prove 0!=1

Asked by  | 27th Jul, 2008, 04:27: PM

Expert Answer:

Usually n factorial is defined in the following way:

 

    n! = 1*2*3*...*n

But this definition does not give a value for 0 factorial. One way to find ir is by working backwards.

We know that:

1! = 1
     2! = 1!*2 
                2! = 2
     3! = 2!*3
                3! = 6
     4! = 3!*4
                4! = 24

In this way a reasonable value for 0! can also be found. 0! (1x0)

How can we fit 0! = 1 into a definition for n! ? Let's rewrite the usual definition with recurrence:

1! = 1
      n! = n*(n-1)! for n > 1

Now it is simple to change the definition to include 0! :

0! = 1

Answered by  | 28th Jul, 2008, 09:13: PM

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