On 7 Apr., 23:25, William Hughes <wpihug...@gmail.com> wrote: > D is the set of all finite lines, so it is not more than > all finite lines. If you remove the collection of all > finite lines then nothing remains.
Consider the lines 0.1 0.11 0.111 ... and so on.
If you have the union 0.111..., then you can remove all finite lines without removin 1/9. > > You have agreed: If you remove any finite > set E from D a non empty set (a different one for every E) > remains. > > You have agreed: If you remove any finite set E from D > what remains contains every natural number.
Of course. > > Note that any line plus its predecessors is a finite set. > So, there is no contradiction in saying that you can > remove any one line (plus its predecessors) but you cannot > remove the collection of all lines
See above. There you can remove the collection of all finite lines without removing the limit since it is not a finite line. This is the same if |N is an actually infinite set.
Do you further consider my three recent questions?