Aesthetic Mathematics - Part 1 - Discovery of 0!

Monday, May 08, 2006

Ever wondered whether 1 is prime or not? or why 0! = 1 or 2^0 = 1?

Journey to the abyss: Lets see why 0! = 1.
Long long ago, when zero was not invented, life was hectic. People were confused about the quantity "nothingness" in maths. Then a brilliant chap known as Aryabhatta discovered 0. Life became relatively peaceful. But people were still confused of how 0 can be placed in current number system, nobody wanted to reinvent the number system. Somehow this dude managed to fit the poor fellow, i.e 0 in the number system peacefully. Every number has a certain behavior, 0 has its own.

I assume you all know what a factorial is, Its not all that difficult as it sounds. Say N is a number, then its factorial will be denoted as N!, which will be equal to N x (N - 1) x (N - 2) ... x 1. Basically multiply the number with the product of all the numbers less than itself.

For example 4! = 4 x 3 x 2 x 1 = 24. Similarly 3! = 3 x 2 x 1 = 6.

And now if you divide 4! by 4, we will be left with, 3!. Lets look into that.

3! = 4! / 4 = 24 / 4 = 6
2! = 3! / 3 = 6 / 3 = 2
1! = 2! / 2 = 2 / 2 = 1
0! = 1! / 1 = 1 / 1 = 1

If you know permutation or combination, you may have come across 0!, and by replacing 0! as 1, you get right answers. Now you don't need to wonder why.

Hurray! Party time, now don't go running nude shouting "Eureka, Eureka", lets not forget our civic sense.