The exercise is;     There are m functions from a one-element set to the set {1, 2, …, m}.   How many functions are there from a two-element set to {1, 2, …, m}?   From a three-element set? Give a recurrence for the number of T(n) of   functions from an n-element set to {1, 2, …, m}. Solve the recurrence.   I've gotten to the point that I "know" there are $m^n$ options to the function $$f:\{1,...,n\}\to \{1,...,m\}$$. How do I set up a recurrence relation and solve it?  I've gotten this far; $$ T(0) = 1 \\ T(1) = m \\ T(n) = T(n - 1) \cdot m $$  Solving it; $$ T(n) = (T(n - 2) \cdot m) \cdot m \\      = ((T(n - 3) \cdot m) \cdot m) \cdot m \\      = T(n - n) \cdot m^n \\      = 1 \cdot m^n = m^n $$  But I'm unsure whether I've even done the correct thing?
I've gotten stuck at the following exercise;     There are m functions from a one-element set to the set {1, 2, …, m}.   How many functions are there from a two-element set to {1, 2, …, m}?   From a three-element set? Give a recurrence for the number of T(n) of   functions from an n-element set to {1, 2, …, m}. Solve the recurrence.   I'm not sure how to begin solving it?
Words for "a bit sad" and "a bit happy"? Accidentally ejected External drive while downloading file, now having problems reading I'm hoping someone can help! I recently downloaded a torrent directly onto an external hard drive, (using a 2009 MacBook Pro and 1TB Seagate Expansion portable Drive) somehow during the download the drive was accidentally ejected, since this incident when I plug the drive back in it’s having problems reading.  The drive works fine for about 10 minutes, I can read/copy/paste and access files but then starts to wreak havoc; apps hangs, it hangs the Finder, etc.  I’ve tried repairing it in Disk Utility, which reads and repairs this disk but problems inevitably continue as described above.  I’ve deleted the Torrent file also. All my files on this external drive so re-formatting is not an option until I can retrieve them. What is this weird colon-member (" : ") syntax in the constructor? Can others in my party go through TSA PreCheck? If I have  (i.e. I have a KTN from TSA and the "pre-check" logo gets printed on my boarding pass) and a travel companion does not, can they go with me through the PreCheck security lines? This is assuming that the travel companion is booked in the same reservation on the same flights and is also a U.S. citizen and not on any no-fly or otherwise increased scrutiny lists.  I'm guessing the answer is no, but I haven't seen anything from TSA specifically addressing this. I changed my Blender Units to Metric System, but when I'm building things, my meshes are transparent, i.e. I can see through faces like in wireframe even though my wireframe is turned off. All faces have a light white in non-wireframe mode, but I can still see through them.   How do I reverse this?  Another issue I get is this    Looks like clipping is not working properly. What are the Alternatives For RemasterSys? How do I print bold text in Python? Given a field $F$, can you necessarily construct a field extension $E \supset F$ such that $\operatorname{Gal}(E/F) = S_n\,$? Viber notification is not in the right position Differentiating $y=x^{2}$ I am reading in a book about differentiating, but I am confused with one of the steps he takes.  We start with:  $$ \begin{align} y &amp;= x^{2} \\ y + \mathrm{d}y &amp;= (x + \mathrm{d}x)^2 \\ y + \mathrm{d}y &amp;= x^2 + x\mathrm{d}x + x\mathrm{d}x + (\mathrm{d}x^2) \end{align} $$  Now the author simplifies this to:  $$y + dy = x^2 + 2x\mathrm{d}x + (\mathrm{d}x^2)$$  I dislike how the middle term is simplified to $2x\mathrm{d}x$ instead of $2(x\mathrm{d}x)$, as I feel like it is more intuitive on what is going.  As in, $2$ of the term $x\mathrm{d}x$, instead of $2x\mathrm{d}x$.  But I fear writing it as $2(x\mathrm{d}x)$ may result in an incorrect distributive property.  Next, he omits the $(dx^2)$:  $$y + \mathrm{d}y = x^2 + 2x \mathrm{d}x$$  Subtract the original $y = x^2$:  $$\mathrm{d}y = 2x \mathrm{d}x$$  Now here is where I get confused:  $$\frac{\mathrm{d}y}{\mathrm{d}x} = 2x$$  How can he just divide both sides by $\mathrm{d}x$!?  If the original term was $2$ of $x\mathrm{d}x$, wouldn't it have to be written out as $2x * 2\mathrm{d}x$, and thus divide both sides by $2\mathrm{d}x$ instead?  I think the root of my confusion is how to properly simplify: $$x\mathrm{d}x + x\mathrm{d}x$$  I trust that he is right, but I am looking for an explanation of why his simplification can work, and why $2(x\mathrm{d}x)$ would be incorrect!  Thank you! Drush installed and running; No Drupal site found even with uri specified After much trial and tribulation, I thought I had drush all ready to roar. Much excitement. But then, no joy...  