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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 ]
 JT Posts: 1,448 Registered: 4/7/12
Re: The ambiguity of 0^0 on N
Posted: Sep 19, 2013 9:44 PM

Den torsdagen den 19:e september 2013 kl. 22:45:47 UTC+2 skrev Dan Christensen:
> On Thursday, September 19, 2013 4:20:17 PM UTC-4, Peter Percival wrote:
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> > Dan Christensen wrote:
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> > > On Thursday, September 19, 2013 11:41:47 AM UTC-4, Helmut Richter wrote:
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> > >> On Thu, 19 Sep 2013, Dan Christensen wrote:
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> > >>> Again, the notion of 0^0 being undefined is not some radical notion.
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> > >>> Many standard textbooks make this assumption. It is probably more
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> > >>> mainstream than assuming 0^0=1. I'm sure that a poll of all math
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> > >>> instructors would confirm this.
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> > >> At least it makes the definition of power series easier. Would you like to
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> > >> see
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> > >> e^x = Sum(i=0,...) x^i/i! for x!= 0
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> > >> = 1 for x = 0
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> > > Yeah, it could get ugly, but until we can actually prove that 0^0=1 from first principles, this would be the prudent thing to do.
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> > The first principle is the definition of x^y, but when I prove 0^0 = 1
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> > from the definition in two lines you object. What you seem to object to
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> > is that it is just two lines.
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> So, why don't we just include Goldbach's Conjecture in the axioms of number theory and move on?
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> Dan
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I think all of this boil down to the use of our hindu arabian numbersystem with zeros. And the question is can really squaring of a quantity regardless granularity give a smaller product then the factors. We partition a the single 1 into 100/100. We now have a square of 10^2.
I now pick five elements thus 5/100 and square them thus 25/100.

Oops 0,05^2 is 1/4 not 1/400, i think this is how the ancient geometricians looked at numbers bijective and zeroless.

How we look at numbers depend upon the very early choices we make like representation.

I think i may have done implementations of numbersystem and arithmetic working using these ancient principles, a long time ago in a galaxy far far away.

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