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Re: 0^0=1
Posted:
May 8, 2012 2:36 PM
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Dan Christensen wrote:
>
>
>
> 0^3 = 1*0*0*0 = 0
> 0^2 = 1*0*0 = 0
> 0^1 = 1*0 = 0
> 0^0 = 1
>
> Can we formalize this argument? How do you go from 0^1 = 0 (a direct
> consequence of the usual definition of ^ on N) to 0^0 = 1?
The usual definition is
x^0 = 1, x^{n+1} = x * x^n.
If, rather, you mean
x^1 = x, x^{n+1} = x * x^n
then you can't get 0^0 = 1.
--
When a true genius appears in the world, you may know him by
this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting
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