WikiDiscuss

On 11/28/05, John E Clifford <clifford-j@sbcglobal.net> wrote:
> --- Jorge Llambías <jjllambias@gmail.com> wrote:
> > The point was that the restriction "every bunch
> > breaks down
> > completely into individuals" for the system of
> > bunches is an
> > independent restriction of all the other thesis
> > listed, it doesn't
> > follow from them but must be imposed. There are
> > systems
> > where it need not hold.
>
> Ahah! Yes, I think that that is true, though I
> don't think your remarks prove it.

Well, I guess you would first need to present it as a fomal
thesis before a formal proof that it is not a theorem could
be given.

> > > > The natural numbers greater than one follow
> > the
> > > > same rules
> > > > as bunches, with "+" being the product and
> > "in"
> > > > being "is a divisor of".
> > > > Then the primes are the individuals and
> > "every
> > > > bunch breaks down
> > > > completely into individuals".
>
> Well, it turns out they aren't. The model
> disconfirms a+a=a at least.

Hmm, right. To have that property, take all the powers of a prime

as equivalent, and 2m = 2*3, etc.

For the case with no individuals you can take for example
the open sets on the real line, with union as "+".

mu'o mi'e xorxes