0^0

[Marc LeBrun]

I agree that 0^0, should usually be taken as 1, as should, more generally, 
N^0, for any N that's a "numberlike" thing.

This is because we want to interpret N^K as the product of K Ns, and an 
empty product's value is naturally and consistently defined to be the 
multiplicative identity.  So this seems to be the convention in discrete math.

The confusion here may arise from mixing contexts.  Most 0^0 things 
encountered near the OEIS only *look like* the 0^0 things that are 
encountered in Calculus classes.  But string-substituting "0"s for "X"s in 
"sin(X)/X" has little connection with vacuous products, so those 
"indefinite form" interpretations don't travel well.

"That'll teach youse guys to eat of the Fruit of the Tree of Knowledge of 
the Difference between Functions and Expressions!"
Signed, The Supreme Fascist.



At 01:24 PM 5/4/2005, Jon Awbrey wrote:
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>but logic says that 0^O = 1,
>as x^y is analogous to x<=y,
>and 0<=0 is true.
>
>ja
>
>Robert G. Wilson v wrote:
> >
> > Everyone,
> >
> > My Calculus classes told me that there are seven indeterminate forms.
> > They being:  0/0,  inf/inf,  0*inf,  inf-inf,  0^0,  inf^0 &  1^inf.
> > The undefined forms are:  a/0 and 0^-inf.
> >
> > Bob.
> >
> > Joshua Zucker wrote:
> >
> > > Apparently seqfans also have a bit of disagreement over whether 0^0 =
> > > 1 or 0 or undefined!  That seems to be the reason for the three
> > > different sequences (the third being A062970).
> > >
> > > --Joshua Zucker
>
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>inquiry e-lab: http://stderr.org/pipermail/inquiry/
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