Why is 0! = 1?

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

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

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

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

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

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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

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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

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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

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