Prove 0! = 1

Discussion in 'Calculator Requests' started by math_celebrity, Apr 14, 2019.

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  1. math_celebrity

    math_celebrity Administrator Staff Member

    Prove 0! = 1

    Let n be a whole number, where n! represents the product of n and all integers below it through 1.

    The factorial formula for n is:
    n! = n · (n - 1) * (n - 2) * ... * 3 * 2 * 1

    Written in partially expanded form, n! is:
    n! = n * (n - 1)!

    Substitute n = 1 into this expression:
    n! = n * (n - 1)!
    1! = 1 * (1 - 1)!
    1! = 1 * (0)!
    For the expression to be true, 0! must equal 1. Otherwise, 1! <> 1 which contradicts the equation above
     

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