Why Does Zero Factorial (0!) Equal One?

Ali
6 min readJun 20, 2023
Photo by Scott Rodgerson on Unsplash

Recently while in a circle of friends and sipping on a glass of tea, the topic of conversation came around to what humanity’s most remarkable discovery was. Someone put forward the notion that it was the internet, and many others readily agreed with this claim. As the conversation on the matter expanded further, I had gotten stuck on the phrase “humanity’s greatest discovery” and wholly disengaged from the ongoing conversation as I started to ponder what humanity’s most remarkable discovery just might be…

As I wandered among terms such as “electricity,” “soccer,” “spacecraft,” and “iPhone” in my head, I suddenly came across what deserved the distinction to be coined as “humanity’s greatest discovery.” In the words of the beloved late artist Bob Ross, “let’s draw a happy tree here” and similarly “let’s draw a circle here and call it zero” to illustrate Al-Khwarizmi’s effort to define nothingness 1200 years ago, which is arguable, in my opinion, humanity’s most remarkable discovery.

That is because the discovery of the concept of zero led to the invention of Algebra. After air, water, and food, humanity’s greatest needs are computers and the internet, both of which are only possible due to the concept of algorithms that forms their basis. That is why the son of man’s greatest discovery must be zero.

In fact, is there even such a thing as meaningful as zero, which defines nothingness? When everything is jolly, swell, and running without a hitch, does anything disrupt that flow as much as the concept of zero does? Why do mathematicians need to come up with unique definitions and rules for math when the topic in question is zero?

For example, while all numbers are divisible by each other, why is dividing by zero an issue? Why does every number multiplied by zero disappear? Whereas each number’s factorial follows the same rule, why does 0! (zero factorial) boggle our minds? I had written an article about dividing by zero earlier; you can read it below.

--

--

Ali

Math Teacher. Content Curator. Soccer player. Maradona fan. Mostly write about the lectures I love to learn better. alikayaspor@gmail.com