I was thinking how to show that $0!=1.$ I came up with this arguement.    $n!=n\times(n-1)!,$ so with $n=1$, we have $1!=1\times0! \implies 0!=1.$ Is this correct ? Or there are some better proofs for this ? Or is it simply an assumption.
How can I prove  from first principles that $0!$ is equal to $1$?
How do I delete data for one game in the iPad Game Center? I have one particular game that saves data through the game center. Somehow the saved game data got messed up which causes the game not to work properly when I a connected to the internet (I.e. When the game center is accessible).   Is there some way to delete all the data belonging to that game only? "Missing return statement" within if / for / while Should you use "who" or "that" when talking about multiple people doing something? Which of the following is correct?        There were 10 people that went to the store.   There were 10 people who went to the store.      Edit:  Which of the following is correct?        There were 10 people that had brown hair.   There were 10 people who had brown hair. Finding $\int x^xdx$ The following  (links to pdf) in the  has no provided source. The book  by Ash and Gross seems to use a similar style. Where can I find hints for typesetting publication standard articles/books as above in TeX. I looked around a bit but couldnt find much from else from keyword searches.  Particularly, I am looking at the chapter headings, title page design, and the mirror effect. Sorry for the title, as I dont really know what its called. Lebesgue integral $\int_{(0, \infty)} \frac{\sin x}{x} dm$ doesn't exist but improper Riemann integral exists How can I disable a tab inside a TabControl? Is there a way to disable a tab in a ? Is there a NumPy function to return the first index of something in an array? I know there is a method for a Python list to return the first index of something:  &gt;&gt;&gt; l = [1, 2, 3] &gt;&gt;&gt; l.index(2) 1   Is there something like that for NumPy arrays? Creating additional Virtual Host Ubuntu Server Do web browsers use different outgoing ports for different tabs? Problem 4.6, I. Martin Isaacs' Character Theory What are the advantages of Light Application objects I was hoping that the introduction of "Light Application object" would do something about the data storage of junction objects, but it doesn't seem to do anything about it.  The  seems limited to why I would use a "Light Application object", what are the advantages? How do I remap the keys on my keyboard? I broke my laptop and had to buy a new one with a new keyboard that I am struggling to get familiar with, especially with the keys like home, page-up, page-down and end, which aren't standardized at all.  I found myself doing this for like the 5th time in the last several years, and I think it is really annoying.   Is there an app that can reliably map one key to another?  By reliably I mean that key mapping works with Shift, Alt, and other modifiers.  UPDATE  Windows 7, Samsung Chronos 7 Allow moderators to edit/delete comments directly from the per-user comment moderation page A while back, a new dashboard was added to the user moderation tools to .  It's great for scouring a user's comment history to find certain comments, but I can't do anything from this dashboard except filter by flagged1, deleted, or active comments, and visit the posts to which the comments are attached where I can then edit or delete them.  Can we have the ability to edit and delete comments from this dashboard just as we're able to from the flag queue? It gets particularly tedious to have to open 100 tabs just to delete 100 spam comments from the posts they're attached to (and no, I'm not making that number up2...).    1 .  2 Alright, fine, I made that up; the actual number of spam comments I had to delete was 111. How to retrieve a module's path? Heat production of magnifying glass Why Magnifying glass(convex lens) produces heat when placed in front of sun? How do I set my DNS when resolv.conf is being overwritten? Most of the info I see online says to edit /etc/resolv.conf, but any changes I make there just get overridden.  $ cat /etc/resolv.conf  # Dynamic resolv.conf(5) file for glibc resolver(3) generated by resolvconf(8) #     DO NOT EDIT THIS FILE BY HAND --  #     YOUR CHANGES WILL BE OVERWRITTEN nameserver 127.0.1.1   It seems that 127.0.1.1 is a local instance of dnsmasq. The dnsmasq docs say to edit /etc/resolv.conf. I tried putting custom nameservers in /etc/resolv.conf.d/base, but the changes didn't show up in /etc/resolv.conf after running sudo resolvconf -u.  FYI, I don't want to change DNS on a per-connection basis, I want to set default DNS settings to use for all connections when not otherwise specified.  UPDATE:  I answered this question myself:   I think it's the best solution since:   It works. It requires the least amount of changes and It still works in conjunction with dnsmasq's DNS cache, rather than bypassing it. I am struggling to understand this. According to truth tables, if $P$ is false, it doesn't matter whether $Q$ is true or not: Either way, $P \implies Q$ is true.  Usually when I see examples of this people make up some crazy premise for $P$ as a way of showing that $Q$ can be true or false when $P$ is something outrageous and obviously untrue, such as "If the moon is made of bacon-wrapped apple-monkey carburetors, then I am a better wakeborder than Gauss."  $P$ is clearly false, but $P \implies Q$ is true no matter what the state of $Q$ is, and I don't understand why.  Are we saying "If $P$ is false, then all bets are off and $Q$ can be anything, either true or false, and not contradict our earlier claim, and if it isn't false, it must be true"?  Otherwise why can't we say that if $P$ is false, then we can't make any claims one way or the other on whether or not it implies anything at all? UK Train - Can I board at a different station This was a question from my textbook. This is how I approached it.   For the first part, you can do c(10,5) so you choose 5 of the 10 to be on a team.   For the second part, you have 10 ways to choose the "best player" and you multiply it by c(10,4) to pick the other 4 players. However, I am not sure how you can exclude the "worst player". Although this sounds subjective, I believe the question is saying that the "best" and "worst" players are distinct, whereas the other players aren't.