If $f:[0,1]\rightarrow [0,1]$ is increasing function. Suppose $0<f(0),f(1)<1$. Show $f$ has fixed point.
Every increasing function from a certain set to itself has at least one fixed point
Analysis Question Involving Real Numbers The Boolean modifier is not working Range of values of skewness and kurtosis for normal distribution I want to know that what is the range of the values of skewness and kurtosis for which the data is considered to be normally distributed.   I have read many arguments and mostly I got mixed up answers. Some says for skewness $(-1,1)$ and $(-2,2)$ for kurtosis is an acceptable range for being normally distributed. Some says $(-1.96,1.96)$ for skewness is an acceptable range. I found a detailed discussion here:  regarding this issue. But I couldn't find any decisive statement.   What is the basis for deciding such an interval? Is this a subjective choice? Or is there any mathematical explanation behind these intervals? How to use a special character as a normal one in Unix shells? What does it mean for something to hold "up to isomorphism"? What antivirus programs are available? What antivirus programs are available for Ubuntu?  We previously used Symantec Endpoint Protection but it does not work in Ubuntu. Proof by Induction: For any integer $n > 0$, $3|(5^{2n} − 1)$. Is there any difference in proving "for any integer $n &gt; 0$, $3|(5^{2n}-1)$" and proving "for any integer $n \ge 0$, $3|(5^{2n} -1)$"? Or are they the same? Interpretation of log transformed predictor and/or response Term or phrase describing action occuring when not watching Subsurf on a crown. How can I smooth some edges and keep others sharp? How can I smooth all crown but don't smooth the top of the crown? I did a subdivision surface, but this didn't work. All crown became smooth and changed form. How can I resize (not compress) multiple images in a MS Word document? In a blank document, I insert images (screenshots - all are of same size and same format) from a folder. I want to resize the images to a desired size. All now I am doing is selecting one image by one, setting its size. Word does not seem to have multiselect working for images.  Ideally, I want to select multiple images set its size in one go with out use of a macro. Fundamental group of a torus with points removed Question 5.33 from "Topology and its Applications"  by Baesner is to compute the fundamental group of the torus ($T^2$) with $n$ points removed. I can "see" in my mind that if we remove one point we get a bouquet of two circles. Less clear is what happens when we remove two (or more) points. Any hints? Writing comments in QGIS Graphical Modeler I want to explain my model step by step so anyone can easely understand what's going on. So, is it possible to write comments in the QGIS's Graphical Modeler? Is there consensus in the field of statistics that one book is the absolute best source and completely covering every aspect of GLM - detailing everything from estimation to inference? Is the use of a hyphen between "non" and an adjective strictly necessary? Do I need to put a "-" between "non" and an adjective? As an example in physics we say "a non isolated photon", "non tight photon"... The context is very formal (paper publications and similar). Is there a general rule? Are there some differences between countries? Missing settings in GNOME control center installed in Ubuntu MATE I installed GNOME Control Center following  to access Google Drive in Ubuntu MATE 16.04 LTS (MATE desktop environment 1.12.1)   The problem is GNOME Control Center is only showing language support, printers, firewall setup and backups... not online accounts or other settings.  This is what I get:  ~$ gnome-control-center gnome-online-accounts   ** (gnome-control-center:5744): WARNING **: Ignoring launcher landscape-client-settings (missing desktop file)  ** (gnome-control-center:5744): WARNING **: Invalid categories System;Settings; for panel software-properties-gtk.desktop  ** (gnome-control-center:5744): WARNING **: Ignoring launcher ubuntuone-installer (missing desktop file)  ** (gnome-control-center:5744): WARNING **: Could not find settings panel "gnome-online-accounts"   Any ideas?  Thanks! I have a directory with ~1M files and need to search for particular patterns. I know how to do it for all the files:  find /path/ -exec grep -H -m 1 'pattern' \{\} \;   The full output is not desired (too slow). Several first hits are OK, so I tried to limit number of the lines:  find /path/ -exec grep -H -m 1 'pattern' \{\} \; | head -n 5   This results in 5 lines followed by  find: `grep' terminated by signal 13   and find continues to work. This is well explained . I tried quit action:  find /path/ -exec grep -H -m 1 'pattern' \{\} \; -quit   This outputs only the first match.  Is it possible to limit find output with specific number of results (like providing an argument to quit similar to head -n)? Can helium disappear from Earth? This is meant to solve this problem once and for all. What is every reason an object isn't showing up in a render or viewport in when using the cycles render engine? I'm looking to cite a number of web pages using bibtex and I was wondering if there was a specific template of the form @&lt;template name here&gt; for doing that. If you could use the following website as an example that would be great