Did you know that in mathematics, 0! (zero factorial) equals 1?

Many people are surprised when they hear this for the first time. “How can nothing equal one?” The truth is, it’s not magic — it comes from a very elegant logic in mathematics.

 

Basically, a factorial means the product of descending numbers. For example:

5! = 5 × 4 × 3 × 2 × 1
1! = 1

 

Now the question arises: what is 0!?

To keep all factorial formulas consistent, 0! must be 1. Otherwise, many mathematical formulas, such as in combinatorics and probability theory, would “break.”

 

For example, in combinatorics, the number of ways to arrange objects is calculated using factorials. If we choose or arrange no objects, there is still exactly one way — doing nothing.

This concept ensures that 0! = 1.

 

This is the beauty of mathematics: even if it sometimes seems strange, every value has a solid reason. Mathematics is the art of creating consistency, and 0! = 1 is one proof of how elegant and orderly the world of numbers is.

 

Dr. Nor Ain Azeany Mohd Nasir

Institute for Mathematical Research, Universiti Putra Malaysia

Date of Input: 20/11/2025 | Updated: 20/11/2025 | norhidayahche