Why is 0! = 1?

Printable View

- September 1st 2009, 07:19 AMpacman0!
Why is 0! = 1?

- September 1st 2009, 07:24 AMynj
it is specially defined.

Since 1!=1*0!. - September 1st 2009, 07:45 AMSoroban

A silly poem I wrote while in college:

Man has wondered

Since time immemorial

Why 1 is the value

Of 0!.

- September 1st 2009, 07:57 AMdhiab
**Hello 0! is a convention without demonstration.**

**Same** - September 1st 2009, 09:17 AMChris L T521
- September 1st 2009, 09:35 AMRobLikesBrunch
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?

Thanks. - September 1st 2009, 09:43 AMmasters
Hi pacman,

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

etc.

Reversing that, we can achieve...

3! = 4!/4

2! = 3!/3

1! = 2!/2

0! = 1!/1 = 1 - September 1st 2009, 09:44 AMChris L T521
See if this helps you: The Gamma Function

- September 1st 2009, 09:44 AMRandom Variable
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) - September 1st 2009, 06:22 PMpacman
**random variable**, can you elaborate further? (Rock)(Rock)(Rock)(Rock)(Rock) thanks! - September 1st 2009, 06:35 PMChris L T521
- September 1st 2009, 06:45 PMpacman
ahhh, that is much CLEARER now. Thanks

**Cris** - September 1st 2009, 07:31 PMpomp
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! - September 1st 2009, 07:42 PMpacman
**Pomp**, i like your way of obtaining 0! = 1 through Combination. - September 1st 2009, 08:32 PMWilmer
If 0! was equal to 0, then n! would = 0,

since we'd have to assume that ! represents 0*1*2......*n