On 22 Mrz., 16:31, William Hughes <wpihug...@gmail.com> wrote: > On Mar 22, 10:05 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > If you want to > > > remove all of the lines you have to remove the set of all > > > lines that are indexed by a natural number. > > > But I don't want to remove a set. > > We have the set of lines. You do not want to leave > any of the lines.
I do not want this or that. I simply prove that for every line l_n the following property is true: Line l_n and all its predecessors do not in any way influence (neither decrease nor increase) the union of all lines, namely |N.
This is certainly a proof that does not force us to "remove a set". But we can look at the set of lines that have this property. The result is the complete set of all lines.
And this mathematical result cannot be violated or re-interpreted. IF actual infinity is true, THEN the above result is true too.
Of course you can say that it is not a contradiction, but only counter- intuitive. But you cannot change the result of my proof. Regards, WM
> There is no way > of doing this that is not equivalent to > removing the set.
So you meanwhile are convinced that induction concerns whole actually infinite sets? Thsi is new.