Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Michael F. Stemper

Posts: 108
Registered: 9/5/13
Re: The ambiguity of 0^0 on N
Posted: Sep 21, 2013 12:00 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 09/20/2013 04:48 PM, Julio Di Egidio wrote:
> "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?


Well, they're isomorphic to a subset of the reals, anyway.

However, what metric on N would you use that would give a
singular, well-defined limit of any function at any point?

--
Michael F. Stemper
This post contains greater than 95% post-consumer bytes by weight.


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

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.