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.