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Thread: Factorial of zer0?

  1. #1 Factorial of zer0? 
    Senior Member MaxPayne's Avatar
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    Can we prove that 0! = 1?
    Also what is 00?
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  2. #2  
    KJW
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    Quote Originally Posted by MaxPayne View Post
    Can we prove that 0! = 1?
    I don't think one can "prove" 0! = 1 because that is a matter of definition of the factorial. However, 0! = 1 is necessary for many combinatoric expressions to work. Also, if one generalises the factorial to non-integers using the gamma function, then 0! = 1 is a natural result.


    Quote Originally Posted by MaxPayne View Post
    Also what is 00?
    An indeterminate form.
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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  3. #3  
    Senior Member MaxPayne's Avatar
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    thank you!!!

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  4. #4  
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    1 = 1! = 1x0!.
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  5. #5  
    KJW
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    Quote Originally Posted by mathman View Post
    1 = 1! = 1x0!.
    Good point.
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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  6. #6  
    Senior Member MaxPayne's Avatar
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    Lol, the second equation assumes, that 0! = 1.
    So can we really use it to prove the former.
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  7. #7  
    KJW
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    Quote Originally Posted by MaxPayne View Post


    Lol, the second equation assumes, that 0! = 1.
    So can we really use it to prove the former.
    No. In the definition of you provided, is axiomatic (part of the definition of ). The second part of the definition is a recursive definition for all integers greater than zero. Being recursive, it requires an initial condition to start from (the first part of the definition). In other words, both parts are necessary to define . Therefore, the second part cannot prove the first part.
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    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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  8. #8  
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    Quote Originally Posted by MaxPayne View Post


    Lol, the second equation assumes, that 0! = 1.
    So can we really use it to prove the former.
    When I first learned about n!, it was simply defined as n(n-1)...1. So it starts with 1! = 1, not 0! = 1.
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  9. #9  
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    Quote Originally Posted by MaxPayne View Post
    Can we prove that 0! = 1?
    Also what is 00?
    Consider this pattern.











    While this isn't a theorem it is proof by logic and it's more about definition.
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  10. #10  
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    n!=n(n-1)!
    => 1!=1*0!
    but 1!=1
    so 0!=1
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  11. #11  
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    Quote Originally Posted by MaxPayne View Post
    Can we prove that 0! = 1?
    Also what is 00?
    What do you do to work out the factorial of zero?
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