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Proof that 0!=1(Zero factorial is equal to one)

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Let n be a whole number

n! is defined as the product of n and all whole numbers less than n

n! = n x (n-1) x (n-2) x (n-3) x ... x 3 x 2 x 1

or in a partially expanded form,

n! = n (n-1)!

We know for certain 1! = 1

Let us obtain an exapnsion for 1!

1! = 1 x (1-1)!

1! = 1 x 0! --------------------------------------eqn (*)

Since we know that 1! is 1,

Substituting 1 in place of 1!

1 = 1 x 0!

0! = 1/1

0! = 1 --------------------proved

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