# Existential Factorial Glass Mug 0! = 1 (Concept by Stella)

Regular price \$ 18.00 Sale price \$ 12.95

The concept for this mug came from the mind of eight-year-old Stella from Southern California. She is now eleven years old and starting her college career. We'll let her explain how she came up with the idea for this mug and why it's awesome.

When I was seven, I went to the Los Angeles Math Circle at UCLA. There, I learned about lots of interesting math, but one of my favorite things was factorials. Factorials are a fascinating concept. Four factorial (4!) is equal to 4 * 3 * 2 *1. 10! would be 10 * 9 * 8 * 7 * 6 * 4 * 3 * 2 * 1. Basically, factorials are when you multiply a number by all the numbers that come before it. How is this helpful? Well, consider how many ways could you choose five marbles from a bag of five marbles (without returning them to the bag). That would be 5 choices for the first marble, 4 for the second, and so on.

But what about 0? What would 0! come out to? I figured out was that 0! = 1. You can come to the same answer two ways: either with a mathematical proof, or a simple logical realization. I first came upon the logical way: “Making no choice is a choice in itself”. This makes sense because if you don’t make a choice, you’re choosing not to make a choice. While this is true in math, it’s also true in the context of life.

However, the math proof is just as elegant and simple. Let’s start with 5!. 5! = 5 * 4 * 3 * 2 * 1.

5!/5 = 4!, the beginning of a pattern.
4!/4 = 3!
3!/3 = 2!
2!/2 = 1!
1!/1 =  0!
And since 1! is 1, then 0! = 1.

My dad and I had a lot of fun with this proof, so for father’s day 2013, I made him a mug with the logical statement “0! = 1 because making no choice is a choice in itself”.

-Stella

Details

Individually boxed.
Dishwasher safe.
Microwave safe.