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January 23rd, 2008, 06:16 AM   #1
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zero factorial (why ??)

Hello
Why 0! has been defined as 1 ??

Why is it so ???
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January 23rd, 2008, 07:18 AM   #2
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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.
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January 23rd, 2008, 06:09 PM   #3
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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!
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January 29th, 2008, 01:53 PM   #4
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Re: zero factorial (why ??)

Quote:
Originally Posted by sangfroid
Hello
Why 0! has been defined as 1 ??

Why is it so ???
Since 1!=1 and in general n!=n*(n-1)!, 0! has to be 1.
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February 1st, 2008, 12:12 PM   #5
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Quote:
Originally Posted by CRGreathouse
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.
Quote:
Originally Posted by cknapp
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!
Games and trivia! See if you can spot the formalist and the Platonist in the quoted posts.
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February 1st, 2008, 02:27 PM   #6
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Yay! Return of the fun & games section!

Although I think it was previously called "games and trivia"
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February 4th, 2008, 04:43 AM   #7
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Quote:
Originally Posted by cknapp
Yay! Return of the fun & games section!

Although I think it was previously called "games and trivia"
:hand motion: These are not the droids you are looking for.
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February 4th, 2008, 06:44 AM   #8
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I find your lack of original conversation disturbing!

With the joke on me for quoting a comic about over-use of quotation.
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September 15th, 2008, 04:28 AM   #9
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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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