In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 28 Jan., 23:46, Virgil <vir...@ligriv.com> wrote: > > In article > > <a635f398-4127-40df-a437-23364ce53...@r14g2000yqe.googlegroups.com>, > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 27 Jan., 23:27, "Jesse F. Hughes" <je...@phiwumbda.org> wrote: > > > > > > > Of course. But why should we agree on a special k? Every natural > > > > > number will do. So we only have to know that k is one of those natural > > > > > numbers that belong to FISONs. As long as we work in FISONs we cannot > > > > > have a non-terminating decimal. > > > > > > I honestly have no idea what you're trying to say here. Why not > > > > simply prove that there is such a k and f? > > > > > Because every natural number is finite. Why fix one of them? > > > > You claim there must be such a natural, so you are obligated to prove it. > > I claim that every natural belongs to a FISON. And I can prove it. No one has denied it as far as I know.
IN the von Nuenann naturals one can go even farther as=]and say that every natural IS a FISON, so the infinite set of naturals and the nifinite set of FISONs in identical.
> Give me a natural, and I tell you one and, on request, several FISONs > where it belongs to. Therefore, as long as you define digits by > natural indexes, there is no chance to leave the domain of terminating > digits.
On can as soon as one recognizes that one can have a set with the properties of a set of all naturals (an inductive set), which, in ZF for example, must occur before one can even define what a natural is.
I have yet to see an axioim suystem for any set theory that is of any value to mathematics in general that does not start by validating the existence of an inductive infinite set. --