# 0! = 1? or why the factorial of zero is equal to one

A long time ago, back in the 10th class (about 8 years ago), I accidentally discovered a rather simple explanation of why the factorial of zero is equal to one.

I talked about this to many teachers, but no one stuck. Therefore, I will simply post this knowledge here, otherwise suddenly someone will come in handy or will lead to certain thoughts. I must say right away that I am not a mathematician, I came across this by accident when I was playing with numbers. I didn’t even know what factorial is then :)

First, let's recall the general theory:

In fact, the factorial of zero is completely computable!

To do this, we need to do a simple sequence of ordinary mathematical operations.

Let's try in action using the example of the factorial

Let's try to calculate factorial 3 in this way

Well, for 1 try

Have you already guessed? :)

Everything is very simple and for scratch:

Voila! Any number in degree 0 is equal to 1. In this, by the way, the weakness of my method, it uses the definition.

Nevertheless, I think this is great :)

Thank you for your attention!

PS:

As many have noticed this is not proof, but just a fun pattern.

I talked about this to many teachers, but no one stuck. Therefore, I will simply post this knowledge here, otherwise suddenly someone will come in handy or will lead to certain thoughts. I must say right away that I am not a mathematician, I came across this by accident when I was playing with numbers. I didn’t even know what factorial is then :)

First, let's recall the general theory:

The factorial of nis the product of all natural numbers up to n inclusive:By definition, they put 0! = 1. Factorial is defined only for non-negative integers.

In fact, the factorial of zero is completely computable!

To do this, we need to do a simple sequence of ordinary mathematical operations.

Let's try in action using the example of the factorial

**n**= 4*(4! = 1 * 2 * 3 * 4 = 24)*- First, take a sequence of
**n**+ (1 or more) numbers, where each subsequent number is greater than the previous one by 1.

For example:**1 2 3 4 5** - Then we raise each number to the power of
**n**and write the results below.

We get:1

^{4}2^{4}3^{4}4^{4}5^{4 }**1 16 81 256 625** - Now we subtract the penultimate one from the last number, and so on.

At the output, we get a series of numbers whose number is less by 1:(16 - 1) (81 - 16) (256 - 81) (625 - 256)

**15 65 175 369** - We repeat the previous step already on the resulting series until one number remains
*(or a series of identical numbers if the number is more than n + 1)*(65 - 15) (175 - 65) (369 - 175)

**50 110 194**

(110 - 50) (194 - 110)**60 84**

(84 - 60)**24**

As a result, we get the factorial of the number four.

Let's try to calculate factorial 3 in this way

*(3! = 1 * 2 * 3 = 6)*We take four numbers to the power of 3 and calculate the “pyramidal difference” (he invented it)

1^{3}2^{3}3^{3}4^{3 }1 8 27 64

(8 - 1) (27 - 8) (64 - 27)7 19 37

(19 - 7 ) (37 - 19)12 18

(18 - 12)6

Everything fits together!

Well, for 1 try

*(1! = 1)*1^{1}2^{1 }1 2

(2 - 1)1

Have you already guessed? :)

Everything is very simple and for scratch:

We take n + 1 numbers to the power of 0, i.e. one

1^{o }1 isenough

Voila! Any number in degree 0 is equal to 1. In this, by the way, the weakness of my method, it uses the definition.

Nevertheless, I think this is great :)

Thank you for your attention!

PS:

As many have noticed this is not proof, but just a fun pattern.