Let's do some Mathematics today!!!

I have one interesting question for you all

Prerequisite - You need to know what factorial of a number is.
Factorial of integer is multiplication of all integers smaller than or equal to n. For example 5! is 5*4*3*2*1 which is 120

Now that you know what factorial is let's find the value of

2! = 2x1=2
3! = 3x2x1 =6 & so on...

So my question what is 0!

If you google it you will find the value of 0!=1. But how??

By definition we only multiply the numbers from n to 1 but in this case 0<1. So what do we even do for zero?

To find this, Let's turn the things upside down i.e go from big numbers to smaller ones & see the pattern

Let's see 4! first
4!=4x3x2x1=24

Now,
3!=6, 2!=2, 1!=1

Try to analyze the pattern here...
3!=4!/4 similarly 2!=3!/3 & so on

To generalize this => (n-1)!=n!/n

Now let's go back to our question i.e value of 0!

we know 1!=1 & by our generalized rule what is the value of 0!

(1-1)! = 0! = 1!/1 which comes out to be "1"

We sometimes just accept things the way they are without even thinking why is it so. This was the case with me as well when i was learning factorials in school until i saw @misterwootube's explaination for this.

Hope you all enjoyed it