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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 ]
 fom Posts: 1,968 Registered: 12/4/12
Re: The ambiguity of 0^0 on N
Posted: Sep 20, 2013 12:50 AM

On 9/19/2013 10:25 PM, Dan Christensen wrote:
> On Thursday, September 19, 2013 11:07:23 PM UTC-4, fom wrote:
>> On 9/19/2013 9:19 PM, Dan Christensen wrote:
>>

>>> On Thursday, September 19, 2013 7:36:04 PM UTC-4, fom wrote:
>>
>>>> On 9/19/2013 1:26 PM, Dan Christensen wrote:
>>
>>>>
>>
>>>>>>
>>
>>>>
>>
>>>>>> Why apart from? Why are you leaving it out?
>>
>>>>
>>
>>>>>
>>
>>>>
>>
>>>>> We can't divide by 0. Unless you want to assign a value to 0/0 as well.
>>
>>>>
>>
>>>>>
>>
>>>>
>>
>>>>
>>
>>>>
>>
>>>> And, what about division is "number theoretic"?
>>
>>>>
>>
>>>
>>
>>> As you can see in my proof, I am actually using the right-cancelability property of natural number multiplication:
>>
>>>
>>
>>> x*y = z*y & y=/=0 => x=z
>>
>>>
>>
>>> "Dividing" both sides by y, to cancel off the factor of y, OK?
>>
>>>
>>
>>
>>
>> Not really.
>>
>>
>>
>> Cancellability is a feature of group operations or, more
>>
>> generally magmas.
>>

>
> It is also a feature (or theorem) of natural number arithmetic, e.g. x*2 = y*2 => x=y
>
>

>>
>>
>> http://en.wikipedia.org/wiki/Cancellation_property
>>
>>
>>
>> So, again, you are invoking a property that is not strictly
>>
>> "number theoretic".
>>

>
> I disagree.
>

>>
>>
>> The axiom of Peano's number theory that addresses equality
>>
>> between natural numbers (other than transitivity, symmetry,
>>
>> reflexiveness, and closure) is given by
>>
>>
>>
>> x=y <-> ( x+1 ) = ( y+1 )
>>
>>
>>
>> Wikipedia lists this as a conditional,
>>
>>
>>
>> ( x+1 ) = ( y+1 ) -> x=y
>>
>>
>>
>> It is axiom 8,
>>
>>
>>
>> http://en.wikipedia.org/wiki/Peano_axioms#The_axioms
>>
>>
>>
>> Now, since you continue to invoke "number theory", perhaps
>>
>> you could provide the formal theory which you seem to
>>
>> think that everyone knows and loves. It is clearly not
>>
>> Peano arithmetic.

>
> If you won't accept x*2 = y*2 => x=y, I afraid there is not much point in continuing this discussion.
>

Once again, familiar discourse common to one
engaging in lies and evasions.

There has never been a point to this discussion
because you have so badly mangled the mathematics
involved with the question.

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