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how come 0! =1?

how come 0! =1?


 

Grade:12

4 Answers

Ashwin Sinha
520 Points
10 years ago

Dear Debjit,

 

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, so a natural question is: what is the value here of 0! ?

A first way to see that 0! = 1 is by working backward. We know that:

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

We can turn this around:

                4! = 24
     3! = 4!/4
                3! = 6
     2! = 3!/3
                2! = 2
     1! = 2!/2
                1! = 1
     0! = 1!/1
                0! = 1



                Good Luck!!!!!!!!!!




              Plz. approve by clicki ng 'Yes' given below!!!!!!!!!!   Plz. Plz. plz.!!!!!!!!!!!!!
Siddharth Thandra AskiitiansExpert-IIT
24 Points
10 years ago

Dear Debjit,

0! = 1!/1 = 1

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jitender lakhanpal
62 Points
10 years ago

Dear DEBJIT DUTTA 

 WE CAN PROVE IT MATHEMATICALLY BY THE DEFINITION OF FACTORIAL

WE KNOW THAT 

(N-1)! = N!/N

AND NOW PUTTING N = 1 HERE WE GET 

0! = 1!/1

 

AND WE KNOW 

1! = 1 SO

0! = 1

 


 

 

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anurag v.
38 Points
10 years ago

using n!=n*(n-1)!

putting n=1, we get 0!=1

plz approve if u like 

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