From a philosophical standpoint, $0!=1$ as it is possible to arrange nothing in one way--there isn't.  Are there any rigorous proofs showing this concept?
How can I prove  from first principles that $0!$ is equal to $1$?
Re-enabling backspace as "go back" in recent Chrome Since start of this summer, I think that Google removed the option of using backspace for returning to previous page or so.   I was wondering, if there exist any chance, of undo-ing this thing? Is there such thing that would help me, such as downgrading Chrome or using any additional add-ons or something such as this for getting this glorious function back?  It's nearly impossible for me to forget this shortcut (as old habits die hard, lol) and keep pressing it and later on using the mouse to go back. Is there an intelligent way to left-align the parts right of &amp; of the two cases environments shown below (if x >= 0, otherwise, if y &lt; 0, otherwise). I wonder if there is a better way than using manual spaces:  \begin{align*}  u(x) &amp;=   \begin{cases}    0        &amp; \text{if } x \geq 0 \\    1        &amp; \text{otherwise}   \end{cases}   \\  \tau &amp;=   \begin{cases}    a+b+c+d  &amp; \text{if } y &lt; 0 \\    1        &amp; \text{otherwise}   \end{cases} \end{align*} I am looking for an adjective/noun for someone who is able to speak/ makes speeches very well and uses words effectively to influence/impress people. I would like to search an entire MS SQL 2000 database for one value. This would be to aid development only. Keep that in mind when considering this question.   This will get all the table names and the column of the data type I'm looking for:  SELECT Columns.COLUMN_NAME, tables.TABLE_NAME FROM INFORMATION_SCHEMA.Columns as Columns  JOIN INFORMATION_SCHEMA.TABLES as tables  On Columns.TABLE_NAME = tables.TABLE_NAME WHERE Columns.DATA_TYPE = 'INT'     I was thinking something like this:  -- Vars DECLARE @COUNTER INT DECLARE @TOTAL INT DECLARE @TABLE CHAR(128) DECLARE @COLUMN CHAR(128) DECLARE @COLUMNTYPE CHAR(128) DECLARE @COLUMNVALUE INT  -- What we are looking for SET @COLUMNTYPE = 'INT' SET @COLUMNVALUE = 3 SET @COUNTER = 0  -- Find out how many possible columns exist SELECT @TOTAL = COUNT(*)   FROM INFORMATION_SCHEMA.Columns as Columns  JOIN INFORMATION_SCHEMA.TABLES as tables  On Columns.TABLE_NAME = tables.TABLE_NAME WHERE Columns.DATA_TYPE = @COLUMNTYPE PRINT CAST(@TOTAL AS CHAR) + 'possible columns' WHILE @COUNTER &lt; @TOTAL BEGIN     SET @COUNTER = @COUNTER +1     -- ADD MAGIC HERE END   Any ideas?  UPDATE I recently found this  that works quite well. I understand that a black hole bends the fabric of space time to a point that no object can escape.   I understand that light travels in a straight line along spacetime unless distorted by gravity. If spacetime is being curved by gravity then light should follow that bend in spacetime.  In Newton's Law of Universal Gravitation, the mass of both objects must be entered, but photon has no mass, why should a massless photon  be affected by gravity in by Newton's equations?  What am I missing? Can I revert to the Mountain Lion style labels instead of Mavericks tags? How? Package incompatibilites: etoolbox, hyperref, and bm, standalone? I am trying to transition to using the etoolbox package, but seem to have run into some difficulties and they appear related to the hyperref and bm packages which to me seem totally unrelated.  The MWE example compiles since \RemoveEToolbox is defined and shows that there is no apparent problem before etoolbox was used.    Commenting out the \def\RemoveEToolbox{} line produces two problems:   With both the \renewcommand, and the usepackage{hyperref} commented, this results in "Runaway argument? Paragraph ended before \bm@test@token was complete". Including the usepackage{hyperref} (with \renewcommand commented) results in "Undefined control  sequence. \Call@AtVeryEndDocument ...cumentHook \@undefined"   But if uncomment the \renewcommand{\bm}{#1} line (effectively doing without any \bm), then this seems to compile.  I have been using this for a while now and things appeared to have been working fine, but now that I attempt to use etoolbox I seem to run into problems.  \documentclass{standalone} \def\RemoveEToolbox{}% Shows that this works fine without {etoolbox}  \usepackage{amsmath} \usepackage{xcolor} \usepackage{bm}  \ifdefined\RemoveEToolbox     \newcommand*{\iftoggle}[3]{#2}% Default to true value of "if" \else     \usepackage{etoolbox}     \newtoggle{paper}     \toggletrue{paper}      %\renewcommand{\bm}[1]{#1}% Why can't I have a normal \bm with {etoolbox}? \fi  % \usepackage{hyperref}  \begin{document}  This document is intended for  \iftoggle{paper}{paper}{electronic} distribution.  \bm{\textcolor{blue}{Solve $x^2-1=0$}}  \begin{align*}     a &amp;= b\\     \iftoggle{paper}{         c &amp;= d\\     }{}     e &amp;= f\\ \end{align*} \end{document} Small snap loop devices visible in gnome-disk-utility OR what is the function of snap ubuntu-core I just realized using gnome-disk-utility (3.18.3.1) that my 16.04 installation is featuring several small loop devices.  In detail:   78 MB Loop Device (/var/lib/snapd/sn_ntu-core_352.snap -> /dev/loop0) 76 MB Loop Device (/var/lib/snapd/sn_ntu-core_216.snap -> /dev/loop1) 79 MB Loop Device (/var/lib/snapd/sn_ntu-core_423.snap -> /dev/loop2) 705 KB Loop Device (/var/lib/snapd/snaps/tpad_12.snap -> /dev/loop3) 684 KB Loop Device (/var/lib/snapd/snaps/tpad_11.snap -> /dev/loop5) 705 KB Loop Device (/var/lib/snapd/snaps/tpad_13.snap -> /dev/loop6)   Image showing gnome-disk-utility    My questions are as follows:   What are those loop devices used for? Is that an expected behaviour in 16.04? Can  I remove them? And if so - how (just by unmounting)? Is there any risk in removing the 2 installed snaps mentioned below (tpad and ubuntu-core)   UPDATE  Installed snaps  According to snap list I do have   tpad (1.8.1) ubuntu-core (16.04.1)   installed. I remember I did tinker with snaps for a short time when  I realized this option - but am pretty unsure if  I  installed those 2 snaps - or if they are pre-/auto-installed.  tpad is a Terminal text editor with GUI-like user interface  I  did install manually, as  I don't use it  I removed it now via sudo snap remove tpad. As a result the 2 loop devices pointing to tpad are gone in gnome-disk-utility.  So - at the current point  I am still having 1 snap installed called ubuntu-core and I don't know what it is used for. The summary of this particular snap is   The ubuntu-core OS snap Display only relevant reputation points Is there a way to summon Dogmeat to you? I've recently started playing Fallout 4, and I've acquired Dogmeat. Long story short, I told him to stay in a small building so I could down a few raiders quietly but I forgot about him and I can't find him. Is there a way to call Dogmeat back or do I have to retrace my steps until I'm reunited with him? Having trouble adding objects to NSMutableArray in Objective C How can I go about determining the number of unique simple paths within an undirected graph? Either for a certain length, or a range of acceptable lengths.  Recall that a simple path is a path with no cycles, so I'm talking about counting the number of paths with no cycle. What is Skynet's ultimate goal after defeating the resistance? Is it stated in any expanded universe what Skynet's plans were after wiping out the Human race (assuming that was its plan)?  Maybe space travel to colonise different planets or something else entirely? Wireless USB Adapter 0bda:c811 Realtek Semiconductor Corp Create a bootable USB on a Mac to install Ubuntu on a PC What is the best way to get a sine wave from a square wave? How can I prove this inequality in a triangle: $\frac{1}{(b+c-a)} +\frac{1}{(c+a-b)} +\frac{1}{(a+b-c)} \gt \frac{1}{a} +\frac{1}{b} +\frac{1}{c}$? If $a,b,c$ are the sides of a triangle then show that- $\frac{1}{(b+c-a)} +\frac{1}{(c+a-b)} +\frac{1}{(a+b-c)} \gt \frac{1}{a} +\frac{1}{b} +\frac{1}{c}$  I got this problem from an old book on algebra. I've been trying for a long time but can't reach the answer.  My try on the question-  We know that in a triangle, the sum of two sides is always greater than the third side  $b+c\gt a$ $\implies$ $b+c-a \gt 0$  $c+a\gt b$ $\implies$ $c+a-b\gt 0$  $a+b \gt c$ $\implies$ $a+b-c\gt 0$  Also,  $\frac {1}{(b+c)} \lt \frac{1}{a}$  $\frac{1}{(c+a)} \lt \frac{1}{b}$  $\frac{1}{(a+b)} \lt \frac{1}{c}$  Adding,  $\frac{1}{(b+c)} + \frac{1}{(c+a)} +\frac{1}{(a+b)} \lt \frac{1}{a} + \frac{1}{b} + \frac{1}{c}$  How do I proceed further? All genuine answers are welcome :) Why do damaged hard drives freeze the entire system? Locking an iPhone if button is broken? My friend's iPhone's sleep/wake button no longer works. Is there any way to turn off the screen besides setting up auto-lock and waiting a few minutes? I'm looking to download and install the latest version of Ubuntu to replace the current version of Windows I had pre-installed on my machine when bought it.   I have some really neat features on the machine that I really am hoping will still work when I move over to Ubuntu.  Can someone please confirm if the below will still work and, if not, how I can get them to work:   The USB ports on my machine The ethernet or Network work port on the machine The HDMI output on the machine and finally, the built in webcam   Thanks Sam