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

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Michael F. Stemper

Posts: 108
Registered: 9/5/13
Re: The ambiguity of 0^0 on N
Posted: Sep 20, 2013 5:17 PM
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On 09/20/2013 02:42 PM, Virgil wrote:

> I can see that
> f(x,y) = x^y is continuous on domain {(x,y): x > 0 and y > 0}
> and can even be extended continuously to both
> {(0,y): y > 0} and
> {(x,0): x > 0}
> but there is no way to extend that function CONTINUOUSLY to
> {(x,y)| x > 0 and y > 0} to {(x,y)| x >= 0 and y >= 0}.
>
> This suggest that for real functions like
> f(x,y) = x^y on {(x,y): x > 0 and y > 0}
> there is no universally acceptable limit value at f(0,0).


That's true for the reals, yes. I believe that the topic under
discussion is "N", the naturals.

--
Michael F. Stemper
Life's too important to take seriously.


Date Subject Author
9/18/13
Read The ambiguity of 0^0 on N
Dan Christensen
9/18/13
Read Re: The ambiguity of 0^0 on N
Peter Percival
9/18/13
Read Re: The ambiguity of 0^0 on N
Dan Christensen
9/18/13
Read Re: The ambiguity of 0^0 on N
Peter Percival
9/18/13
Read Re: The ambiguity of 0^0 on N
Virgil
9/18/13
Read Re: The ambiguity of 0^0 on N
Dan Christensen
9/18/13
Read Re: The ambiguity of 0^0 on N
Rotwang
9/18/13
Read Re: The ambiguity of 0^0 on N
Rock Brentwood
9/18/13
Read Re: The ambiguity of 0^0 on N
Rotwang
9/19/13
Read Re: The ambiguity of 0^0 on N
Dan Christensen
9/19/13
Read Re: The ambiguity of 0^0 on N
Peter Percival
9/19/13
Read Re: The ambiguity of 0^0 on N
Dan Christensen
9/19/13
Read Re: The ambiguity of 0^0 on N
Peter Percival
9/19/13
Read Re: The ambiguity of 0^0 on N
Dan Christensen
9/19/13
Read Re: The ambiguity of 0^0 on N
fom
9/19/13
Read Re: The ambiguity of 0^0 on N
Dan Christensen
9/19/13
Read Re: The ambiguity of 0^0 on N
fom
9/19/13
Read Re: The ambiguity of 0^0 on N
Dan Christensen
9/20/13
Read Re: The ambiguity of 0^0 on N
fom
9/19/13
Read Re: The ambiguity of 0^0 on N
Virgil
9/19/13
Read Re: The ambiguity of 0^0 on N
Virgil
9/19/13
Read Re: The ambiguity of 0^0 on N
Rotwang
9/18/13
Read Re: The ambiguity of 0^0 on N
Virgil
9/18/13
Read Re: The ambiguity of 0^0 on N
fom
9/18/13
Read Re: The ambiguity of 0^0 on N
Rotwang
9/28/13
Read Re: The ambiguity of 0^0 on N
Shmuel (Seymour J.) Metz
9/29/13
Read Re: The ambiguity of 0^0 on N
Marshall
9/19/13
Read Re: The ambiguity of 0^0 on N
Dan Christensen
9/19/13
Read Re: The ambiguity of 0^0 on N
Dan Christensen
9/19/13
Read Re: The ambiguity of 0^0 on N
Peter Percival
9/19/13
Read Re: The ambiguity of 0^0 on N
Dan Christensen
9/19/13
Read Re: The ambiguity of 0^0 on N
Michael F. Stemper
9/19/13
Read Re: The ambiguity of 0^0 on N
Dan Christensen
9/19/13
Read Re: The ambiguity of 0^0 on N
Peter Percival
9/19/13
Read Re: The ambiguity of 0^0 on N
Dan Christensen
9/19/13
Read Re: The ambiguity of 0^0 on N
fom
9/19/13
Read Re: The ambiguity of 0^0 on N
Dan Christensen
9/19/13
Read Re: The ambiguity of 0^0 on N
fom
9/19/13
Read Re: The ambiguity of 0^0 on N
Dan Christensen
9/19/13
Read Re: The ambiguity of 0^0 on N
fom
9/19/13
Read Re: The ambiguity of 0^0 on N
Dan Christensen
9/20/13
Read Re: The ambiguity of 0^0 on N
fom
9/20/13
Read Re: The ambiguity of 0^0 on N
Dan Christensen
9/20/13
Read Re: The ambiguity of 0^0 on N
fom
9/19/13
Read Re: The ambiguity of 0^0 on N
fom
9/19/13
Read Re: The ambiguity of 0^0 on N
