In article <47d84a88-950f-4091-8dcb-13cdaa3b2e62@z4g2000vbz.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 13 Feb., 09:48, Virgil <vir...@ligriv.com> wrote: > > In article > > <1b2bb717-425f-488d-b50c-e442f20af...@fe28g2000vbb.googlegroups.com>, > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 12 Feb., 20:40, William Hughes <wpihug...@gmail.com> wrote: > > > > > What do you understand by being equal "as potentially infinite > > > > > sequences"? > > > > > > two potentially infinite sequences x and y are > > > > equal iff every FIS of x is a FIS of y and > > > > every FIS of y is a FIS of x. > > > > > Every means: up to every natural number. > > > > Which includes being up to all natural numbers. > > No. After all there is nothing after all natural numbers.
No on implied there were. But if not all, name an exception! > > > > > > > > > > You can use induction to show that two potentially > > > > infinite sequences are equal (you only need > > > > "every" not "all"). > > > > > Up to every n there is a line l identical to d. > > > > Only in Wolkenmuekenheim. > > For which n is this line lacking?
The n's for which the nth line of the list is not a FIS of d depends on the list and the d, so
Show me your list and I will show you a 'd' such that
NO line of the list is a FIS of 'd'. > > > > Since for every line of length n, d is of length at least n+1, at least > > everywhere else besides Wolkenmuekenheim, WMs claim does not hold true > > outside it. > > For every line of lenght n there is a line of length n^n^n, so d of > legth n+1 has no problems with accomodation. > > > > And inside Wolkenmuekenheim all lines are finite. > > Do you know of an infinite line? A line inexed by omega, for instance? > > > > > > > > > For every FIS of d there is a line. You cannot find a line for all FIS > > > (because all FIS do not exist). > > > > But for each finite line l,there is FIS of d longer than l. > > Again for each FIS of d there is a longer l.
But not any l longer than d, or even as long, if each l is finite.
The point is that for any listing of binary sequences, finite or infinite, one can define a diagonal which is not listed.
And no matter how loudly WM screams that it is not so, it remains so. --
