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Topic: Equivalent Definition of Exponentiation on N
Replies: 85   Last Post: Dec 2, 2013 10:07 PM

 Messages: [ Previous | Next ]
 Jussi Piitulainen Posts: 355 Registered: 12/12/04
Re: Equivalent Definition of Exponentiation on N
Posted: Nov 14, 2013 3:42 AM

Peter Percival writes:
> Dan Christensen wrote:
> > On Wednesday, November 13, 2013 5:22:21 PM UTC-5, Bart Goddard wrote:
> >>
> >> You should be able to dope this out, because the exact
> >> same reasoning you're using, could be used to assert,
> >> equally validly, that 2^2 should be left undefined.

> >
> > Wrong again, Barty.

>
> Why? Why not say
>
> ALL(a):ALL(b):ALL(c):[a e n & b e n & c e n =>
> [~a=2 => a^b * a^c => a^(b+c)]]
>
> Above you arbitrarily exclude a=0, why not exclude a=2 instead?

Dan starts from the fact that lots of people have long insisted that
0^0 must not be defined. It's been for no reason or for bogus reasons,
but it's been and still is. Dan's got that right.

Powers like 2^2 don't have such history. I think that's the only
difference.

That's not a formal reason, so why shouldn't 2^2 be undefined? It
could be so why shouldn't it? When convenience is not a reason and
formal simplicity is not a reason, what is?

Date Subject Author
11/13/13 Dan Christensen
11/13/13 William Elliot
11/13/13 Dan Christensen
11/15/13 Shmuel (Seymour J.) Metz
11/13/13 Robin Chapman
11/13/13 Peter Percival
11/13/13 Dan Christensen
11/13/13 Peter Percival
11/13/13 Dan Christensen
11/13/13 Bart Goddard
11/13/13 Dan Christensen
11/13/13 Bart Goddard
11/13/13 Dan Christensen
11/13/13 Bart Goddard
11/13/13 Dan Christensen
11/13/13 Bart Goddard
11/13/13 Dan Christensen
11/13/13 Bart Goddard
11/13/13 Dan Christensen
11/13/13 Bart Goddard
11/13/13 Dan Christensen
11/14/13 Peter Percival
11/14/13 Jussi Piitulainen
11/14/13 Dan Christensen
11/14/13 Peter Percival
11/14/13 Dan Christensen
11/14/13 Bart Goddard
11/16/13 gnasher729
11/14/13 Bart Goddard
11/14/13 Dan Christensen
11/14/13 Peter Percival
11/14/13 Dan Christensen
11/14/13 quasi
11/14/13 Dan Christensen
11/14/13 quasi
11/14/13 Dan Christensen
11/14/13 Brian Q. Hutchings
11/15/13 Dan Christensen
11/15/13 Bart Goddard
11/15/13 Dan Christensen
11/15/13 Bart Goddard
11/15/13 Dan Christensen
11/15/13 Bart Goddard
11/15/13 Dan Christensen
11/15/13 Bart Goddard
11/15/13 Dan Christensen
11/15/13 Bart Goddard
11/16/13 Bart Goddard
11/16/13 Dan Christensen
11/16/13 Bart Goddard
11/16/13 fom
11/15/13 Dan Christensen
11/14/13 Dan Christensen
11/14/13 Peter Percival
11/14/13 Peter Percival
11/14/13 Robin Chapman
11/14/13 Peter Percival
11/15/13 Robin Chapman
11/15/13 Peter Percival
11/17/13 Marshall
11/14/13 Bart Goddard
11/14/13 Dan Christensen
11/14/13 Bart Goddard
11/14/13 fom
11/13/13 David C. Ullrich
11/13/13 Dan Christensen
11/13/13 Peter Percival
11/13/13 Dan Christensen
11/13/13 Peter Percival
11/13/13 Dan Christensen
11/15/13 Shmuel (Seymour J.) Metz
11/15/13 Jussi Piitulainen
11/25/13 Shmuel (Seymour J.) Metz
11/26/13 Jussi Piitulainen
11/16/13 gnasher729
11/17/13 Dan Christensen
11/17/13 Peter Percival
11/17/13 Dan Christensen
11/17/13 Peter Percival
11/17/13 Dan Christensen
11/19/13 Dan Christensen
11/19/13 LudovicoVan
11/19/13 Dan Christensen
11/29/13 Dan Christensen
12/2/13 Brian Q. Hutchings