Why does 0! = 1 ?

A factorial multiplies the number by all the smaller numbers down to 1. For example
4! = 4 x 3 x 2 x 1 = 24
3! = 3 x 2 x 1 = 6
2! = 2 x 1 =2
1! is just 1 (obviously)

In "Do You Feel Lucky?" we use a lot of "factorials" in sums. A factorial has a sign like this: !

But the BIG question is: what does 0! = ? The answer is also 1.
In the book we showed how the Pure Mathematicians came to this result:

However this wasn't good enough for a supervillain known as "The Mathster". He challenged us to give a proper reason, and this is the best we came up with:

If you have 3 playing cards in your hand, you can arrange them in 3! different ways. In other words you can put them in 3 x 2 x 1 = 6 different orders. (It's all explained in "Do You Feel Lucky?")
If you have 2 cards, you can put them in 2! different ways which is 2.
If you just have 1 card you can only arrange it 1! ways which is 1.
But if you have ZERO cards then there's also one way of doing that!

You might have to think about the last bit like this: if there was NO way of having zero cards, then wherever you went or whatever you were doing, it would be impossible not to have at least one card on you. Even if you were in the bath.

So 0! = 1.
There, that's our best answer. Let us hope that The Mathster now stops bothering us with tough questions and blends back into his secret civilian identity which is being a Murderous Maths fan called David Small.

Back to "Do You Feel Lucky?"
Murderous Maths Main Index Page

Why does 0! = 1 ?

A factorial multiplies the number by all the smaller numbers down to 1. For example 4! = 4 x 3 x 2 x 1 = 24 3! = 3 x 2 x 1 = 6 2! = 2 x 1 =2 1! is just 1 (obviously)

In "Do You Feel Lucky?" we use a lot of "factorials" in sums. A factorial has a sign like this: !

But the BIG question is: what does 0! = ? The answer is also 1. In the book we showed how the Pure Mathematicians came to this result: However this wasn't good enough for a supervillain known as "The Mathster". He challenged us to give a proper reason, and this is the best we came up with:

You might have to think about the last bit like this: if there was NO way of having zero cards, then wherever you went or whatever you were doing, it would be impossible not to have at least one card on you. Even if you were in the bath.

So 0! = 1. There, that's our best answer. Let us hope that The Mathster now stops bothering us with tough questions and blends back into his secret civilian identity which is being a Murderous Maths fan called David Small. Back to "Do You Feel Lucky?" Murderous Maths Main Index Page

A factorial multiplies the number by all the smaller numbers down to 1. For example
4! = 4 x 3 x 2 x 1 = 24
3! = 3 x 2 x 1 = 6
2! = 2 x 1 =2
1! is just 1 (obviously)

But the BIG question is: what does 0! = ? The answer is also 1.
In the book we showed how the Pure Mathematicians came to this result:

However this wasn't good enough for a supervillain known as "The Mathster". He challenged us to give a proper reason, and this is the best we came up with:

So 0! = 1.
There, that's our best answer. Let us hope that The Mathster now stops bothering us with tough questions and blends back into his secret civilian identity which is being a Murderous Maths fan called David Small.

Back to "Do You Feel Lucky?"
Murderous Maths Main Index Page