In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 10 Mrz., 10:28, William Hughes <wpihug...@gmail.com> wrote: > > On Mar 10, 10:02 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > On 9 Mrz., 23:53, William Hughes <wpihug...@gmail.com> wrote: > > > > We will say x is coFIS to (y) iff > > > > > > i. We have (x) associated to x and > > > > (y) associated to y > > > > > > ii. For every n, (x) and (y) produce the same > > > > finite string. > > > > > "Every given n" is tantamount to "there is a last given n". > > > > I do not talk about "every given n" but about "every n" > > (this means from 1 to n for every n). Note that > > "there is a last n" but it is not a findable natural > > number. > > Better say "a not fixable natural number". > > > > Note that you do not need the x_n to exist to say > > something about them. > > That is true. For instance we can say that a natural number is either > even or odd.
Only existing natural numbers need be either, WM's non-existing naturals can be neither or both. > > > For example, you can say no > > x_n that will ever exist will be equal to 0. > > Yes, that is another example.
Not for the von Neumann naturals. > > > If you say x is coFIS to y you are saying something > > about x_n and y_n that may not exist at this time. > > That is the hardest problem. There are some properties which can be > determined (like the examples above). There are other which cannot. > > But in every case we know that there is a line of the list that is > identical with the FIS of d, both existing or not existing yet. > Identity implis coFISionality. Do you deny this?
But the set of lines and d are not identical at all. d ha no member which is a line and the set f lines has no member which is natural, al the lines are lists/sets of naturals, none is a natural by itself.
Bit in Wolkenmuekenheim there does not appear to be any distinction between a set and one of its members. --