Drush is working. The sites operate fine via MAMP. Regardless, a "drush cc all" command returns:   No Drupal site found, only 'drush' cache was cleared.                                          [warning] 'all' cache was cleared.                                                                       [success]   This question has stumped drupalcon attendees and very experienced developers. Any ideas?  I am on Mac OS 10.9.3 using MAMP (free) Version 3.0.5  Here is my drush status:   Drupal version         :  7.29-dev                                 Site URI               :  http://default                           Database driver        :  mysql                                    Database hostname      :  localhost                                Database username      :  db_user                             Database name          :  db_name                        PHP executable         :  /usr/bin/php                             PHP configuration      :                                           PHP OS                 :  Darwin                                   Drush version          :  7.0-dev                                  Drush temp directory   :  /tmp                                     Drush configuration    :                                           Drush alias files      :                                           Drupal root            :  /Applications/MAMP/htdocs/mysite.dev   Site path              :  sites/default       Have tried executing drush from /Applications/MAMP/htdocs/mysite.dev; from /Applications/MAMP/htdocs/mysite.dev/sites/default; and using drush cc all --uri=http://localhost/mysite.dev  Tried running drush from sites/default. Same result. Xcode - How to fix 'NSUnknownKeyException', reason: … this class is not key value coding-compliant for the key X" error? I am often logged in several SSH sessions at once. To logout from several sessions, I press CTRL+d, until I am back on my local machine. However, I occasionally press it once too many, and my terminal exits. Is there a way to make CTRL+d unable to close my terminal ? I am using terminator as my terminal emulator. Make all footnotes numbered subsequently, but one with a symbol Session ID from scheduled jobs Here's the scenario.  I have a remote application which is invoked from an HTTP callout.  In this callout, I am passing the session ID.  The application can then do its stuff without needing a username and password.  However, I want to be able to invoke the application from a scheduled job, and getsessionid() returns null in this case.  Is there any way around this?  I am trying very hard to avoid storing sfdc usernames and passwords on my remote server, and I want to avoid the hassle of using oAuth with all the complications of client secrets, etc. I’m studying a PhD in Theoretical Physics (quantum field theory, to be specific), but I would like to learn more about black holes (and related areas. Does anyone have any suggestions for textbooks/available notes on these subjects for people without much background in them? Obviously I’m very comfortable with mathematics and physics in general so I’m not looking for “pop science” material. ReSharper likes to point out multiple functions per ASP.NET page that could be made static. Does it help me if I do make them static? Should I make them static and move them to a utility class? Until recently  had one single reputation point, you can see it in this old screenshot:    Now it has over 2K reputation all of a sudden.. what has caused this? Has it affected "real" members as well? Terminal method of formatting storage drive I want to know how to format a storage drive from the terminal. Helpful things to provide in the answer would be often used options for commands and base knowledge that one can use to extrapolate future uses. Specifically I would like to know how to format in the different file systems such as NTFS, FAT32, EXT4, etc. Information on how to partition the drive via terminal is also wanted.  I am trying to format a high capacity external hard drive (EHDD) into NTFS - from the terminal.   I know I can use gparted for this as well as other GUI programs, but I still want to now how to do it from the terminal. How Do I Opt Out of Privileges? According to  , gold badge holders can now unilaterally close questions as duplicates. I hold seven gold badges for tags on SO, which means I can, on my own, close questions as duplicates for those tagged questions.  Simply put: DO NOT WANT.  However, I do not see any ability in SO (the only SE site I spend much time in) to opt out of any privileges, let alone this one.  Is there a spot that I'm just not seeing that allows me to turn off this new privilege?