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. > > 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.
But according to your implicitely made assumption it should be true for all n. The lines of the list, if written into one single line, L, yield: The potentially infinite sequences L and d are equal. 123... = L 1 12 123 ...
> > Your first claim is that there is a line l such that > d and l are equal as potentially infinite sequences.
For every n this is true. > > Your other claim is that there is no line > l such that d and l are equal as potentially infinite > sequences.
For every FIS of d there is a line. You cannot find a line for all FIS (because all FIS do not exist). > > You are asserting a contradiction.
It is a contradiction only when confusing every and all.