On 10 Apr., 22:53, William Hughes <wpihug...@gmail.com> wrote:
> > > > the sum of the > > > > FISON is S(n) = n(n+1)/2. So we construct a bijection > > > > f(n) : n --> S(n). > > > > Is this bijection finite or infinite? > > > > The bijection is an infinite set with finite elements. > > > And why should we not remove all these infinitely many finite > > elements, > > We can remove the collection of all these elements. > What we cannot do is remove > the collection of all finite lines without changing > the union of the remaining lines.
That depends on the question whether the union of all finite lines is an infinite line. > > Thus, the fact that there is no line (along with > all its predecessors) that cannot be removed > is not a contradiction.
It is not a contradiction with mathematics. So far I agree. But it would be a contradiction in case someone (and there are many here around) maintained ~P for some d_n if there is a proof of P for all FISs of d: For all n: d_1, d_2, ..., d_n have the property P.
Matheology requires: The sequence of all d_n constitutes the real number. The sequence of all d_1, ..., d_n does not constitute a real number. This shows a contradiction in matheology.
But it will last some while until matheologians, who are too inflexible to learn that their pet has died, will have died out. After all this is pet is the queen of their hearts.