In article <email@example.com>, WM <firstname.lastname@example.org> 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. > > > > 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.
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.
And inside Wolkenmuekenheim all lines are finite.
> > 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. > > > > You are asserting a contradiction. > > It is a contradiction only when confusing every and all.
The only way that some statement about a natural can fail to be true for all naturals is when there exists some natural for which it is false. --