Date: 05/24/99 at 19:10:23 From: Aubree Subject: 0! My question is this: Why does 0! = 1? I have no idea about this one. My Algebra II teacher admits that he doesn't know. I have also asked the two physics teachers. Everyone tells me 'because it does'. I don't like having to accept this logic because I am the kind of person who usually needs a reason for things. I would really appreciate any help you could provide. Thank you.
Date: 05/24/99 at 23:49:17 From: Doctor Tom Subject: Re: 0! "Because it does" isn't a bad answer. Actually, what happens is this - if you define it to be anything else, then lots of other formulas in math don't work when you plug zero into them. Here's a simple example: How many ways can you choose k things out of a set of n things? For example, how many ways can you choose 2 things out of a set of 4? The answer is 6. If the 4 things are A, B, C, and D, here they are: AB, AC, AD, BC, BD, CD In general, the formula for "how many ways can you choose k things from a set of n?" is given by: n! ------ k!(n-k)! In our example, n = 4; k = 2: 4! 24 ------- = ----- = 6. 2!(4-2)! 2(2) How many ways can you choose zero things? Exactly one way, right? Just take none of them - anything else you do is wrong. So if k = 0, the formula should give 1, right? n! 1 --------- = ----- = 1 0!(n-0)! 0! If 0! is anything but 1, the formula doesn't work. There are LOTS of examples like this, but most of them require a lot of math. - Doctor Tom, The Math Forum http://mathforum.org/dr.math/
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