
Re: The ambiguity of 0^0 on N
Posted:
Sep 19, 2013 10:19 PM


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?
Dan Download my DC Proof 2.0 software at http://www.dcproof.com
> > > What axiom of number theory ensures closure under division? > > > > You cannot distinguish an additive group from a multiplicative > > group except in relation to a ring structure. Otherwise > > the difference is mere purport. > > > > Relative to ring theory, one may speak of division as some > > essential numeric operation. In fact, that is what characterizes > > "division rings". > > > > http://en.wikipedia.org/wiki/Division_ring > > > > So, you reject "set theoretic" considerations, but you invoke > > "ring theoretic" considerations (or, since I am not going to > > research obscure notions of "division", some other > > "???theoretic" considerations which are not "numbertheoretic" > > considerations). > > > > You cannot invoke "number theory" as a restriction and then > > use arguments outside of "number theory" in your defense. > > > > In "number theory" you cannot divide by 2 unless you wish > > to assign natural numbers to > > > > 1/2, 3/2, 5/2, ..., (2n+1)/2, ... > > > > n in {0, 1, 2, ...} > > > > > > The standard definitions based upon the established operations > > of the language of the theory suffice to prove the fundamental > > theorem. If you wish to begin from the exponentiation associated > > with the fundamental theorem then you need to present a different > > theory for consideration as "number theory".

