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Math Help - 0!=1

  1. #1
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    0!=1

    Why does 0!=1?
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  2. #2
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    That is just the way mathemations defined it. Because for zero the factorial is undefined, the reason why mathemations defined it that way is because a lot of time in, for example, infinite series the denominators the the following pattern. 1,1,2,6,24,120,.... You see the pattern? Thus, if we define 0!=1 then the pattern is easily as 0!,1!,2!,3!,.....

    Also there is a way to further define the factorial for non-negative number, that is called the Gamma function. And in the Gamma function, the function of 1 is 0!=1.
    Last edited by ThePerfectHacker; June 5th 2008 at 01:11 PM.
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  3. #3
    TD!
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    As ThePerfectHacker said, this is just a matter of definition.
    If you look at the factorials recursively, it makes sense though.

    ...
    4! = 5!/5 = (5*4*3*2*1)/5 = 24
    3! = 4!/4 = (4*3*2*1)/4 = 6
    2! = 3!/3 = (3*2*1)/3 = 2
    1! = 2!/2 = (2*1)/2 = 1
    0! = 1!/1 = 1/1 = 1
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  4. #4
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    Factorial of any number

    Hi,

    Anyone know the generalized formula for the factorial of any number?

    I know it involves gamma and stuff, but could not find the proper stuff so that we could calculate 0.5! for example.
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  5. #5
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    Quote Originally Posted by cmart022
    Hi,

    Anyone know the generalized formula for the factorial of any number?

    I know it involves gamma and stuff, but could not find the proper stuff so that we could calculate 0.5! for example.
    As always a good idea to start by looking at the wikipedia article.

    There it will tell you that anoung many other things:

    <br />
\Gamma(z+1)=z!<br />

    and:

    <br />
\Gamma(z)=\int_0^{\infty} t^{z-1}e^{-t}\ dt<br />

    RonL
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by helpmeplease View Post
    Why does 0!=1?
    how is it that helpmeplease has 0 posts even though we know he has at least 1, namely, the one i quoted?
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  7. #7
    Forum Admin topsquark's Avatar
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    Perhaps he has 0! posts?

    -Dan
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  8. #8
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by topsquark View Post
    Perhaps he has 0! posts?

    -Dan
    lol
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  9. #9
    Senior Member ecMathGeek's Avatar
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    Is starting new threads reflected in the post count?

    Posting this reply, my post ticker went up one, but if I had started a new thread to post this reply would my post count have changed? It's not something I have checked before.
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  10. #10
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by ecMathGeek View Post
    Is starting new threads reflected in the post count?
    yes it is. look at this user for example. as of this moment, he has one post and it is from a thread that he started. you can also look up in the members list for all the users who have 1 post count, you'll realize that most of them started threads
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  11. #11
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    0!=1, because for positive n numbers the factorial means how many different sequences can be made out of n things: How many ways can you put the n things in one row on a table for example?

    Extending to zero:
    If you don't have any things to put into order, there is only one way to do that. That way, that there is nothing on the table. It is one. You cannot do anything else with zero objects, other than "not putting anything on the table". But it's not zero possibilities but one.

    This is no proof just a way to understand that it's not just a simple convention.
    (Sorry for digging this up but this question came up in another topic.)
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  12. #12
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    Well having n!=n(n-1)! let n=1 and the conclusion follows.
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  13. #13
    MHF Contributor arbolis's Avatar
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    Well having let and the conclusion follows.
    That makes sens. Never thought about that before.
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  14. #14
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by arbolis View Post
    That makes sens. Never thought about that before.
    Me either. great isn't it! i love how Kriz can come up with these things
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  15. #15
    MHF Contributor ebaines's Avatar
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    Quote Originally Posted by Krizalid View Post
    Well having n!=n(n-1)! let n=1 and the conclusion follows.
    By that argument if you let  n = 0 you get  0! = 0(-1!) = 0. Doesn't seem to work....
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