why 0!=1

Why 0! = 1

  • Wisdom
Reading Time for this post: 3 minutes

All of us know 0! = 1 by calculator or general knowledge, but do you know why is it so? What is the proof of the equation to be correct? Well, there is 3 proving method behind this mystery.

1. Mathematically Proving 0! = 1

Firstly, we know that factorial series of n is

n!= n*(n-1)*(n-2)*(n-3)*…*2*1
4!= 4*3*2*1=24
3!= 3*2*1=6=\frac{4!}{4}
2!= 2*1=2=\frac{3!}{3}

From here we know by going down factorial series, it can also be expressed as

1!= \frac{2!}{2}=1


0!= \frac{1!}{1}=1

2. Graph Extrapolation Proving 0! = 1

Graph of extrapolation of y=x!,
At 0!, the graph lies accurately at 1.

3. Logically Proving 0! = 1

Factorial is used to show the number of possible arrangement pattern of a situation,

For example,

3! means 3 object arranged randomly, thus we can get 6 possible arrangement

6 different possible arrangement of the 3 objects

Hence by logical thinking, if 1!, we only have 1 object, which we will only have 1 possible arrangement, thus the result is 1

For the same situation, if 0!, which we have 0 objects to be arranged. Thus, we will have only 1 option to arrange the object, which is just arranging the nothing in the space.

Hence by the proof of all these 3 methods, I believe you now understand why 0! = 1, which confused you so much in your school. You can now brag it in front of your friends the wisdom of 0!

We hope that this post is insightful for you. Good luck and all the best!

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