On 25 Jan., 19:52, "Jesse F. Hughes" <je...@phiwumbda.org> wrote: > WM <mueck...@rz.fh-augsburg.de> writes: > >> Is t_i(i) also defined for every i in N? > > > Yes, of course, with absolute certainty. > > >> Assuming you will say yes, then I must ask: > > >> Is d(i) therefore defined for every i in N? > > > Yes, of course, with absolute certainty. > > > And nothing of that takes us out of the domain of all terminating > > decimals, because ; > > >> > In ZF every n in N is finite. > > > and with it every FISON. > > Well, let's not get ahead of ourselves just yet. > > You agree that, for every i in N, d(i) is defined. > > I suppose you also agree that, for every i in N, d(i) != 0 and > d(i) != 9, right? > > Okay, so d(i) is defined for every i in N, and d(i) is non-zero and > not nine. > > Clearly, d is a non-terminating decimal.
The set of all FISONs is not terminating. Is there a non-terminating FISON? No.
Try to understand that and evaluate the consequences. It is useless to go on unless you got it that we work in the domain of terminating decimals. Nevertheless there is not the least restriction of the number of digits.