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 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. >
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.

