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Topic: Zero Factorial
Replies: 4   Last Post: Sep 28, 2000 8:43 PM

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Brian Harvey

Posts: 127
Registered: 12/6/04
Re: Zero Factorial
Posted: Sep 19, 2000 7:13 PM
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mikstu3141@aol.com (Mikstu3141) writes:
>Any suggestions as to how to approach 0!=1 with an Algebra II class? Thanks-

I think the key point is that whenever a mathematical idea is extended
beyond its original range, (1) the extension is to some extent arbitrary,
but (2) one wants to preserve as much as possible the old rules about
that idea.

So, for example, when we invent negative integers we are confronted with
the question of what (-1)*(-1) should be. In a sense we could pick any
answer we want, but it turns out that only one answer preserves the
associative and distributive laws.

Similarly, in extending the idea of factorial down to 0!, we'd like to
preserve the defining recurrence relation for factorial:
n! = n * (n-1)!
Plug in n=1 and you see that 0! must be 1 to preserve this rule.

You can then try n=0 to see that there can't be a (-1)! preserving
the rule.

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