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Topic: Leaving 0^0 undefined -- A number-theoretic rationale
Replies: 48   Last Post: Sep 15, 2013 1:06 PM

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Dan Christensen

Posts: 8,142
Registered: 7/9/08
Re: Leaving 0^0 undefined -- A number-theoretic rationale
Posted: Sep 12, 2013 12:26 AM
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On Wednesday, September 11, 2013 5:09:52 PM UTC-4, Peter Percival wrote:
> Dan Christensen wrote:
>
>
>

> >
>
> > Show me a contradiction that arises from 0^0 = 0.
>
>
>
> The product of the empty set is 1, hence 0^0 = 1. That contradicts 0^0
>
> = 0. Therefore 0^0 doesn't = 0.
>


You are talking about some other set-theoretic notion of exponentiation, not the usual arithmetic operator that we are discussing here.

More convincing would be obtaining a contradiction by assuming only 0^0=0 along with the usual rules of natural-number arithmetic, including the usual Laws of Exponents.

Dan
Download my DC Proof 2.0 software at http://www.dcproof.com


Date Subject Author
9/11/13
Read Leaving 0^0 undefined -- A number-theoretic rationale
Dan Christensen
9/11/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Peter Percival
9/11/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
FredJeffries@gmail.com
9/11/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Dan Christensen
9/11/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Peter Percival
9/11/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Brian Q. Hutchings
9/11/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Dan Christensen
9/12/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Peter Percival
9/12/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Dan Christensen
9/11/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Dan Christensen
9/12/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Peter Percival
9/12/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Dan Christensen
9/12/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Michael F. Stemper
9/12/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Peter Percival
9/12/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Dan Christensen
9/12/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Peter Percival
9/12/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Shmuel (Seymour J.) Metz
9/12/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Peter Percival
9/12/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Shmuel (Seymour J.) Metz
9/12/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Robin Chapman
9/12/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Peter Percival
9/12/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Peter Percival
9/12/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
David C. Ullrich
9/12/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Dan Christensen
9/12/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Peter Percival
9/12/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Dan Christensen
9/13/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
David C. Ullrich
9/13/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Peter Percival
9/13/13
Read how about an examplar
Brian Q. Hutchings
9/12/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
LudovicoVan
9/12/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Peter Percival
9/13/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Michael F. Stemper
9/13/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
LudovicoVan
9/12/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
FredJeffries@gmail.com
9/12/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
LudovicoVan
9/13/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
David C. Ullrich
9/13/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Michael F. Stemper
9/12/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Shmuel (Seymour J.) Metz
9/13/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Dan Christensen
9/13/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Robin Chapman
9/13/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Peter Percival
9/13/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Dan Christensen
9/13/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Brian Q. Hutchings
9/14/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Robert Lewis
9/14/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Brian Q. Hutchings
9/14/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Peter Percival
9/15/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Brian Q. Hutchings
9/14/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
fom
9/15/13
Read Re: Leaving 0^0 undefined -- A number-theoretic rationale
Michael F. Stemper

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