```Date: Mar 24, 2013 6:56 AM
Author: trj
Subject: Re: Matheology § 224

> Your proof covers all lines.  We have for all lines l> of the list.> >   if l and all its predecessors are removed>   and no other line is removed,>   then the union of all lines is not changed"> > > > > However, there is no information about what will> happen if you try to apply this to two> lines e.g. l along with all its predecessors> and m along with all its predecessors.> > Now it is easy to see what will happen in this> case.   Since we can replace l and m with> one of either l or m, we know what will happen> if we remove two lines.> > Since we can replace l,m and p with> one of either l or m or p, we know what will happen> if we remove three lines.> > It is easy to see we know what> will happen if we remove a natural> number of finite lines.> > However, we do not know what will happen> if we remove an infinite number of> finite lines.>      If you really want to accept this potential infinite nonsense,then the exact same will happen when you remove an infinite setof lines as when you remove a finite set of lines. Because anyparticular set of lines will be finite.
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