gt; __('Sub Models', THEME_NAME),         'add_new'               =&gt; __('New Model', THEME_NAME),         'add_new_item'          =&gt; __('Add new Model', THEME_NAME),         'edit_item'             =&gt; __('Edit Model', THEME_NAME),         'new_item'              =&gt; __('New Model', THEME_NAME),         'all_items'             =&gt; __('All Sub Models', THEME_NAME),         'view_item'             =&gt; __('Watch Model', THEME_NAME),         'search_items'          =&gt; __('Search Models', THEME_NAME),         'not_found'             =&gt;  __('No Models found', THEME_NAME),         'not_found_in_trash'    =&gt; __('No Models found in trash', THEME_NAME),          'parent_item_colon'     =&gt; '',         'menu_name'             =&gt; __('Sub Models', THEME_NAME),      );      $args = array(         'labels'                =&gt; $labels,         'public'                =&gt; true,         'publicly_queryable'    =&gt; true,         'show_ui'               =&gt; true,          'show_in_menu'          =&gt; true,          'query_var'             =&gt; true,         'rewrite'               =&gt; array('slug' =&gt; 'submodels'),         'capability_type'       =&gt; 'post',         'has_archive'           =&gt; true,          'hierarchical'          =&gt; true,         'menu_position'         =&gt; 5,         'menu_icon'             =&gt; get_stylesheet_directory_uri().'/images/cpt/subcars.png',                     'supports'              =&gt; array('title', 'thumbnail', 'revisions', 'page-attributes')     );      register_post_type('submodelscpt',$args); } add_action('init', 'register_submodelcpt');   Did anyone encounter such an issuse? can you think of a reason this might happen?   Another weird thing when i change this:    To this:     The posts list loads correctly... Script for modifying file content in specified files I tried searching previous questions but none worked, or I couldn't adapt them to my needs.  I want to write a script that asks for:   folder criteria old string new string   And replace every file in the specified folder and subfolders (and force user to type one) with specific criteria (for example, it must be a ".cue" file), and:   If the file is read-only, disable it. Search for specified old string in the file content and replace it with new string , and save changes in same file. If the file was read-only, enable it again.   I have this code so far, but I don't know what to do in the do part:  @echo off   setLocal enableDELAYedexpansion  :START set "var2=" set /P var2="type folder "  if "%var2%"=="" goto ERROR  set /p old="old string ? " set /p new="new string ? " set /p files="what criteria ? " echo modifying files...  for /r "%var2%" %%v in (%%files) do (  ???  ) pause  goto START  :ERROR echo type something!! goto START How to remove my passport from a blacklist in Indian Immigration? How do I send SMS from PC through Android Phone or to Android Phone? I'm looking for an app that will let me type text messages on my PC and send the SMSs directly from the PC through my phone, or save the messages to the phone for later use.  I'm basically looking at something like Nokia PC Suite's equivalent.  EDIT:  Google Voice is only for US, doesn't work in India at least, and also defeats the purpose (it will go through the internet, why, when it's possible through the usb cable/modem/wifi). DesktopSMS is a good program, but kept crashing, for some reason. PDANet worked for me. But I liked the tiny . It's weird, and I had to change the bluecove library jar file for Windows 7 x64, but it's compact (a concern for me). I've switched from Drupal 7.14 to 7.15 three weeks ago and therefore, I'm encountering a series of very sophisticated (for me) memory limit errors.  Those errors occur any time I'm trying to clear cache in performance or to run update scripts.  My hosting company has increased my memory limit in php.ini up to 126 M, 256 M, 512 M, and even 1024 M. But the errors still occur. I've migrated my site from shared to VPS, But the error incredibly still occurs. I have no way and no idea how to move forward.   Here are the errors:   Fatal error: Allowed memory size of 536870912 bytes exhausted (tried to allocate 30 bytes) in /home/example/public_html/sites/all/modules/views/views.module on line 416 Fatal error: Allowed memory size of 536870912 bytes exhausted (tried to allocate 108 bytes) in /home/example/public_html/includes/menu.inc on line 2736 Fatal error: Allowed memory size of 536870912 bytes exhausted (tried to allocate 71 bytes) in /home/example/public_html/sites/all/modules/chain_menu_access/chain_menu_access.module on line 59 allocate 64 bytes) in /home/example/public_html/sites/all/modules/views/includes/base.inc on line 93 Is there a problem with closing the lid of a MacBook Pro when using an external monitor? I am using an external monitor and the only way (that doesn't involve jumping through hoops) to turn off the MacBook Pro monitor is to close the lid.  