On Tue, 2004-12-07 at 20:52, Décio Luiz Gazzoni Filho wrote:

> On Tuesday 07 December 2004 18:20, you wrote:

> > --- In primenumbers@yahoogroups.com, Paul Leyland <pcl@w...> wrote:

> > > The set of prime numbers is all numbers that are not composite, by

> > > definition.

> >

> > Whoa there! That leaves a mighty narrow definition of "numbers".

> > Units? Rationals?

>

> Let's not be pedantic here. From the context it's pretty clear that we're

> talking about integers, so the only gap in Paul's declaration relates to

> units. Furthermore, even if his definition was not 100% mathematically

> correct, I think his point was well communicated, and that's what matters

> here -- he's not trying to write a book, but rather point out the flaw in the

> previous poster's definiton.

Thanks Decio.

Two people, including Rick and another by personal email, have told me I

omitted the unit. Nobody told me I omitted zero. I freely admit that I

should have included them. As for rationals, irrationals, algebraics,

transcendentals, gaussian integers, complex numbers, quaternions and all

the rest of the zoo, I think it pretty obvious from context that the

area of discourse was N or Z. Otherwise, I may have been tempted to

point out that 3 is prime but that 2 is (1+i)(1-i) and 5 is (2+i)(2-i)

in the Gaussians.

After that clarification, can someone please tell me why in Z or N that

2, 3 and 5 need singling as special cases?

Paul