At 06:31 PM 5/17/01 -0300, you wrote:
>Robert Shaw wrote:
> >
> >> For example, if you just have x -> x! and x -> sqrt(x),
> >> can you get as close as you want to any number? This is
> >> an extreme case, because you can't ()! non-integer numbers
> >> [calling x! = Gamma(x + 1) is cheating!!!]
> >
> > Well, if you start with 0 or 1, you can only reach 0 or 1
> > respectively. Start with 2 and you can a single sequence of
> > numbers between 1 and 2
> >
>Of course you have to start non-trivially :-)
>
> > If you start with 3 you can only generate a countable infinity
> > of numbers. Take the factorial n times, then the square root
> > m times. Because of the sparsity of the factorials I'd suspect
> > this set isn't dense.
> >
>My intuition says that this set *is* dense - of course, it's
>hard to prove stuff with numbers in the range of 3!!!!!!!
Is that ((((((3!)!)!)!)!)!)! or (((3!)!!)!!)!! or (((3!!)!!)!!)! or
(((((3!!)!)!)!)!)! or . . . ?
;-)
-- Ronn! :)
