Well, normally if we ask someone about factorial of 5, one would normally say 5*4*3*2*1 which comes as 120.

So how did we came to this? Or if we want to generalize this we can say multiply the number into its decreasing order till 1 i.e. multiplying a number below it till it reaches 1

Formula wise we can say

n! = n* (n-1)!

where ! indicates factorial for a given number.

Further disintegration of the formulae can be put forward as,

n! = (n-1)(n-2)(n-3).......* 1.

Before we dive into the topic in hand, lets understand why factorial was brought into the mathematical foray.

Discovered by Daniel Bernoulli, the factorial concept is used in many mathematical concepts such as probability, permutations and combinations, sequences and series, etc. 

For example if we want to find how a set of 3 numbers {1, 2, 3} can be represented, we can say that by finding factorial of number 3. Let's prove the same by finding the all possible combinations

{1,2,3} {1,3,2} {2,3,1} {2,1,3} {3,1,2} {3,2,1}

Well 6 combinations that I can find about.. which seems to be the max.

Now lets find 3! which would be 3*2*1 i.e. 6

Or we can say there are 6 possible ways to represent a set of 3.

Similarly for a set of 0, there would be exact 1 way to represent a null set. Isn't it?? So can we say 0 factorial is 1!!

OMG, did we just prove it.. well before we get to the case this works under the assumption there can be a empty set or null set.

Its similar to say 1, whose factorial is also 1 since there is also only one possible way to represent a set of one.

{1} Similarly 0 is also considered a number which would indicate nothingness in a set i.e. a null set {}

So only one possible way to represent the same. That's it for the synopsis today.

Till next time, remember the geek talks...   

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