Does closing the lid causes any problems? I have read the following on :     You can still run a single external monitor if you close the lid of   your laptop, but that restricts airflow and exposes your display to a   lot of heat. Not good. Javascript - Change html tag type Given a DateTime object, how do I get an ISO 8601 date in string format? Was it just coincidence that Tahir Mahmood went on stage? What is the correct pronunciation of "the"? The is sometimes pronounced &quot;tha&quot; (/ðə/) or &quot;thi&quot; (/ðiː/). Which is the correct pronunciation of this word? Are both correct and used interchangeably at specific places? If the second question is correct, please provide the rule of pronouncing at different places. How to filter by messages, not by conversation? I have been emailing my Gmail account error messages from a project I am working on.   I am trying to use Gmail filters/labels to sort out the class of errors.  But because the subject line is basically always the same even if I have a specific filter for 3 known error cases, the label is applied to the conversation, instead of the specific message.  Therefore, all the errors get all the filters.  I do not yet want to delete the errors, but would rather file them separately.   I have not yet used the NOT contains string yet, but that looks to be non-scalable as I get to the fourth or fifth error case I am done with handling.  Is there any option other than turning off Conversations for all my email?  (I guess I could use one of my spare accounts to turn off conversations and do the work there but would be nice to have such an option). What is the difference between a HMAC and a hash of data? Are there strange attractors whose coordinates are "almost integers"? Defining the Complex numbers I posted this question nearly 10 days ago, but am still really not satisfied with the answers I got, I have no prior education in abstract algebra, group theory, or other abstractions, and most of the answers I got involved defining sets, groups and other things I am unfamiliar with, my question was,  How does one know the notion of real numbers is compatible with the axioms defined for complex numbers, ie how does one know that by defining an operator '$i$' with the property that $i^2=-1$, we will not in some way contradict some statement that is an outcome of the real numbers.  For example if I defined an operator x with the property that $x^{2n}=-1$, and $x^{2n+1}=1$, for all integers n, this operator is not consistent when used compatibly with properties of the real numbers, since I would have $x^2=-1$, $x^3=1$,thus $x^5=-1$, but I defined $x^5$ to be equal to 1.  How do I know I wont encounter such a contradiction based upon the axioms of the complex numbers.  I reiterate here again, Please don't use terminology, or abstract math, that hasn't been taught in say a thorough collage level calculus 1 course.  Here's a link to the same question I asked 8 or so days ago: Both the Romulans and the Federation have regularly violated the Treaty when it suits them. Starfleet has obviously developed and manufactured cloaking/stealth technology and the Romulans make regular excursions across the Neutral Zone. They obviously aren't declaring all-out war, so what penalties or sanctions have been imposed for violations?  -edit added for clarity-  Has either side ever 'punished' their own people for any violations of the Treaty? `tail -f` until text is seen I've got a CI server with a command-line interface that allows me to remotely kick-off a job (jenkins CI server and the jenkins-cli.jar tool).  After I kick the job off I tail -f the log (sorry for the messy command):  ssh -t my-jenkins-host.com "tail -f \"/var/lib/jenkins/jobs/$job_name/builds/\`ls -ltr /var/lib/jenkins/jobs/$job_name/builds/ | grep '^l' | tail -n 1|awk '{print \$9}'\`/log\""   After the job successfully completes, usually after at least 5 minutes, I get the following line on the output:  Finished: SUCCESS   Is there a good way to stop tailing the log at this point? i.e. is there like a tail_until 'some line' my-file.log command?  BONUS: extra credit if you can supply an answer that returns 0 when SUCCESS is matched, 1 when FAILURE is matched, and your solution works on mac! (which i believe is bsd based) If I had a very shallow question, then I am sorry. $x,y,z\in\mathbb{N}^{+}$ and$$\frac{x}{y+z}+\frac{y}{x+z}+\frac{z}{y+x}=4$$find $x,y,z$.  I try with AM-GM, just get$$ \frac{x}{y+z}+\frac{y}{x+z}+\frac{z}{y+x}\geq\frac{3}{2}$$  This means that the equation must have a real solution, but can not be sure there is an integer solution.  Let: $x=ay=abz$, then the equation becomes:$$\frac{ab}{a+b}+\frac{b}{ab+1}+\frac{1}{a^2+ab}=4$$  Which makes the problem become non-homogeneous, and seems to become more difficult. I have no more ideas. Could anyone help me? Thanks a lot. How do I get to the Universe Repository in supported versions of Ubuntu? Can non basic lands be tapped for colorless mana? For example,  has a mana fixing ability, but it doesn't say you can tap it for mana. Other non-basic lands have a mana ability listed on the card. Should I assume that Evolving Winds cannot be tapped for mana?  Basic lands don't have mana tapping abilities listed, but are assumed you can tap them for mana of the color they represent.