Why zero factorial is 1?

Answer 1

Here is a cool trick a coworker of mine had shown me. It's not textbook but it works:

n! = (n+1)! / (n+1)

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0! = 1! / 1

0! = 1 / 1

0! = 1

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3! = 4! / 4

3! = 24 / 4

3! = 6

let check our work

3! = 1*2*3 = 6

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9! = 10! / 10

9! = 3,628,800 / 10

9! = 362,880

lets check our work

3! = 1*2*3*4*5*6*7*8*9 = 362,880