How did the convention of 'multiplying' using $4\times 3$ become $4\cdot 3$?
Why does the symbol for the multiplication operation change shape?
No CUDA and GPU option Dark matter and dark energy references I've been looking for questions about dark matter, and I've read some very interesting answers. However, I desire too look into it deeply.   This is not actually a question. I'm asking the community to recommend interesting references to understanding dark matter and dark energy.   I accept all sort of references: notes, books, scientific papers etc.  Let us assume some background on classical physics, thermodynamics and basics about quantum theory. Which folder is recycle bin in on Win7? How to check files there? I was using another account before. Let me call it account A. And I deleted a lot of files to the Recycle Bin at that time. But before I removed account A I forgot to empty the Recycle Bin.   My question is, are my files still there? I've searched and found that the Recycle Bin may live in $Recycle.Bin, but I can't open files there so I can't know what they are. Any help how to open deleted files or how to delete them permanently? How to open a PDF file from terminal? I used to work on the Mac terminal before and I used:   open file2open.pdf   and the PDF file would be opened on preview or whatever my default viewer was. When I use it in the terminal in Ubuntu I get this error message:   Couldn't get a file descriptor referring to the console $n\in N, a_{n+1} = a_n (1 - a_n)$ , $0 < a_0 < 1$. Prove that $\lim\limits_{n\to\infty} a_n\cdot n = 1$. $n\in N,   a_{n+1} = a_n  (1 - a_n)$ , $0 &lt; a_0 &lt; 1$. Prove that $\lim\limits_{n\to\infty} a_n\cdot n = 1$. I proved that $\lim\limits_{n\to\infty} a_n = 0$ and that $a_n$ is strictly decreasing. I tried Cezaro Stolz but didn't get anywhere. Thanks in advance. Payment from Apple for developer Why the middle mouse button in Blender 2.80 changes the orthographic view to perspective? If I choose an orthographic view by using the numpad and then try to orbit the geometry by clicking the middle mouse button Blender goes from orthographic to perspective. Why is that the default now? Wouldn't it be more logical if instead of that Blender kept the orthographic mode? In other words: Why Auto Perspective is turned on by default? Help Understanding How Long It Will Take To Heat My Wire Can the Artificer Artillerist's tiny-sized Eldritch Cannon that is not held in hand still ride or be carried elsewhere on the body? Is it OK to require users to have a third party login account? For a web app I'm developing I was dreading having to   Require users to create yet another account / password to keep in mind. Handle retrieval of lost passwords etc.   What many sites (like this one for instance) has started offering is to use a third party account to create an account.   What I wonder is whether it would be considered OK to require having third party account, i.e. $\operatorname{rank}(T^3) + \operatorname{rank}(T) \geq 2\operatorname{rank}(T^2)$ for finite-dimensional $V$ Consider a finite-dimensional vector space $V$ over the field $\mathbb{F}$ with a linear operator $T.$ Prove that we have $\operatorname{rank}(T^3) + \operatorname{rank}(T) \geq 2 \operatorname{rank}(T^2).$   First, let us assume that $\dim_{\mathbb{F}}(V) = n.$ Our immediate observations include that $T^3(V) \subseteq T^2(V) \subseteq T(V)$ so that $\operatorname{rank}(T^3) \leq \operatorname{rank}(T^2) \leq \operatorname{rank}(T)$ and $\operatorname{rank}(T^3) \geq \operatorname{rank}(T) + \operatorname{rank}(T^2) - n$ by Sylvester's Rank Inequality. Can we do some manipulations with what we have to get the desired inequality, or do we require something else? How to setup Squid Proxy (for localhost services and Tor and I2P) How to print the full NumPy array, without truncation? This is the gift that my dad sent (to) me This is the gift that my dad sent me on my birthday.   Vs   This is the gift that my dad sent to me on my birthday.  Is to required?   Also   Presenting you guys, the trailer of the film.   Vs   Presenting to you guys, the trailer of the film.    Is to required? I have a bit of code where I've written a SOQL query that returns a list of SObject records, however I need a Set&lt;Id&gt; structure to pass to another method that I don't have control of (and thus can't change the method signature of).  How can I turn my returned List&lt;SObject&gt; into a Set&lt;Id&gt;? Is the best option just a for loop? How do I recover lost/inaccessible data from my storage device? What steps can I take to try to recover lost or inaccessible data from any storage device?  Answers:   This applies to any computer storage device, e.g. internal/external hard drives, USB sticks, flash memory. The most important thing is to STOP using it, any type of I/O can ruin your chances of a recovery.     We have separate questions covering common problems with USB flash drives in greater detail: bash function cannot change the value of a local variable when called by $() The following code works differently depending on which way Parse_Short_Switches() is called.  After calling the function 'Parse_Short_Switches' by using result=$(Parse_Short_Switches), the value of $error_flag is NOT set to -1 as I would expect.  After calling the function 'Parse_Short_Switches' by simply using Parse_Short_Switches, the the value of $error_flag is set to -1 as I would expect.  Any help would be greatly appreciated.  Thanks  #!/bin/bash  function Parse_Short_Switches() { echo "error_flag inside of the function= $error_flag" 1&gt;&amp;2 error_flag="-1" echo "blah blah ..." }  # --- MAIN --- error_flag="999" echo "error_flag= $error_flag" #result=$(Parse_Short_Switches) Parse_Short_Switches echo "error_flag= $error_flag" why can't i select two objects in edit mode?     I am trying to make a face from two different meshes but can't perform the action GUI does not start Initially, the computer was showing the error as mentioned in   question. Fixing it resulted in the above error.  Please take look at the last line   Started GNOME display manager... and deal with any system changes..p link was shut down.....     One more thing before all this problem I have edited xorg.conf file to use  as suggested on .  I don't know if that's the reason but I thought it is important to share. How can I display additional boot and shutdown information on the Windows 7 welcome screen? There is a small tweak, I believe it is a registry key, that allows to display additional information on the Welcome and Shutting down screens of Windows 7 (and most likely Vista, too). I have activated this tweak on one of my systems; unfortunately I forgot how I did it, and I can't seem to find the website that originally gave me that information.  Usually, the Windows 7 welcome screen will just display "Welcome" when logging in. With the tweak activated, my Welcome screen gives status information such as "Loading user settings" or "Preparing desktop". When shutting down, the default screen simply says "Shutting down". With the tweak activated, it gives additional status information such as "Stopping Windows services". This appears the same way that Windows gives information when updates are installed or configured during the startup or shutdown procedure, and I find them quite helpful in getting a feel for what task takes how long during that process.  The only setting I was able to find is the Boot log checkbox on the Boot tab of the msconfig application. However, this results in Windows displaying console logs of drivers it is loading, etc., instead of the animated Windows title. This is NOT the setting I am looking for. The "additional boot information" setting that I have activated on this system still displays the regular animated Windows logo, and only replaces the strings displayed on the blue Welcome and Shutdown screens.  Could someone direct me to the registry key (or whatever setting) that is used to get this behaviour?  Edit: Here are a few pictures of the enhanced Welcome and Shutdown screens taken with my mobile phone—they're in German though.   Login screen "Waiting for User Profile Service"   Login screen "Preparing desktop"   Logout screen "Stopping Windows services":