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. > > > > > > 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? > > 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.