Why is 0! = 1?

Results 1 to 15 of 16

- September 1st 2009, 07:19 AM #1

- September 1st 2009, 07:24 AM #2

- Joined
- Jul 2009
- Posts
- 254

- September 1st 2009, 07:45 AM #3

- Joined
- May 2006
- From
- Lexington, MA (USA)
- Posts
- 11,548
- Thanks
- 539

- September 1st 2009, 07:57 AM #4

- September 1st 2009, 09:17 AM #5

- September 1st 2009, 09:35 AM #6

- Joined
- Jul 2009
- Posts
- 44

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 AM #7

- Joined
- Jan 2008
- From
- Big Stone Gap, Virginia
- Posts
- 2,551
- Thanks
- 11
- Awards
- 1

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 AM #8
See if this helps you: The Gamma Function

- September 1st 2009, 09:44 AM #9

- September 1st 2009, 06:22 PM #10

- September 1st 2009, 06:35 PM #11

- September 1st 2009, 06:45 PM #12

- September 1st 2009, 07:31 PM #13

- Joined
- Jun 2009
- Posts
- 220
- Thanks
- 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!

- September 1st 2009, 07:42 PM #14

- September 1st 2009, 08:32 PM #15

- Joined
- Dec 2007
- From
- Ottawa, Canada
- Posts
- 3,069
- Thanks
- 65