Why is 0! = 1?
I tried figuring out the Gamma function from Wikipedia a few weeks ago...but didn't understand it that well. Do you know any website where I can find a proper introduction to it? Or should I just wait until they cover it in one of my future college courses....once I start college?
I posted this in another thread, but I'll repost it here.
See if this helps.
n! is defined as 1 * 2 * 3 * . . . * n
And with a little manipulation, we can show that 0! = 1 by demonstrating that...
1! = 1
2! = 1! * 2
3! = 2! * 3
4! = 3! * 4
Reversing that, we can achieve...
3! = 4!/4
2! = 3!/3
1! = 2!/2
0! = 1!/1 = 1
So many different ways! I like this.
The way I was taught was using the fact that that there are ways of picking k items from a set of n, where
If we think about it, it should be that there is only 1 way of choosing no items from a set of n items, therefore and so,
Some of the other explanations are nicer I think, but there's my two cents!