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 set
of lines as when you remove a finite set of lines. Because any
particular set of lines will be finite.