January 23rd, 2008, 06:16 AM  #1 
Newbie Joined: Sep 2007 Posts: 24 Thanks: 0  zero factorial (why ??)
Hello Why 0! has been defined as 1 ?? Why is it so ??? 
January 23rd, 2008, 07:18 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
By analogy: 10! = 10 * 9! 1! = 1 * 0! From a physical definition: n! is the number of ways to order n objects, and there is 1 way to order 0 elements. To make combinatorial identities hold  there are a lot that depend on 0! = 1 that would have to be rewritten if it were anything else. 
January 23rd, 2008, 06:09 PM  #3 
Senior Member Joined: Oct 2007 From: Chicago Posts: 1,701 Thanks: 3 
Since it's a definition, it can be whatever we feel like defining it to be. It turns out that 1 is the most useful. Don't you love math: Anything is possible, as long as your axioms are consistent! 
January 29th, 2008, 01:53 PM  #4  
Global Moderator Joined: May 2007 Posts: 6,763 Thanks: 697  Re: zero factorial (why ??) Quote:
 
February 1st, 2008, 12:12 PM  #5  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Quote:
Quote:
 
February 1st, 2008, 02:27 PM  #6 
Senior Member Joined: Oct 2007 From: Chicago Posts: 1,701 Thanks: 3 
Yay! Return of the fun & games section! Although I think it was previously called "games and trivia" 
February 4th, 2008, 04:43 AM  #7  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Quote:
 
February 4th, 2008, 06:44 AM  #8 
Senior Member Joined: Oct 2007 From: Chicago Posts: 1,701 Thanks: 3 
I find your lack of original conversation disturbing! With the joke on me for quoting a comic about overuse of quotation. 
September 15th, 2008, 04:28 AM  #9 
Newbie Joined: Sep 2008 Posts: 2 Thanks: 0  Re: zero factorial (why ??)
The reason for choosing 0!=1 is not base on some personal choice or just because it works; it a based on a fact that most mathematicians overlook. The fact is that, unlike any other number, zero exist in a multidimensional state. It is dimensionless. This means that the factorial of every other number is defined to be dimension dependent; it exist in only one plane. But the number of ways zero can be arranged in any plane is just one. This theory I believe has not been brought up by any mathematician yet. I'm still working of the formal prove that axiom seem to be inexplicable just because they fall into multidimensional arenas. I hope others will take it up too. 

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