Why is 0! = 1?
Why is 0! = 1?
it is specially defined.
A silly poem I wrote while in college:
Man has wondered
Since time immemorial
Why 1 is the value
Hello 0! is a convention without demonstration.
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
Let's say that 0! is equal to something else, say 2.
then the taylor series of expanded about would be
which would imply that
and all hell would break loose (Giggle)
random variable, can you elaborate further? (Rock)(Rock)(Rock)(Rock)(Rock) thanks!
ahhh, that is much CLEARER now. Thanks Cris
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!
Pomp, i like your way of obtaining 0! = 1 through Combination.
If 0! was equal to 0, then n! would = 0,
since we'd have to assume that ! represents 0*1*2......*n