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Topic: Formal proof of the ambiguity of 0^0
Replies: 163   Last Post: Nov 13, 2013 10:45 AM

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 Jussi Piitulainen Posts: 355 Registered: 12/12/04
Re: Formal proof of the ambiguity of 0^0
Posted: Nov 4, 2013 1:46 AM
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fom writes:
> On 11/3/2013 8:32 AM, Jussi Piitulainen wrote:
> > fom writes:
> >

> >> On 11/3/2013 4:53 AM, Robin Chapman wrote:
> >>> On 02/11/2013 21:38, Virgil wrote:
> >>>> In article <685bd338-7570-426a-b2cb-07089fa9693f@googlegroups.com>,
> >>>> PotatoSauce <kiwisquash@gmail.com> wrote:
> >>>>

> >>>>> In practice, 0^0 = 1 works just fine.
> >>>>
> >>>> Unless one wants 0^X to be continuous at X = 0.

> >>>
> >>> Not every function is continuous ....
> >>>

> >>
> >> Should summation forms
> >>
> >>
> >> Sum k -oo to oo ( a_k * x^k )
> >>
> >> a_k = 0 when |k| > M for some natural number M
> >>
> >>
> >> over the reals be continuous?

> >
> > I'm missing the relevance of your question.

[...]

> It had merely been a poor choice.
>
> That is a polynomial form.
>
> If 0^0 =/= 1, then a_0 * x^0 does not have a uniform
> interpretation for all possible values of x.

Ok, thanks. Now it seems to me that you meant to write

sum (k = 0 to M) a_k x^k

starting the index at 0, so k < 0 was a mistake, and you didn't mean
it as an example of any problem with 0^0 = 1. Then it's fine.

> I had understood the exchanges in terms of deciding
> priority with respect to a continuous 0^x.

Yes, Virgil brought that up, as still quoted above, when extension to
reals was mentioned. Otherwise the current thread has been narrowly
about axioms for natural numbers.

[...]

Date Subject Author
10/16/13 Dan Christensen
10/16/13 Brian Q. Hutchings
11/1/13 ross.finlayson@gmail.com
10/17/13 Robin Chapman
10/17/13 Bart Goddard
10/17/13 Dan Christensen
10/17/13 fom
10/17/13 Bart Goddard
10/17/13 Dan Christensen
10/17/13 Bart Goddard
10/17/13 Dan Christensen
10/17/13 Peter Percival
10/17/13 Dan Christensen
10/17/13 Dan Christensen
11/2/13 Brian Q. Hutchings
10/17/13 Bart Goddard
10/17/13 Dan Christensen
10/18/13 Bart Goddard
10/17/13 Dan Christensen
10/17/13 Ben Bacarisse
10/17/13 Dan Christensen
10/17/13 Robin Chapman
10/17/13 Dan Christensen
10/17/13 Bart Goddard
10/17/13 Dan Christensen
10/17/13 Brian Q. Hutchings
10/17/13 Brian Q. Hutchings
10/18/13 Robin Chapman
10/18/13 Dan Christensen
10/23/13 Shmuel (Seymour J.) Metz
10/25/13 Bart Goddard
10/29/13 Dan Christensen
10/30/13 Bart Goddard
10/30/13 Dan Christensen
10/30/13 Bart Goddard
10/30/13 Dan Christensen
10/30/13 Bart Goddard
10/30/13 Robin Chapman
10/30/13 Bart Goddard
10/30/13 Peter Percival
10/30/13 Richard Tobin
10/30/13 fom
10/31/13 David Bernier
10/31/13 David Bernier
10/30/13 Dan Christensen
10/30/13 Bart Goddard
10/30/13 Dan Christensen
10/31/13 Bart Goddard
10/31/13 Dan Christensen
10/31/13 Bart Goddard
10/31/13 Dan Christensen
10/31/13 Bart Goddard
10/30/13 Peter Percival
10/30/13 JT
10/30/13 Dan Christensen
10/30/13 Peter Percival
10/30/13 Dan Christensen
10/30/13 Brian Q. Hutchings
10/30/13 Brian Q. Hutchings
10/30/13 JT
10/30/13 Peter Percival
10/30/13 JT
10/30/13 JT
10/30/13 Brian Q. Hutchings
10/18/13 Robin Chapman
10/18/13 Dan Christensen
10/18/13 fom
10/18/13 Dan Christensen
10/18/13 fom
10/18/13 Dan Christensen
10/18/13 Peter Percival
10/18/13 Dan Christensen
10/20/13 Dan Christensen
10/20/13 Bart Goddard
10/20/13 Dan Christensen
10/20/13 Bart Goddard
10/20/13 Dan Christensen
10/20/13 Bart Goddard
10/20/13 Michael F. Stemper
10/20/13 Bart Goddard
10/20/13 Dan Christensen
10/23/13 Brian Q. Hutchings
10/20/13 Dan Christensen
10/20/13 Bart Goddard
10/20/13 Dan Christensen
10/20/13 Bart Goddard
10/20/13 Dan Christensen
10/21/13 Bart Goddard
10/21/13 Dan Christensen
10/21/13 Peter Percival
10/21/13 Bart Goddard
10/21/13 Dan Christensen
10/21/13 Bart Goddard
10/21/13 Peter Percival
10/21/13 fom
10/21/13 Bart Goddard
10/21/13 JT
10/21/13 Dan Christensen
10/21/13 JT
10/21/13 Dan Christensen
10/20/13 Peter Percival
10/20/13 Dan Christensen
10/23/13 Dan Christensen
10/23/13 fom
11/1/13 Dan Christensen
11/1/13 Bart Goddard
11/1/13 Dan Christensen
11/1/13 Bart Goddard
11/1/13 Dan Christensen
11/1/13 fom
11/1/13 Dan Christensen
11/1/13 Bart Goddard
11/1/13 Dan Christensen
11/1/13 Bart Goddard
11/1/13 Dan Christensen
11/1/13 Bart Goddard
11/1/13 Dan Christensen
11/1/13 Bart Goddard
11/1/13 Brian Q. Hutchings
11/1/13 Dan Christensen
11/1/13 Brian Q. Hutchings
11/2/13 Robin Chapman
11/1/13 Dan Christensen
11/1/13 Bart Goddard
11/1/13 ross.finlayson@gmail.com
11/3/13 ross.finlayson@gmail.com
11/3/13 Brian Q. Hutchings
11/1/13 Dan Christensen
11/2/13 Bart Goddard
11/2/13 Dan Christensen
11/2/13 Bart Goddard
11/12/13 Bart Goddard
11/12/13 Bart Goddard
11/12/13 Bart Goddard
11/12/13 Bart Goddard
11/13/13 Bart Goddard
11/13/13 Bart Goddard
11/2/13 Virgil
11/2/13 Dan Christensen
11/2/13 Bart Goddard
11/2/13 Paul
11/3/13 Bart Goddard
11/2/13 Dan Christensen
11/2/13 Dan Christensen
11/2/13 Ki Song
11/2/13 Virgil
11/2/13 Michael F. Stemper
11/2/13 Virgil
11/3/13 Michael F. Stemper
11/3/13 Robin Chapman
11/3/13 fom
11/3/13 Jussi Piitulainen
11/3/13 fom
11/4/13 Jussi Piitulainen
11/3/13 JT
11/3/13 JT
11/12/13 Dan Christensen
11/13/13 Dan Christensen

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