On 9 Mrz., 16:00, William Hughes <wpihug...@gmail.com> wrote: > So this is WM's explanation. > > When he says > > No findable line of L is coFIS > with d > > and > > g is coFIS with d > > he is not using the same d. > > d like L_m is changable. > > So let us use (d) to indicate the function. > The function (d) is not changable, though > its value may be.
What do you understand by the not changeable function (d)?
================ The function d is the set of all natural numbers n mapped on all FISs d_1, d_2, ..., d_n together with the prescription of how the mapping has to be done? ================
That would be actual infinity again.
"The function (d)" is nothing but that what is written in letters above, included between ============= and ========== where possibly the word "every" has to be inserted whereever the word "all" appears.
Can you understand that? That is the description that is possible in actual infinity. By the way this is similar to the paths of the Binary Tree: Each finite paths can be denoted by strings like 0.0001110010110. Each infinite path cannot be denoted other than by a finite description like "always turn left" or "0.110110110..."
> > Do you agree with the statement > > g is not coFIS with (d)
(d) is *not* an actual infinite sequence like "0.110110110..." is not an actual infinite sequence but a word of 14 letters (that can be interpreted as indicating an actual infinite string - if one believes in actual infinity). In potential infinity the function (d) always - during the lifetime of the universe - has a finite maximum, not always the same though. But there is always a last FIS. And this FIS is coFIS with this FIS. What could be simpler than to state that d, which is nothing but every FIS up to a maximum FIS d_1, ..., d_max is coFIS with this maximum FIS d_1, ..., d_max which is simultaneously the line 1, 2, ..., max?