Why is 0!=1?: Unraveling the interesting truth

Introduction

Have you ever wondered what that exclamation mark in your calculator is? That is the factorial sign. A non-negative number’s factorial is the product of that number by all the natural numbers coming before it (denoted by x!, where x is the number).
Eg. 4!= 4x3x2x1 = 24
1!=1
Factorials of negative and fractional numbers are undefined. [If you enter -1! in your calculator, it reads it as -(1!). So, you get a valid output.]
However, entering zero factorial into a calculator will give 1 as the output. Why is this so? No, your calculator is not broken. To solve for zero factorial, we first need to go to the basic definition of factorial.

Solving for 0!

y! is defined as y multiplied by (y-1)!
Eg. 5! = 5 x 4!
Following the pattern,
2!=2 x 1!
1! = 1 x 0!
As we know, 1! =1
∴ 1 = 1 x 0!
The only value of zero factorial that satisfies this equation is 1. Therefore, zero factorial must be equal to 1.
∴ Zero factorial is equal to 1.

Fun fact: 10! seconds is exactly equal to 6 weeks.

Click here to read about the factorial of 0 in detail.

You might also like: Monty Hall Problem