
Re: The ambiguity of 0^0 on N
Posted:
Sep 19, 2013 11:25 PM


On Thursday, September 19, 2013 11:07:23 PM UTC4, fom wrote: > On 9/19/2013 9:19 PM, Dan Christensen wrote: > > > On Thursday, September 19, 2013 7:36:04 PM UTC4, 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 rightcancelability 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.
Dan Download my DC Proof 2.0 software at http://www.dcproof.com

