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Topic: The ambiguity of 0^0 on N
Replies: 106   Last Post: Sep 29, 2013 10:06 AM

 Messages: [ Previous | Next ]
 Dan Christensen Posts: 8,161 Registered: 7/9/08
Re: The ambiguity of 0^0 on N
Posted: Sep 19, 2013 11:28 PM

On Thursday, September 19, 2013 11:24:08 PM UTC-4, fom wrote:
> On 9/19/2013 10:10 PM, Dan Christensen wrote:
>

> > On Thursday, September 19, 2013 10:42:09 PM UTC-4, fom wrote:
>
> >> On 9/19/2013 9:24 PM, Dan Christensen wrote:
>
> >>
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> >>> On Thursday, September 19, 2013 7:36:57 PM UTC-4, fom wrote:
>
> >>
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> >>>
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> >>
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> >>> Then it should be easy to prove 0^0=1 using only natural number arithmetic. How about it?
>
> >>
>
> >>>
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> >>
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> >>
>
> >>
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> >> One can "prove" nothing to another
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> >>
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> >> when the latter refuses to provide
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> >>
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> >> the requested justifications upon
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> >>
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> >> which the claim of the latter is
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> >>
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> >> based.
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> >>
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> >>
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> >>
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> >> Chicken scratch is not honest toil.
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> >>
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> >>
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> >>
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> >> The recursive definition of operations
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> >>
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> >> follows from Skolem's work.
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> >>
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> >>
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> >>
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> >> The class-based definition of 0
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> >>
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> >> follows from Frege's work.
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> >>
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> >>
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> >>
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> >> You have no definitions.
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> >>
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> >
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> > Choose any definitions or axioms you like. I'm not fussy. Just don't assume from the start that 0^0=1, e.g that x^0=1 for all natural numbers x.
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> >
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> Apparently you are "fussy".
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>
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> On your account, one must conclude that 0 is
>
> not a natural number.
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>
>
> You have objected to that conclusion.

This is getting creepy.

Dan

Date Subject Author
9/18/13 Dan Christensen
9/18/13 Peter Percival
9/18/13 Dan Christensen
9/18/13 Peter Percival
9/18/13 Virgil
9/18/13 Dan Christensen
9/18/13 Rotwang
9/18/13 Rock Brentwood
9/18/13 Rotwang
9/19/13 Dan Christensen
9/19/13 Peter Percival
9/19/13 Dan Christensen
9/19/13 Peter Percival
9/19/13 Dan Christensen
9/19/13 fom
9/19/13 Dan Christensen
9/19/13 fom
9/19/13 Dan Christensen
9/20/13 fom
9/19/13 Virgil
9/19/13 Virgil
9/19/13 Rotwang
9/18/13 Virgil
9/18/13 fom
9/18/13 Rotwang
9/28/13 Shmuel (Seymour J.) Metz
9/29/13 Marshall
9/19/13 Dan Christensen
9/19/13 Dan Christensen
9/19/13 Peter Percival
9/19/13 Dan Christensen
9/19/13 Michael F. Stemper
9/19/13 Dan Christensen
9/19/13 Peter Percival
9/19/13 Dan Christensen
9/19/13 fom
9/19/13 Dan Christensen
9/19/13 fom
9/19/13 Dan Christensen
9/19/13 fom
9/19/13 Dan Christensen
9/20/13 fom
9/20/13 Dan Christensen
9/20/13 fom
9/19/13 fom
9/19/13 fom
9/19/13 Dan Christensen
9/19/13 fom
9/19/13 Peter Percival
9/19/13 Dan Christensen
9/19/13 fom
9/19/13 Rotwang
9/19/13 Dan Christensen
9/19/13 Helmut Richter
9/19/13 Dan Christensen
9/19/13 Peter Percival
9/19/13 Dan Christensen
9/19/13 Peter Percival
9/19/13 Dan Christensen
9/19/13 fom
9/19/13 fom
9/19/13 JT
9/19/13 JT
9/19/13 Michael F. Stemper
9/19/13 JT
9/19/13 JT
9/19/13 JT
9/19/13 Helmut Richter
9/28/13 Shmuel (Seymour J.) Metz
9/19/13 fom
9/19/13 Peter Percival
9/19/13 Dan Christensen
9/19/13 Peter Percival
9/19/13 Karl-Olav Nyberg
9/19/13 fom
9/19/13 fom
9/19/13 Rotwang
9/19/13 Dan Christensen
9/19/13 fom
9/25/13 Rotwang
9/26/13 Dan Christensen
9/27/13 Brian Q. Hutchings
9/19/13 fom
9/18/13 Rock Brentwood
9/19/13 Dan Christensen
9/19/13 Dan Christensen
9/19/13 Rotwang
9/19/13 Dan Christensen
9/19/13 fom
9/20/13 Dan Christensen
9/20/13 fom
9/20/13 Dan Christensen
9/20/13 Peter Percival
9/20/13 Peter Percival
9/20/13 Dan Christensen
9/20/13 Virgil
9/20/13 Peter Percival
9/20/13 fom
9/20/13 Michael F. Stemper
9/20/13 LudovicoVan
9/21/13 Michael F. Stemper
9/21/13 LudovicoVan
9/21/13 Richard Tobin
9/20/13 Peter Percival
9/20/13 Peter Percival
9/21/13 Dan Christensen
9/19/13 Karl-Olav Nyberg