fom
9/19/13
Read Re: The ambiguity of 0^0 on N
Dan Christensen
9/19/13
Read Re: The ambiguity of 0^0 on N
fom
9/19/13
Read Re: The ambiguity of 0^0 on N
Peter Percival
9/19/13
Read Re: The ambiguity of 0^0 on N
Dan Christensen
9/19/13
Read Re: The ambiguity of 0^0 on N
fom
9/19/13
Read Re: The ambiguity of 0^0 on N
Rotwang
9/19/13
Read Re: The ambiguity of 0^0 on N
Dan Christensen
9/19/13
Read Re: The ambiguity of 0^0 on N
Helmut Richter
9/19/13
Read Re: The ambiguity of 0^0 on N
Dan Christensen
9/19/13
Read Re: The ambiguity of 0^0 on N
Peter Percival
9/19/13
Read Re: The ambiguity of 0^0 on N
Dan Christensen
9/19/13
Read Re: The ambiguity of 0^0 on N
Peter Percival
9/19/13
Read Re: The ambiguity of 0^0 on N
Dan Christensen
9/19/13
Read Re: The ambiguity of 0^0 on N
fom
9/19/13
Read Re: The ambiguity of 0^0 on N
fom
9/19/13
Read Re: The ambiguity of 0^0 on N
JT
9/19/13
Read Re: The ambiguity of 0^0 on N
JT
9/19/13
Read Re: The ambiguity of 0^0 on N
Michael F. Stemper
9/19/13
Read Re: The ambiguity of 0^0 on N
JT
9/19/13
Read Re: The ambiguity of 0^0 on N
JT
9/19/13
Read Re: The ambiguity of 0^0 on N
JT
9/19/13
Read Re: The ambiguity of 0^0 on N
Helmut Richter
9/28/13
Read Re: The ambiguity of 0^0 on N
Shmuel (Seymour J.) Metz
9/19/13
Read Re: The ambiguity of 0^0 on N
fom
9/19/13
Read Re: The ambiguity of 0^0 on N
Peter Percival
9/19/13
Read Re: The ambiguity of 0^0 on N
Dan Christensen
9/19/13
Read Re: The ambiguity of 0^0 on N
Peter Percival
9/19/13
Read Re: The ambiguity of 0^0 on N
Karl-Olav Nyberg
9/19/13
Read Re: The ambiguity of 0^0 on N
fom
9/19/13
Read Re: The ambiguity of 0^0 on N
fom
9/19/13
Read Re: The ambiguity of 0^0 on N
Rotwang
9/19/13
Read Re: The ambiguity of 0^0 on N
Dan Christensen
9/19/13
Read Re: The ambiguity of 0^0 on N
fom
9/25/13
Read Re: The ambiguity of 0^0 on N
Rotwang
9/26/13
Read Re: The ambiguity of 0^0 on N
Dan Christensen
9/27/13
Read Re: The ambiguity of 0^0 on N
Brian Q. Hutchings
9/19/13
Read Re: The ambiguity of 0^0 on N
fom
9/18/13
Read Re: The ambiguity of 0^0 on N
Rock Brentwood
9/19/13
Read Re: The ambiguity of 0^0 on N
Dan Christensen
9/19/13
Read Re: The ambiguity of 0^0 on N
Dan Christensen
9/19/13
Read Re: The ambiguity of 0^0 on N
Rotwang
9/19/13
Read Re: The ambiguity of 0^0 on N
Dan Christensen
9/19/13
Read Re: The ambiguity of 0^0 on N
fom
9/20/13
Read Re: The ambiguity of 0^0 on N
Dan Christensen
9/20/13
Read Re: The ambiguity of 0^0 on N
fom
9/20/13
Read Re: The ambiguity of 0^0 on N
Dan Christensen
9/20/13
Read Re: The ambiguity of 0^0 on N
Peter Percival
9/20/13
Read Re: The ambiguity of 0^0 on N
Peter Percival
9/20/13
Read Re: The ambiguity of 0^0 on N
Dan Christensen
9/20/13
Read Re: The ambiguity of 0^0 on N
Virgil
9/20/13
Read Re: The ambiguity of 0^0 on N
Peter Percival
9/20/13
Read Re: The ambiguity of 0^0 on N
fom
9/20/13
Read Re: The ambiguity of 0^0 on N
Michael F. Stemper
9/20/13
Read Re: The ambiguity of 0^0 on N
LudovicoVan
9/21/13
Read Re: The ambiguity of 0^0 on N
Michael F. Stemper
9/21/13
Read Re: The ambiguity of 0^0 on N
LudovicoVan
9/21/13
Read Re: The ambiguity of 0^0 on N
Richard Tobin
9/20/13
Read Re: The ambiguity of 0^0 on N
Peter Percival
9/20/13
Read Re: The ambiguity of 0^0 on N
Peter Percival
9/21/13
Read Re: The ambiguity of 0^0 on N
Dan Christensen
9/19/13
Read Re: The ambiguity of 0^0 on N
Karl-Olav Nyberg

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