On 30 Jan., 00:16, William Hughes <wpihug...@gmail.com> wrote: > On Jan 29, 10:11 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 29 Jan., 21:28, William Hughes <wpihug...@gmail.com> wrote: > > <snip> > > > > It does, however, imply that d in not one > > > of the lines of the list L > > > For that sake you must check all lines. Can you check what is not > > existing? > > So now your claim is > > We can know > > There does not exist a natural number n > such that d is equal to the nth line > of L > > but we cannot know > > d is not one of the lines of L
You are trying hard to misunderstand!
For a potentially infinite set L we can know: d is not in line number n. But a potentially infinite set is not actually infinite. And without actually infinite sets, you have no uncountability. For instance, all finite subsets of |N make up a countable power set. Only the actually infinite subsets make up an uncountable power set. But "actually infinite" means a number larger than every n. It is easy to understand that this number can never be exhausted by finite numbers n. Therefore we cannot prove that d is missing in the actually infinity list from "for every n in |N, there is no line n that contains d".
We will never know something for all lines as we will never be able to know all lines, since beyond every line n there are infinitely many following.