There exists $N\in \Bbb{N} $ such that $N>2$ and for all $n>N$,$\phi(N)<\phi(n)$ / $\{\frac {\phi(n)}n:n\in\Bbb{N}\}$ has finitely many limit points.
Limit points of the set $\{\frac {\varphi(n) }n : n\in \mathbb{N}\}$
Python metaheuristic packages I need to use a metaheuristic algorithm to solve an optimization problem on a Python codebase.  Metaheuristics usually need to be written in C++ or Java as they involve a lot of iterations, while Python is weak from this point of view.  Questions:   do any Python metaheuristic packages which wrap faster languages as C++/Java exist? do any Python metaheuristic packages based on maybe cython on numba exist? other solutions? All my properties are zero, and my array is zero, even though I have populated them with numbers and objects Inversion/non-inversion in wh-questions with long phrases after the wh-words Can a sentence like this:      "I don't know who the first man that made such and such thing in such and such place was,"    be grammatically correct if we don't put "was" at the end of the long phrase, that is, if we write:      "I don't know who was the first man that made such and such thing in such and such place"?    I can see in Google Books examples that in such cases the verb is often put after the wh-word, but I don't know if there is a grammar rule to support this. Some examples:  "We do not know who was the first man who ascended above a poor and humble people to become Egypt's first king ..."  "... we do not know what was the ultimate judgment of the various members of the community ..."  "I do not know who was the first to suggest a connection between the problem of free will and the breakdown ..."  "I do not know what was the date of this change in me, nor of the train of ideas ..."  "We do not know what was the primitive text from which Codex Bezae derived its Latin or its Greek ..."  "We do not know what was the practice in the days of the monarchy, but the story of Athaliah shows ..." I am aware that there are plenty of threads on intensifiers(very, rather, pretty, quite, fairly, etc.), both on this site and on the web, because of their ambiguity in terms of meaning. What I have learned is that their meaning can change depending on which country you are from, which context they are used, or your intonation. So instead of comparing all intensifiers, I decided to make my question more specific. I chose to focus on the word pretty because of its "common" usage.  So as we can see, the word pretty has two meanings and unfortunately they are "pretty" opposite. My question is can you tell me, just by taking into account  the example sentences below, in which sentences "pretty" means "fairly,", and in which it means "very?"  Does "Tom looks pretty tired" always mean "Tom looks a little/fairly tired" ? Preserve blend mode effect when underneath layers are disabled? (Photoshop) Analysis Question Involving Real Numbers Preventing robots from crawling specific part of a page Are both expressions correct? If yes, do they have different meanings? It seems to me that I came across both of them in books, but I'm not sure. How to check if a macro value is empty or will not create text with plain TeX conditionals? I have a macro which holds some text value, e.g. \macro{some text}. If it is empty, I would like for nothing to appear in the document, but it has some content of any kind which would produce text displayed in the document, I would like a message to appear, "Text: some text".   \macro{} would be considered empty. \def\somedata{}, \macro{\somedata} would be considered empty. \macro{0} would be considered not empty.   I have tried making a TeX conditional which can check if the value is not empty, but nothing I tried works, e.g.:  \ifx #1 {} \else     Text: #1 \fi  \ifx#1{} \else     Text: #1 \fi  \ifx #1 \nil \else     Text: #1 \fi  \ifx#1!="" \else     Text: #1 \fi   What is the correct syntax for creating a conditional in plain TeX with checks if a value is not empty? Is there a place where I can look what updates I've installed? Determinant of a specially structured matrix ($a$'s on the diagonal, all other entries equal to $b$) How do I disable X at boot time so that the system boots in text mode? Is it possible to disable X at boot time? I'm setting up a server so it would be nice if it wouldn't load the graphical interface every time I boot. Export beamer slides to powerpoint/openoffice-impress/keynote editable format I usually prepare my talks using powerpoint/openoffice-impress/keynote, where I explaing programs, pseudocodes, etc. Recently I was thinking about creating text-only, code-only and pseudocode-only slides with beamer and then exporting them somehow to powerpoint where I modify them to add figures or some minor details for polishing the presentation, which are usually