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Re: 0^0=1
Posted:
May 2, 2012 3:28 PM
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On May 2, 2:51 pm, Rotwang <sg...@hotmail.co.uk> wrote:
> On 02/05/2012 17:19, Dan Christensen wrote:
>
> > [...]
>
> > More often the definition is given informally in introductory notes as
> > something like:
>
> > n! = 1 * 2 * 3 * ... * (n-1) * n (or the reverse)
>
> > This is what motivated my own recursive definition. Fortunately, it is
> > entirely consistent with the recursive definition you give here.
>
> [from another article]
>
> > If you want to cook it so you get a nice little recursive definition,
> > even it doesn't make any sense, you should choose 1. But why should it
> > be a nice little recursive definition? IMHO the product of an empty
> > list of numbers is nonsense.
>
> And what about the sum of an empty list of numbers? Compare the informal
> definition of factorial you give above to the informal definition of
> multiplication given to primary school students:
>
> m*n = m + m + m + ... + m (n m's)
>
> Given the above, how do you choose to define m*0? You could choose 0 if
> you want a nice little recursive definition, but why should
> multiplication have a nice little recursive definition? Is the sum of an
> empty list of numbers nonsense in your opinion?
[snipping more nonsense]
Yes.
You are talking about very different functions. Addition and
multiplication are binary functions defined on some set of numbers --
say the natural numbers (including 0). Your sum function is defined on
the set of variable length lists of those numbers. There is no reason
to think that multiplying a number by zero must give you the same
result as the sum of an empty list of numbers.
Dan
Download my DC Proof 2.0 software at http://www.dcproof.com
Also see video demo
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