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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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LudovicoVan

Posts: 3,201
From: London
Registered: 2/8/08
Re: The ambiguity of 0^0 on N
Posted: Sep 20, 2013 5:48 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

"Michael F. Stemper" <michael.stemper@gmail.com> wrote in message
news:l1ie0g$rpg$1@dont-email.me...
> 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.


Aren't the naturals a subset of the reals?

Julio




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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