hard to do with beamer. I googled a bit around and found that beamer can export to PDF or PS but not to powerpoint. I wonder anyway if you know some possibility of conversion from beamer to on-screen editable powerpoint/openoffice-impress/keynote. Blender 2.8 : python code to switch shading mode (between wireframe and solid mode) If i switch between solid and wireframe mode, i can see in the info window that these commands are invoked :  bpy.data.screens["Layout"].shading.type = 'WIREFRAME' bpy.data.screens["Layout"].shading.type = 'SOLID'   Now i want to execute this command using python console. So i cut and paste the codes into python console but i got this error :   &gt;&gt;&gt; bpy.data.screens["Layout"].shading.type = 'WIREFRAME' Traceback (most recent call last):   File "&lt;blender_console&gt;", line 1, in &lt;module&gt; AttributeError: 'Screen' object has no attribute 'shading'  &gt;&gt;&gt; bpy.data.screens["Layout"].shading.type = 'SOLID' Traceback (most recent call last):   File "&lt;blender_console&gt;", line 1, in &lt;module&gt; AttributeError: 'Screen' object has no attribute 'shading'   Does anyone know why ? and what the correct script should i use in python console ?  Thanks why each left ideal of this is minimal? Top Bar background does not persist when scrolling horizontally Update  A month Several months later, a new top bar, and the bug still exists. An answer has already been posted that would fix the bug, so is this something that the dev team plans on fixing?  There are also a host of other problems caused by this, especially on the  and . Again, this would be fixed with  html{min-width:1000px;}   There is a slight bug with small windows on both the new meta and main site(s)?, shown here. The problem is that the top bar coloring doesn't stretch across when you resize and scroll left or right.        On Meta, when a horizontal scroll bar is needed, the black background will only be as wide as the width of the viewport, but when you scroll the coloring will not shift.  To reproduce:   Make screen as large as possible, or wait until the menu bar starts expanding Make it smaller and smaller until horizontal scrollbar appears, then scroll left and right. How to open nautilus without a desktop? I'm using xmonad, and I would like to open a nautilus window to a certain directory, because I like the convenience of browsing inside an encrypted zip file without unzipping it, which nautilus allows.   however, opening nautilus, even with a path argument starts a desktop on the monitor I'm using (There are 8 xmonad monitors) The desktop is inoperative and renders that monitor useless until nautilus is killed.  Is there any way to open just a nautilus window without any desktop starting? Possible Duplicate:          I have seen  in SQL. I wonder how would you approach the opposite problem: splitting coma delimited string into rows of data:  Lets say I have tables:  userTypedTags(userID,commaSeparatedTags) 'one entry per user tags(tagID,name)   And want to insert data into table  userTag(userID,tagID) 'multiple entries per user   Inspired by  question  EDIT  Thanks for the answers, actually more then one deserves to be accepted but I can only pick one, and the  with recursions seems pretty clean to me. It works on SQL Server 2005 and above.   For earlier version of SQL Server the solution  can be used.  For working with text data type  will be helpful. Thanks again. What recourse do I have if I believe a moderator has abused their privileges? One or more of the following things happened to me on a Stack Exchange site:   My post(s) were wrongly deleted or locked by a moderator A moderator posted a wrong comment on one of my posts I was suspended, but did not do anything wrong I asked a meta question, but the question was closed and/or deleted A moderator discredited me in public ...   I think a moderator has abused their power, but I feel powerless against them.  What recourse do I have now? What can I do when I feel that a moderator has abused their power, and has been repeatedly unfair in their dealings with me? I have association bonus on superuser.com. After that I've started a bounty worst of 50 rep and earned more than 10 rep. Now I have 89 rep (38 of which is earned at superuser which is more than 10) but still not able to answer protected questions.  So, currently new user with 10 rep can answer protected question and I with 89 (38) rep can't.   How does it work now: after registration on new Stack Exchange site you get 101 rep Association Bonus and are able to answer protected questions only when you have 111+ rep on that site. How should it work: after registration on new stackexchange site you get 101 rep Association Bonus and are able to answer protected questions only when you have earned 10+ rep on that site.