Prove 0! = 1 | MathCelebrity Forum

Prove 0! = 1

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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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