On 3/22/2013 1:21 PM, WM wrote: > 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.
So now you have two complete infinities.
The infinity of objects comprising |N.
The infinity of finite lines whose sequentially ordered elements are from |N.
Which one is *the* infinity?
Or, if there are many, how do they stand in relation to one another?