In article <zqSdnWW7vftipLXVnZ2dnUVZ_uSdnZ2d@[EMAIL PROTECTED]
>,
konyberg@[EMAIL PROTECTED]
says...
>=20
> "Mike" <m.fee@[EMAIL PROTECTED]
> skrev i melding=20
> news:MPG.22924fcd1b8289f2989819@[EMAIL PROTECTED]
> In article <g07jqb$gbu$1@[EMAIL PROTECTED]
>,
feldmann.denis.asupprimer@[EMAIL PROTECTED]
> says...
> > orangatang1@[EMAIL PROTECTED]
a =E9crit :
> > > On 11 May, 17:59, "Jon G." <jon8...@[EMAIL PROTECTED]
> wrote:
> > >> Solve,
> > >>
> > >> a_0*x^0 + a_1*x^1 + a_2*x^2 + ... +a_n*x^n =3D 0
> > >>
> > >
> > >
> > >
> > >
> > > x =3D 0
> > >
> > >
> > >
> > x^0=3D1, smartalec
> >
> not so for x=3D0.
>=20
> If the binomial theoreme is correct (and it is) then 0^0 =3D 1.
>=20
If the binomial theory is correct (and it is) then, either one must
_define=
_ 0^0 as equal to 1, or alternately one may=20
accept that x=3D0 is a special case of the binomial theorum.
On the other hand, if x is considered as a complex number (and it probably
=
should be as we are solving a polynomial),=20
then x^x (x : complex) is undefined at x=3D0, due to the fact that x^x =3D
=
exp(xlog(x)) and log(0) is undefined (I am sure=20
we won't disagree about that).
Generally, the value of 0^0 is context dependent and is often better left
u=
ndefined. If you do want to define it as=20
having a value (i.e. 0^0 =3D 1), you should accept that this definition
is=
more for the sake of convenience within a=20
specific area of mathematics (for example combinitorics), than
correctness.
Mike
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